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  • 1.
    Abril, Daniel
    et al.
    IIIA, Institut d'Investigació en Intelligència Artificial – CSIC, Consejo Superior de Investigaciones Científicas, Bellaterra, Spain / UAB, Universitat Autónoma de Barcelona, Bellaterra, Spain.
    Navarro-Arribas, Guillermo
    DEIC, Dep. Enginyeria de la Informació i de les Comunicacions, UAB, Universitat Autònoma de Barcelona, Bellaterra, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. IIIA, Institut d'Investigació en Intelligència Artificial – CSIC, Consejo Superior de Investigaciones Científicas, Bellaterra, Spain.
    Spherical Microaggregation: Anonymizing Sparse Vector Spaces2015In: Computers & security (Print), ISSN 0167-4048, E-ISSN 1872-6208, Vol. 49, p. 28-44Article in journal (Refereed)
    Abstract [en]

    Unstructured texts are a very popular data type and still widely unexplored in the privacy preserving data mining field. We consider the problem of providing public information about a set of confidential documents. To that end we have developed a method to protect a Vector Space Model (VSM), to make it public even if the documents it represents are private. This method is inspired by microaggregation, a popular protection method from statistical disclosure control, and adapted to work with sparse and high dimensional data sets.

  • 2.
    Abril, Daniel
    et al.
    IIIA, Institut d'Investigació en Intel·ligència Artificial, CSIC, Consejo Superior de Investigaciones Científicas, Campus UAB s/n, Bellaterra, Spain / UAB, Universitat Autònoma de Barcelona, Campus UAB s/n, Bellaterra, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. IIIA, Institut d'Investigació en Intel·ligència Artificial, CSIC, Consejo Superior de Investigaciones Científicas, Campus UAB s/n, Bellaterra, Spain.
    Navarro-Arribas, Guillermo
    DEIC, Dep. Enginyeria de la Informació i de les Comunicacions, UAB, Universitat Autònoma de Barcelona, Campus UAB s/n, Bellaterra, Spain.
    Supervised Learning Using a Symmetric Bilinear Form for Record Linkage2015In: Information Fusion, ISSN 1566-2535, E-ISSN 1872-6305, Vol. 26, p. 144-153Article in journal (Refereed)
    Abstract [en]

    Record Linkage is used to link records of two different files corresponding to the same individuals. These algorithms are used for database integration. In data privacy, these algorithms are used to evaluate the disclosure risk of a protected data set by linking records that belong to the same individual. The degree of success when linking the original (unprotected data) with the protected data gives an estimation of the disclosure risk.

    In this paper we propose a new parameterized aggregation operator and a supervised learning method for disclosure risk assessment. The parameterized operator is a symmetric bilinear form and the supervised learning method is formalized as an optimization problem. The target of the optimization problem is to find the values of the aggregation parameters that maximize the number of re-identification (or correct links). We evaluate and compare our proposal with other non-parametrized variations of record linkage, such as those using the Mahalanobis distance and the Euclidean distance (one of the most used approaches for this purpose). Additionally, we also compare it with other previously presented parameterized aggregation operators for record linkage such as the weighted mean and the Choquet integral. From these comparisons we show how the proposed aggregation operator is able to overcome or at least achieve similar results than the other parameterized operators. We also study which are the necessary optimization problem conditions to consider the described aggregation functions as metric functions.

  • 3.
    Alcantud, Jose Carlos R.
    et al.
    BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Salamanca, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Decomposition theorems and extension principles for hesitant fuzzy sets2018In: Information Fusion, ISSN 1566-2535, E-ISSN 1872-6305, Vol. 41, p. 48-56Article in journal (Refereed)
    Abstract [en]

    We prove a decomposition theorem for hesitant fuzzy sets, which states that every typical hesitant fuzzy set on a set can be represented by a well-structured family of fuzzy sets on that set. This decomposition is expressed by the novel concept of hesitant fuzzy set associated with a family of hesitant fuzzy sets, in terms of newly defined families of their cuts. Our result supposes the first representation theorem of hesitant fuzzy sets in the literature. Other related representation results are proven. We also define two novel extension principles that extend crisp functions to functions that map hesitant fuzzy sets into hesitant fuzzy sets.

  • 4.
    Aliahmadipour, Laya
    et al.
    Faculty of Mathematics and Computer, Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Eslami, Esfandiar
    Faculty of Mathematics and Computer, Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.
    On Hesitant Fuzzy Clustering and Clustering of Hesitant Fuzzy Data2017In: Fuzzy sets, rough sets, multisets and clustering: Part I / [ed] Vicenç Torra, Anders Dahlbom & Yasuo Narukawa, Springer, 2017, p. 157-168Chapter in book (Refereed)
    Abstract [en]

    Since the notion of hesitant fuzzy set was introduced, some clustering algorithms have been proposed to cluster hesitant fuzzy data. Beside of hesitation in data, there is some hesitation in the clustering (classification) of a crisp data set. This hesitation may be arise in the selection process of a suitable clustering (classification) algorithm and initial parametrization of a clustering (classification) algorithm. Hesitant fuzzy set theory is a suitable tool to deal with this kind of problems. In this study, we introduce two different points of view to apply hesitant fuzzy sets in the data mining tasks, specially in the clustering algorithms.

  • 5.
    Aliahmadipour, Laya
    et al.
    Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Eslami, Esfandiar
    Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
    Eftekhari, Mahdi
    Department of Computer Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran.
    A definition for hesitant fuzzy partitions2016In: International Journal of Computational Intelligence Systems, ISSN 1875-6891, E-ISSN 1875-6883, Vol. 9, no 3, p. 497-505Article in journal (Refereed)
    Abstract [en]

    In this paper, we define hesitant fuzzy partitions (H-fuzzy partitions) to consider the results of standard fuzzy clustering family (e.g. fuzzy c-means and intuitionistic fuzzy c-means). We define a method to construct H-fuzzy partitions from a set of fuzzy clusters obtained from several executions of fuzzy clustering algorithms with various initialization of their parameters. Our purpose is to consider some local optimal solutions to find a global optimal solution also letting the user to consider various reliable membership values and cluster centers to evaluate her/his problem using different cluster validity indices.

  • 6.
    Armengol, Eva
    et al.
    CSIC - Spanish Council for Scientific Research, IIIA - Artificial Intelligence Research Institute, Bellaterra, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Generalization-Based k-Anonymization2015In: Modeling Decisions for Artificial Intelligence: 12th International Conference, MDAI 2015, Skövde, Sweden, September 21–23, 2015: Proceedings / [ed] Vicenç Torra & Yasuo Narukawa, Springer, 2015, p. 207-218Conference paper (Refereed)
    Abstract [en]

    Microaggregation is an anonymization technique consistingon partitioning the data into clusters no smaller thankelements andthen replacing the whole cluster by its prototypical representant. Mostof microaggregation techniques work on numerical attributes. However,many data sets are described by heterogeneous types of data, i.e., nu-merical and categorical attributes. In this paper we propose a new mi-croaggregation method for achieving a compliantk-anonymous maskedfile for categorical microdata based on generalization. The goal is to builda generalized description satisfied by at leastkdomain objects and toreplace these domain objects by the description. The way to constructthat generalization is similar that the one used in growing decision trees.Records that cannot be generalized satisfactorily are discarded, thereforesome information is lost. In the experiments we performed we prove thatthe new approach gives good results.

  • 7.
    Armengol, Eva
    et al.
    IIIA - Artificial Intelligence Research Institute, CSIC - Spanish Council for Scientific Research, Catalonia, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Partial Domain Theories for Privacy2016In: Modeling Decisions for Artificial Intelligence: 13th International Conference, MDAI 2016 Sant Julià de Lòria, Andorra, September 19–21, 2016, Proceedings, Springer, 2016, p. 217-226Conference paper (Refereed)
    Abstract [en]

    Generalization and Suppression are two of the most used techniques to achieve k-anonymity. However, the generalization concept is also used in machine learning to obtain domain models useful for the classification task, and the suppression is the way to achieve such generalization. In this paper we want to address the anonymization of data preserving the classification task. What we propose is to use machine learning methods to obtain partial domain theories formed by partial descriptions of classes. Differently than in machine learning, we impose that such descriptions be as specific as possible, i.e., formed by the maximum number of attributes. This is achieved by suppressing some values of some records. In our method, we suppress only a particular value of an attribute in only a subset of records, that is, we use local suppression. This avoids one of the problems of global suppression that is the loss of more information than necessary.

  • 8.
    Bae, Juhee
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Karlsson, Alexander
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Mellin, Jonas
    University of Skövde, The Informatics Research Centre. University of Skövde, School of Informatics.
    Ståhl, Niclas
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Complex Data Analysis2019In: Data science in Practice / [ed] Alan Said, Vicenç Torra, Springer, 2019, p. 157-169Chapter in book (Refereed)
    Abstract [en]

    Data science applications often need to deal with data that does not fit into the standard entity-attribute-value model. In this chapter we discuss three of these other types of data. We discuss texts, images and graphs. The importance of social media is one of the reason for the interest on graphs as they are a way to represent social networks and, in general, any type of interaction between people. In this chapter we present examples of tools that can be used to extract information and, thus, analyze these three types of data. In particular, we discuss topic modeling using a hierarchical statistical model as a way to extract relevant topics from texts, image analysis using convolutional neural networks, and measures and visual methods to summarize information from graphs.

  • 9.
    Bae, Juhee
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Ventocilla, Elio
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Riveiro, Maria
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    On the Visualization of Discrete Non-additive Measures2018In: Aggregation Functions in Theory and in Practice AGOP 2017 / [ed] Torra V, Mesiar R, Baets B, Springer, 2018, p. 200-210Conference paper (Refereed)
    Abstract [en]

    Non-additive measures generalize additive measures, and have been utilized in several applications. They are used to represent different types of uncertainty and also to represent importance in data aggregation. As non-additive measures are set functions, the number of values to be considered grows exponentially. This makes difficult their definition but also their interpretation and understanding. In order to support understability, this paper explores the topic of visualizing discrete non-additive measures using node-link diagram representations.

  • 10.
    Bae, Juhee
    et al.
    Högskolan i Skövde, Institutionen för informationsteknologi.
    Ventocilla, Elio
    Högskolan i Skövde, Institutionen för informationsteknologi.
    Riveiro, Maria
    Högskolan i Skövde, Institutionen för informationsteknologi.
    Torra, Vicenç
    Högskolan i Skövde, Institutionen för informationsteknologi.
    On the Visualization of Discrete Non-additive Measures2018In: Aggregation Functions in Theory and in Practice AGOP 2017 / [ed] Torra V, Mesiar R, Baets B, Springer, 2018, p. 200-210Conference paper (Refereed)
    Abstract [en]

    Non-additive measures generalize additive measures, and have been utilized in several applications. They are used to represent different types of uncertainty and also to represent importance in data aggregation. As non-additive measures are set functions, the number of values to be considered grows exponentially. This makes difficult their definition but also their interpretation and understanding. In order to support understability, this paper explores the topic of visualizing discrete non-additive measures using node-link diagram representations.

  • 11.
    Casas-Roma, Jordi
    et al.
    Faculty of Computer Science, Multimedia and Telecommunications, Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya (UOC), Barcelona, Spain.
    Herrera-Joancomarti, Jordi
    Department of Information and Communications Engineering, Universitat Autònoma de Barcelona (UAB), Bellaterra, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    k-Degree Anonymity And Edge Selection: Improving Data Utility In Large Networks2017In: Knowledge and Information Systems, ISSN 0219-1377, E-ISSN 0219-3116, Vol. 50, no 2, p. 447-474Article in journal (Refereed)
    Abstract [en]

    The problem of anonymization in large networks and the utility of released data are considered in this paper. Although there are some anonymization methods for networks, most of them cannot be applied in large networks because of their complexity. In this paper, we devise a simple and efficient algorithm for k-degree anonymity in large networks. Our algorithm constructs a k-degree anonymous network by the minimum number of edge modifications. We compare our algorithm with other well-known k-degree anonymous algorithms and demonstrate that information loss in real networks is lowered. Moreover, we consider the edge relevance in order to improve the data utility on anonymized networks. By considering the neighbourhood centrality score of each edge, we preserve the most important edges of the network, reducing the information loss and increasing the data utility. An evaluation of clustering processes is performed on our algorithm, proving that edge neighbourhood centrality increases data utility. Lastly, we apply our algorithm to different large real datasets and demonstrate their efficiency and practical utility.

  • 12.
    Casas-Roma, Jordi
    et al.
    Faculty of Computer Science, Multimedia and Telecommunications, Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya, Barcelona, Spain.
    Herrera-Joancomartí, Jordi
    Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Bellaterra, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    A survey of graph-modification techniques for privacy-preserving on networks2017In: Artificial Intelligence Review, ISSN 0269-2821, E-ISSN 1573-7462, Vol. 47, no 3, p. 341-366Article in journal (Refereed)
    Abstract [en]

    Recently, a huge amount of social networks have been made publicly available. In parallel, several definitions and methods have been proposed to protect users’ privacy when publicly releasing these data. Some of them were picked out from relational dataset anonymization techniques, which are riper than network anonymization techniques. In this paper we summarize privacy-preserving techniques, focusing on graph-modification methods which alter graph’s structure and release the entire anonymous network. These methods allow researchers and third-parties to apply all graph-mining processes on anonymous data, from local to global knowledge extraction.

  • 13.
    Ghorbani, Ali
    et al.
    University of New Brunswick, Canada.
    Torra, VincençUniversity of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.Hişil, HüseyinYasar University, Turkey.Miri, AliRyerson University, Canada.Koltuksuz, AhmetYasar University, Turkey.Zhang, JieNanyang Technological University, Singapore.Sensoy, MuratOzyegin University, Turkey.García-Alfaro, JoaquínTélécom SudParis, France.Zincir, IbrahimYasar University, Turkey.
    2015 Thirteenth Annual Conference on Privacy, Security and Trust2015Conference proceedings (editor) (Refereed)
  • 14.
    Halas, Radomir
    et al.
    Palacký University Olomouc, Faculty of Science, Department of Algebra and Geometry, Olomouc, Czech Republic.
    Mesiar, Radko
    Palacký University Olomouc, Faculty of Science, Department of Algebra and Geometry, Olomouc, Czech Republic / Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Bratislava, Slovakia.
    Pocs, Jozef
    Palacký University Olomouc, Faculty of Science, Department of Algebra and Geometry, Olomouc, Czech Republic / Mathematical Institute, Slovak Academy of Sciences, Košice, Slovakia.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    A note on some algebraic properties of discrete Sugeno integrals2019In: Fuzzy sets and systems (Print), ISSN 0165-0114, E-ISSN 1872-6801, Vol. 355, p. 110-120Article in journal (Refereed)
    Abstract [en]

    Based on the link between Sugeno integrals and fuzzy measures, we discuss several algebraic properties of discrete Sugeno integrals. We recall that the composition of Sugeno integrals is again a Sugeno integral, and that each Sugeno integral can be obtained as a composition of binary Sugeno integrals. In particular, we discuss the associativity, dominance, commuting and bisymmetry of Sugeno integrals.

  • 15.
    Koloseni, David
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. Department of Mathematics, University of Dar es salaam, Tanzania.
    Helldin, Tove
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Absolute and relative preferences in AHP-like matrices2018In: Data Science and Knowledge Engineering for Sensing Decision Support: Proceedings of the 13th International FLINS Conference (FLINS 2018) / [ed] Jun Liu, Jie Lu, Yang Xu, Luis Martinez, Etienne E Kerre, SINGAPORE: World Scientific Publishing Co. Pte. Ltd. , 2018, Vol. 11, p. 260-267Conference paper (Refereed)
    Abstract [en]

    The Analytical Hierarchy Process (AHP) has been extensively used to interview experts in order to find the weights of the criteria. We call AHP-like matrices relative preferences of weights. In this paper we propose another type of matrix that we call a absolute preference matrix. They are also used to find weights, and we propose that they can be applied to find the weights of weighted means and also of the Choquet integral.

  • 16.
    Koloseni, David
    et al.
    Department of Mathematics, University of Dar es Salaam, Tanzania.
    Helldin, Tove
    University of Skövde, School of Informatics. University of Skövde, Informatics Research Environment.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, Informatics Research Environment. Hamilton Institute, Maynooth University, Maynooth, Ireland.
    AHP-Like Matrices and Structures: Absolute and Relative Preferences2020In: Mathematics, E-ISSN 2227-7390, Vol. 8, no 5, article id 813Article in journal (Refereed)
    Abstract [en]

    Aggregation functions are extensively used in decision making processes to combine available information. Arithmetic mean and weighted mean are some of the most used ones. In order to use a weighted mean, we need to define its weights. The Analytical Hierarchy Process (AHP) is a well known technique used to obtain weights based on interviews with experts. From the interviews we define a matrix of pairwise comparisons of the importance of the weights. We call these AHP-like matrices absolute preferences of weights. We propose another type of matrix that we call a relative preference matrix. We define this matrix with the same goal—to find the weights for weighted aggregators. We discuss how it can be used for eliciting the weights for the weighted mean and define a similar approach for the Choquet integral.

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  • 17.
    Kuchaki Rafsanjani, Marjan
    et al.
    Department of Computer Science, Shadid Bahonar University of Kerman, Iran.
    Aliahmadipour, Laya
    Department of Computer Science, Shadid Bahonar University of Kerman, Iran.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    An application of Hesitant Fuzzy Sets to Elect an Efficient Cluster Head in Ad Hoc Networks2016Conference paper (Other academic)
  • 18.
    Livraga, Giovanni
    et al.
    Università degli Studi di Milano, Crema, Italy.
    Torra, VicençUniversity of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.Aldini, AlessandroUniversity of Urbino, Urbino, Italy.Martinelli, FabioIIT-CNR, Pisa, Italy.Suri, NeerajTU Darmstadt, Germany.
    Data Privacy Management and Security Assurance: 11th International Workshop, DPM 2016 and 5th International Workshop, QASA 2016, Heraklion, Crete, Greece, September 26-27, 2016, Proceedings2016Conference proceedings (editor) (Refereed)
  • 19.
    Nanni, Mirco
    et al.
    CNR, ISTI, Rome, Italy.
    Andrienko, Gennady
    IAIS Fraunhofer, Germany / City University London, England, UK.
    Barabási, Albert-László
    Northeastern University, Boston, USA.
    Boldrini, Chiara
    CNR, IIT, Rome, Italy.
    Bonchi, Francesco
    ISI Foundation, Italy / Eurecat, Spain.
    Cattuto, Ciro
    University of Torino, Italy / ISI Foundation, Italy.
    Chiaromonte, Francesca
    Sant’Anna School of Advanced Studies Pisa, Italy / Penn State University, USA.
    Comande, Giovanni
    Sant’Anna School of Advanced Studies Pisa, Italy.
    Conti, Marco
    IIT-CNR, Italy.
    Coté, Mark
    King’s College London, UK.
    Dignum, Frank
    Umeå University, Sweden.
    Dignum, Virginia
    Umeå University, Sweden.
    Domingo-Ferrer, Josep
    Universitat Rovira i Virgili, Catalonia.
    Ferragina, Paolo
    University of Pisa, Italy.
    Giannotti, Fosca
    ISTI-CNR, Italy.
    Guidotti, Riccardo
    University of Pisa, Italy.
    Helbing, Dirk
    ETH Zurich, Switzerland.
    Kaski, Kimmo
    Aalto University School of Science, Finland.
    Kertesz, Janos
    Central European University, Hungary.
    Lehmann, Sune
    Technical University of Denmark.
    Lepri, Bruno
    FBK, Italy.
    Lukowicz, Paul
    DFKI, Germany.
    Matwin, Stan
    Dalhousie University, Canada / Polish Academy of Sciences, Poland.
    Jiménez, David Megías
    Universitat Oberta de Catalunya.
    Monreale, Anna
    University of Pisa, Italy.
    Morik, Katharina
    TU Dortmund University, Germany.
    Oliver, Nuria
    ELLIS Alicante, Spain / Data-Pop Alliance, USA.
    Passarella, Andrea
    IIT-CNR, Italy.
    Passerini, Andrea
    Universita degli Studi di Trento.
    Pedreschi, Dino
    University of Pisa, Italy.
    Pentland, Alex
    MIT, USA.
    Pianesi, Fabio
    EIT Digital, Italy.
    Pratesi, Francesca
    University of Pisa, Italy.
    Rinzivillo, Salvatore
    ISTI-CNR, Italy.
    Ruggieri, Salvatore
    University of Pisa, Italy.
    Siebes, Arno
    Universiteit Utrecht, The Netherlands.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, Informatics Research Environment. Maynooth University, Ireland.
    Trasarti, Roberto
    ISTI-CNR, Italy.
    van den Hoven, Jeroen
    TU Delft, The Netherlands.
    Vespignani, Alessandro
    Northeastern University, USA.
    Give more data, awareness and control to individual citizens, and they will help COVID-19 containment2020In: Transactions on Data Privacy, ISSN 1888-5063, E-ISSN 2013-1631, Vol. 13, no 1, p. 61-66Article in journal (Refereed)
    Abstract [en]

    The rapid dynamics of COVID-19 calls for quick and effective tracking of virus transmission chains and early detection of outbreaks, especially in the "phase 2" of the pandemic, when lockdown and other restriction measures are progressively withdrawn, in order to avoid or minimize contagion resurgence. For this purpose, contact-tracing apps are being proposed for large scale adoption by many countries. A centralized approach, where data sensed by the app are all sent to a nation-wide server, raises concerns about citizens' privacy and needlessly strong digital surveillance, thus alerting us to the need to minimize personal data collection and avoiding location tracking. We advocate the conceptual advantage of a decentralized approach, where both contact and location data are collected exclusively in individual citizens' "personal data stores", to be shared separately and selectively (e.g., with a backend system, but possibly also with other citizens), voluntarily, only when the citizen has tested positive for COVID-19, and with a privacy preserving level of granularity. This approach better protects the personal sphere of citizens and affords multiple benefits: it allows for detailed information gathering for infected people in a privacy-preserving fashion; and, in turn this enables both contact tracing, and, the early detection of outbreak hotspots on more finely-granulated geographic scale. The decentralized approach is also scalable to large populations, in that only the data of positive patients need be handled at a central level. Our recommendation is two-fold. First to extend existing decentralized architectures with a light touch, in order to manage the collection of location data locally on the device, and allowthe user to share spatio-temporal aggregates - if and when they want and for specific aims - with health authorities, for instance. Second, we favour a longerterm pursuit of realizing a Personal Data Store vision, giving users the opportunity to contribute to collective good in the measure they want, enhancing self-awareness, and cultivating collective efforts for rebuilding society.

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  • 20. Narukawa, Yasuo
    et al.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    New results on hesitant fuzzy sets: score functions2015In: The 12th International Conference on Modeling Decisions for Artificial Intelligence: CD-ROM Proceedings, MDAI - HiS , 2015Conference paper (Refereed)
  • 21.
    Rodríguez, R. M.
    et al.
    Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain.
    Bedregal, B.
    Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte, Natal, Brazil.
    Bustince, H.
    Department of Automatic and Computation and Institute of Smart Cities, Public University of Navarra, Pamplona, Spain.
    Dong, Y. C.
    Business School, Sichuan University, Chengdu, China.
    Farhadinia, B.
    Department of Mathematics, Quchan University of Advanced Technology, Iran.
    Kahraman, C.
    Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey.
    Martínez, L.
    Department of Computer Science, University of Jaén, Jaén, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Xu, Y. J.
    Business School, Hohai University, Nanjing, China.
    Xu, Z. S.
    Business School, Sichuan University, Chengdu, China.
    Herrera, F.
    Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain / Faculty of Computing and Information Technology, King Abdulaziz University, North Jeddah, Saudi Arabia.
    A Position and Perspective Analysis of Hesitant Fuzzy Sets on Information Fusion in Decision Making: Towards High Quality Progress2016In: Information Fusion, ISSN 1566-2535, E-ISSN 1872-6305, Vol. 29, p. 89-97Article in journal (Refereed)
    Abstract [en]

    The necessity of dealing with uncertainty in real world problems has been a long-term research challenge which has originated different methodologies and theories. Recently, the concept of Hesitant Fuzzy Sets (HFSs) has been introduced to model the uncertainty that often appears when it is necessary to establish the membership degree of an element and there are some possible values that make to hesitate about which one would be the right one. Many researchers have paid attention on this concept who have proposed diverse extensions, relationships with other types of fuzzy sets, different types of operators to compute with this type of information, applications on information fusion and decision-making, etc.

    Nevertheless, some of these proposals are questionable, because they are straightforward extensions of previous works or they do not use the concept of HFSs in a suitable way. Therefore, this position paper studies the necessity of HFSs and provides a discussion about current proposals including a guideline that the proposals should follow and some challenges of HFSs.

  • 22.
    Rodríguez, Rosa M.
    et al.
    University of Granada, Granada, Spain.
    Martínez, Luis
    University of Jaén, Jaén, Spain.
    Herrera, Francisco
    University of Granada, Granada, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    A Review of Hesitant Fuzzy Sets: Quantitative and Qualitative Extensions2016In: Fuzzy Logic in Its 50th Year: New Developments, Directions and Challenges / [ed] Cengiz Kahraman, Uzay Kaymak, Adnan Yazici, Springer, 2016, p. 109-128Chapter in book (Other academic)
    Abstract [en]

    Since the concept of fuzzy set was introduced, different extensions and generalizations have been proposed to manage the uncertainty in different problems. This chapter is focused in a recent extension so-called hesitant fuzzy set. Many researchers have paid attention on it and have proposed different extensions both in quantitative and qualitative contexts. Several concepts, basic operations and its extensions are revised in this chapter.

  • 23.
    Said, Alan
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Data Science: An Introduction2019In: Data Science in Practice / [ed] Alan Said, Vicenç Torra, Springer, 2019, p. 1-6Chapter in book (Refereed)
    Abstract [en]

    This chapter gives a general introduction to data science as a concept and to the topics covered in this book. First, we present a rough definition of data science, and point out how it relates to the areas of statistics, machine learning and big data technologies. Then, we review some of the most relevant tools that can be used in data science ranging from optimization to software. We also discuss the relevance of building models from data. The chapter ends with a detailed review of the structure of the book.

  • 24.
    Salas, Julian
    et al.
    Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya (UOC), Center for Cybersecurity Research of Catalonia (CYBERCAT), Barcelona, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    A General Algorithm for k-anonymity on Dynamic Databases2018In: Data Privacy Management, Cryptocurrencies and Blockchain Technology: ESORICS 2018 International Workshops, DPM 2018 and CBT 2018, Barcelona, Spain, September 6-7, 2018, Proceedings / [ed] Joaquin Garcia-Alfaro, Jordi Herrera-Joancomartí, Giovanni Livraga, Ruben Rios, Cham: Springer, 2018, Vol. 11025, p. 407-414Conference paper (Refereed)
    Abstract [en]

    In this work we present an algorithm for k-anonymization of datasets that are changing over time. It is intended for preventing identity disclosure in dynamic datasets via microaggregation. It supports adding, deleting and updating records in a database, while keeping k-anonymity on each release. We carry out experiments on database anonymization. We expected that the additional constraints for k-anonymization of dynamic databases would entail a larger information loss, however it stays close to MDAV's information loss for static databases. Finally, we carry out a proof of concept experiment with directed degree sequence anonymization, in which the removal or addition of records, implies the modification of other records.

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  • 25.
    Salas, Julian
    et al.
    Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili, Tarragona, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Improving the characterization of P-stability for applications in network privacy2016In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 206, p. 109-114Article in journal (Refereed)
    Abstract [en]

    Recently, we have found that the concept of P-stability has interesting applications in network privacy. In the context of Online Social Networks it may be used for obtaining a fully polynomial randomized approximation scheme for graph masking and measuring disclosure risk. Also by using the characterization for P-stable sequences from Jerrum, McKay and Sinclair (1992) it is possible to obtain optimal approximations for the problem of k-degree anonymity. In this paper, we present results on P-stability considering the additional restriction that the degree sequence must not intersect the edges of an excluded graph X, improving earlier results on P-stability. As a consequence we extend the P-stable classes of scale-free networks from Torra et al. (2015), obtain an optimal solution for k-anonymity and prove that all the known conditions for P-stability are sufficient for sequences to be graphic. (C) 2016 Elsevier B.V. All rights reserved.

  • 26.
    Salas, Julián
    et al.
    Internet Interdisciplinary Institute (IN3), CYBERCAT-Center for Cybersecurity Research of Catalonia, Universitat Oberta de Catalunya (UOC), Barcelona, Spain.
    Megías, David
    Internet Interdisciplinary Institute (IN3), CYBERCAT-Center for Cybersecurity Research of Catalonia, Universitat Oberta de Catalunya (UOC), Barcelona, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    SwapMob: Swapping trajectories for mobility anonymization2018In: Privacy in Statistical Databases: UNESCO Chair in Data Privacy, International Conference, PSD 2018, Valencia, Spain, September 26–28, 2018, Proceedings / [ed] Josep Domingo-Ferrer, Fransisco Montes, Springer, 2018, p. 331-346Conference paper (Refereed)
    Abstract [en]

    Mobility data mining can improve decision making, from planning transports in metropolitan areas to localizing services in towns. However, unrestricted access to such data may reveal sensible locations and pose safety risks if the data is associated to a specific moving individual. This is one of the many reasons to consider trajectory anonymization. Some anonymization methods rely on grouping individual registers on a database and publishing summaries in such a way that individual information is protected inside the group. Other approaches consist of adding noise, such as differential privacy, in a way that the presence of an individual cannot be inferred from the data. In this paper, we present a perturbative anonymization method based on swapping segments for trajectory data (SwapMob). It preserves the aggregate information of the spatial database and at the same time, provides anonymity to the individuals. We have performed tests on a set of GPS trajectories of 10,357 taxis during the period of Feb. 2 to Feb. 8, 2008, within Beijing. We show that home addresses and POIs of specific individuals cannot be inferred after anonymizing them with SwapMob, and remark that the aggregate mobility data is preserved without changes, such as the average length of trajectories or the number of cars and their directions on any given zone at a specific time.

  • 27.
    Salas, Julián
    et al.
    Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya (UOC), Barcelona, Spain / CYBERCAT-Center for Cybersecurity Research of Catalonia, Barcelona, Spain.
    Megías, David
    Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya (UOC), Barcelona, Spain / CYBERCAT-Center for Cybersecurity Research of Catalonia, Barcelona, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, Informatics Research Environment. Hamilton Institute, Maynooth University, Ireland.
    Toger, Marina
    Department of Economic and Cultural Geography, Uppsala University, Sweden.
    Dahne, Joel
    Department of Mathematics, Uppsala University, Sweden.
    Sainudiin, Raazesh
    Department of Mathematics, Uppsala University, Sweden / Combient Competence Centre for Data Engineering Sciences, Uppsala University, Sweden.
    Swapping trajectories with a sufficient sanitizer2020In: Pattern Recognition Letters, ISSN 0167-8655, E-ISSN 1872-7344, Vol. 131, p. 474-480Article in journal (Refereed)
    Abstract [en]

    Real-time mobility data is useful for several applications such as planning transports in metropolitan areas or localizing services in towns. However, if such data is collected without any privacy protection it may reveal sensible locations and pose safety risks to an individual associated to it. Thus, mobility data must be anonymized preferably at the time of collection. In this paper, we consider the SwapMob algorithm that mitigates privacy risks by swapping partial trajectories. We formalize the concept of sufficient sanitizer and show that the SwapMob algorithm is a sufficient sanitizer for various statistical decision problems. That is, it preserves the aggregate information of the spatial database in the form of sufficient statistics and also provides privacy to the individuals. This may be used for personalized assistants taking advantage of users’ locations, so they can ensure user privacy while providing accurate response to the user requirements. We measure the privacy provided by SwapMob as the Adversary Information Gain, which measures the capability of an adversary to leverage his knowledge of exact data points to infer a larger segment of the sanitized trajectory. We test the utility of the data obtained after applying SwapMob sanitization in terms of Origin-Destination matrices, a fundamental tool in transportation modelling.

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  • 28.
    Salas, Julián
    et al.
    IIIA-CSIC, Consejo Superior de Investigaciones Científicas, Institut d’Investigació en Intelligència Artificial, Campus Universitat Autònoma de Barcelona, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. IIIA-CSIC, Consejo Superior de Investigaciones Científicas, Institut d’Investigació en Intelligència Artificial, Campus Universitat Autònoma de Barcelona, Spain.
    Graphic sequences, distances and k-degree anonymity2015In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 188, no 1, p. 25-31Article in journal (Refereed)
    Abstract [en]

    In this paper we study conditions to approximate a given graph by a regular one. We obtain optimal conditions for a few metrics such as the edge rotation distance for graphs, the rectilinear and the Euclidean distance over degree sequences. Then, we require the approximation to have at least kk copies of each value in the degree sequence, this is a property proceeding from data privacy that is called kk-degree anonymity.

    We give a sufficient condition in order for a degree sequence to be graphic that depends only on its length and its maximum and minimum degrees. Using this condition we give an optimal solution of kk-degree anonymity for the Euclidean distance when the sum of the degrees in the anonymized degree sequence is even. We present algorithms that may be used for obtaining all the mentioned anonymizations.

  • 29.
    Saleh, Emran
    et al.
    Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain.
    Valls, Aida
    Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain.
    Moreno, Antonio
    Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Tarragona, Spain.
    Romero-Aroca, Pedro
    Ophthalmic Service, University Hospital Sant Joan de Reus, Institut d’Investigació Sanitària Pere Virgili (IISPV), Universitat Rovira i Virgili, Reus, Spain.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Bustince, Humberto
    Departamento de Automàtica y Computación, Universidad Pública de Navarra, Institute of Smart Cities, Pamplona, Spain.
    Learning Fuzzy Measures for Aggregation in Fuzzy Rule-Based Models2018In: Modeling Decisions for Artificial Intelligence: 15th International Conference, MDAI 2018, Mallorca, Spain, October 15–18, 2018, Proceedings / [ed] Vicenç Torra, Yasuo Narukawa, Isabel Aguiló, Manuel González-Hidalgo, Springer, 2018, p. 114-127Conference paper (Refereed)
    Abstract [en]

    Fuzzy measures are used to express background knowledge of the information sources. In fuzzy rule-based models, the rule confidence gives an important information about the final classes and their relevance. This work proposes to use fuzzy measures and integrals to combine rules confidences when making a decision. A Sugeno $$\lambda $$ -measure and a distorted probability have been used in this process. A clinical decision support system (CDSS) has been built by applying this approach to a medical dataset. Then we use our system to estimate the risk of developing diabetic retinopathy. We show performance results comparing our system with others in the literature. 

  • 30.
    Senavirathne, Navoda
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Approximating Robust Linear Regression With An Integral Privacy Guarantee2018In: 2018 16th Annual Conference on Privacy, Security and Trust (PST) / [ed] Kieran McLaughlin, Ali Ghorbani, Sakir Sezer, Rongxing Lu, Liqun Chen, Robert H. Deng, Paul Miller, Stephen Marsh, Jason Nurse, IEEE, 2018, p. 85-94Conference paper (Refereed)
    Abstract [en]

    Most of the privacy-preserving techniques suffer from an inevitable utility loss due to different perturbations carried out on the input data or the models in order to gain privacy. When it comes to machine learning (ML) based prediction models, accuracy is the key criterion for model selection. Thus, an accuracy loss due to privacy implementations is undesirable. The motivation of this work, is to implement the privacy model "integral privacy" and to evaluate its eligibility as a technique for machine learning model selection while preserving model utility. In this paper, a linear regression approximation method is implemented based on integral privacy which ensures high accuracy and robustness while maintaining a degree of privacy for ML models. The proposed method uses a re-sampling based estimator to construct linear regression model which is coupled with a rounding based data discretization method to support integral privacy principles. The implementation is evaluated in comparison with differential privacy in terms of privacy, accuracy and robustness of the output ML models. In comparison, integral privacy based solution provides a better solution with respect to the above criteria.

  • 31.
    Senavirathne, Navoda
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. Hamilton Institute, Maynooth University, Maynooth, Ireland.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. Hamilton Institute, Maynooth University, Maynooth, Ireland.
    Integral Privacy Compliant Statistics Computation2019In: Data Privacy Management, Cryptocurrencies and Blockchain Technology: ESORICS 2019 International Workshops, DPM 2019 and CBT 2019, Luxembourg, September 26–27, 2019, Proceedings / [ed] Cristina Pérez-Solà, Guillermo Navarro-Arribas, Alex Biryukov, Joaquin Garcia-Alfaro, Cham: Springer, 2019, Vol. 11737, p. 22-38Conference paper (Refereed)
    Abstract [en]

    Data analysis is expected to provide accurate descriptions of the data. However, this is in opposition to privacy requirements when working with sensitive data. In this case, there is a need to ensure that no disclosure of sensitive information takes place by releasing the data analysis results. Therefore, privacy-preserving data analysis has become significant. Enforcing strict privacy guarantees can significantly distort data or the results of the data analysis, thus limiting their analytical utility (i.e., differential privacy). In an attempt to address this issue, in this paper we discuss how “integral privacy”; a re-sampling based privacy model; can be used to compute descriptive statistics of a given dataset with high utility. In integral privacy, privacy is achieved through the notion of stability, which leads to release of the least susceptible data analysis result towards the changes in the input dataset. Here, stability is explained by the relative frequency of different generators (re-samples of data) that lead to the same data analysis results. In this work, we compare the results of integrally private statistics with respect to different theoretical data distributions and real world data with differing parameters. Moreover, the results are compared with statistics obtained through differential privacy. Finally, through empirical analysis, it is shown that the integral privacy based approach has high utility and robustness compared to differential privacy. Due to the computational complexity of the method we propose that integral privacy to be more suitable towards small datasets where differential privacy performs poorly. However, adopting an efficient re-sampling mechanism can further improve the computational efficiency in terms of integral privacy. © 2019, The Author(s).

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  • 32.
    Senavirathne, Navoda
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. Maynooth University Hamilton Institute, Kildare, Ireland.
    Integrally private model selection for decision trees2019In: Computers & security (Print), ISSN 0167-4048, E-ISSN 1872-6208, Vol. 83, p. 167-181Article in journal (Refereed)
    Abstract [en]

    Privacy attacks targeting machine learning models are evolving. One of the primary goals of such attacks is to infer information about the training data used to construct the models. “Integral Privacy” focuses on machine learning and statistical models which explain how we can utilize intruder's uncertainty to provide a privacy guarantee against model comparison attacks. Through experimental results, we show how the distribution of models can be used to achieve integral privacy. Here, we observe two categories of machine learning models based on their frequency of occurrence in the model space. Then we explain the privacy implications of selecting each of them based on a new attack model and empirical results. Also, we provide recommendations for private model selection based on the accuracy and stability of the models along with the diversity of training data that can be used to generate the models. 

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  • 33.
    Senavirathne, Navoda
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. Hamilton Institute, Maynooth University, Maynooth, Ireland.
    Rounding based continuous data discretization for statistical disclosure control2019In: Journal of Ambient Intelligence and Humanized Computing, ISSN 1868-5137, E-ISSN 1868-5145, p. 1-19Article in journal (Refereed)
    Abstract [en]

    “Rounding” can be understood as a way to coarsen continuous data. That is, low level and infrequent values are replaced by high-level and more frequent representative values. This concept is explored as a method for data privacy with techniques like rounding, microaggregation, and generalisation. This concept is explored as a method for data privacy in statistical disclosure control literature with perturbative techniques like rounding, microaggregation and non-perturbative methods like generalisation. Even though “rounding” is well known as a numerical data protection method, it has not been studied in depth or evaluated empirically to the best of our knowledge. This work is motivated by three objectives, (1) to study the alternative methods of obtaining the rounding values to represent a given continuous variable, (2) to empirically evaluate rounding as a data protection technique based on information loss (IL) and disclosure risk (DR), and (3) to analyse the impact of data rounding on machine learning based models. Here, in order to obtain the rounding values we consider discretization methods introduced in the unsupervised machine learning literature along with microaggregation and re-sampling based approaches. The results indicate that microaggregation based techniques are preferred over unsupervised discretization methods due to their fair trade-off between IL and DR. 

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  • 34.
    Stokes, Klara
    et al.
    Universitat Oberta de Catalunya, Barcelona, Spain.
    Torra, Vicenç
    Consejo Superior de Investigaciones Científicas (CSIC), Spain.
    Multiple releases of k-anonymous data sets and k-anonymous relational databases2012In: International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, ISSN 0218-4885, Vol. 20, no 6, p. 839-853Article in journal (Refereed)
    Abstract [en]

    In data privacy, the evaluation of the disclosure risk has to take into account the fact that several releases of the same or similar information about a population are common. In this paper we discuss this issue within the scope of k-anonymity. We also show how this issue is related to the publication of privacy protected databases that consist of linked tables. We present algorithms for the implementation of k-anonymity for this type of data.

  • 35.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Tarragona, Spain.
    Torra, Vicenç
    Universitat Autònoma de Barcelona (UAB), Spain.
    On some clustering approaches for graphs2011In: Fuzzy Systems (FUZZ), 2011, IEEE conference proceedings, 2011, p. 409-415Conference paper (Refereed)
    Abstract [en]

    In this paper we discuss some tools for graph perturbation with applications to data privacy. We present and analyse two different approaches. One is based on matrix decomposition and the other on graph partitioning. We discuss these methods and show that they belong to two traditions in data protection: noise addition/microaggregation and k-anonymity.

  • 36.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Tarragona, Spain.
    Torra, Vicenç
    Universitat Autònoma de Barcelona (UAB), Spain.
    On the Relationship Between Clustering and Coding Theory2012In: 2012 IEEE International Conference on Fuzzy Systems: Brisbane, Australia (June 10-15, 2012) / [ed] Hussein Abbass, Daryl Essam & Ruhul Sarker, IEEE conference proceedings, 2012, p. Article number 6250783-Conference paper (Refereed)
    Abstract [en]

    In this paper we discuss the relations between clustering and error correcting codes. We show that clustering can be used for constructing error correcting codes. We review the previous works found in the literature about this issue, and propose a modification of a previous work that can be used for code construction from a set of proposed codewords.

  • 37.
    Stokes, Klara
    et al.
    Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
    Torra, Vicenç
    IIIA, Institut d’Investigació en Intel ligència Artificial CSIC, Consejo Superior de Investigaciones Científicas, Bellaterra, Catalonia, Spain.
    Reidentification and k-anonymity: a model for disclosure risk in graphs2012In: Soft Computing - A Fusion of Foundations, Methodologies and Applications, ISSN 1432-7643, E-ISSN 1433-7479, Vol. 16, no 10, p. 1657-1670Article in journal (Refereed)
    Abstract [en]

    In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modeling the anonymity of a database table and we prove that n-confusion is a generalization of k-anonymity. After a short survey on the different available definitions of k-anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k, l)-anonymous graph. Our definition of (k, l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally, we provide a set of algorithms for k-anonymization of graphs.

  • 38.
    Torra, Vicenc
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    On the Analysis of Utility and Risk for Masked Data in Big Data: A Small Data Analysis2018In: Frontiers in Artificial Intelligence and Applications: Artificial Intelligence Research and Development / [ed] Zoe Falomir, Karina Gibert, Enric Plaza, IOS Press , 2018, Vol. 308, p. 200-209Conference paper (Refereed)
    Abstract [en]

    Data privacy studies methods to ensure that disclosure of sensitive information does not take place. Masking methods are applied to databases prior to their release so that intruders cannot access sensitive information. Masking methods modify the data reducing its quality. Information loss measures have been defined to evaluate in what extent data is still useful for particular analysis. In the case of big data, masking data and evaluating its utility is a complex problem. In this paper we focus on information loss measurement and we explore if we can estimate or give bounds of information loss for large data sets using only random subsets of the whole data set.

  • 39.
    Torra, Vicenc
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Some properties of Choquet integral based probability functions2015In: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 19, no 1, p. 35-47Article in journal (Refereed)
    Abstract [en]

    The Choquet integral permits us to integrate a function with respect to a non-additive measure. When the measure is additive it corresponds to the Lebesgue integral. This integral was used recently to define families of probability-density functions. They are the exponential family of Choquet integral (CI) based class-conditional probability-density functions, and the exponential family of Choquet– Mahalanobis integral (CMI) based class-conditional probability-density functions. The latter being a generalization of the former, and also a generalization of the normal distribution.

    In this paper we study some properties of these distributions, and study the application of a few normality tests.

  • 40.
    Torra, Vicenc
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Transparency and Disclosure Risk in Data Privacy2015In: Proceedings of the Workshops of the EDBT/ICDT 2015 Joint Conference (EDBT/ICDT) / [ed] Peter M. Fischer, Gustavo Alonso, Marcelo Arenas, Floris Geerts, 2015, p. 246-Conference paper (Other academic)
    Abstract [en]

    k-Anonymity and differential privacy can be considered examples of Boolean definitions of disclosure risk. In contrast, record linkage and uniqueness are examples of quantitative measures of risk. Record linkage is a powerful approach because it can model different types of scenarios in which an adversary attacks a protected database with some information and background knowledge. Transparency holds in data privacy when data is published together with details on their processing. This includes the data protection method used and its parameters. Intruders can use this information to improve their attacks. Specific record linkage algorithms can be defined to take into account this information, and to define more accurate disclosure risk measures. Machine learning and optimization techniques also permits us to increase the  effectiveness of record linkage algorithms. This talk will be focused on disclosure risk measures based on record linkage. We will describe how we can improve the performance of the algorithms under the transparency principle, as well as using machine learning and optimization techniques.

  • 41.
    Torra, Vicenc
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Transparency and microaggregation2015In: UNECE SDC 2015, 2015Conference paper (Other academic)
    Abstract [en]

    Transparency has an important effect on disclosure risk. In general, masking methods have to be evaluated taking into account that intruders can use all available information to attack the data. When the masking method as well as their parameters are disclosed, this information can also be used by an intruder. In this talk we will review results on the effects of transparency in disclosure risk assessment for microdata giving special emphasis to microaggregation.

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  • 42.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    A fuzzy microaggregation algorithm using fuzzy c-means2015In: Artificial Intelligence Research and Development / [ed] Eva Armengol, Dionís Boixader, Francisco Grimaldo, IOS Press, 2015, p. 214-223Conference paper (Refereed)
    Abstract [en]

    Masking methods are used in data privacy to avoid the disclosure of sensitive information. Microaggregation is a perturbative masking method that has been proven effective. Data masked using microaggregation can be attacked when the intruder has information of the masking method and the parameters used. Publishing this information is usual under the transparency principle. Fuzzy microaggregation was introduced a few years ago to avoid this type of transparency attacks. In this paper we propose a new simpler method for microaggregation based on fuzzy c-means. We discuss the effectiveness of the approach. One of the advantages of this approach is its computational complexity.

  • 43.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Choquet integral: distributions and decisions2016In: 83rd meeting of the European Working Group on Multicriteria Decision Aiding! / [ed] Núria Agell, Barcelona: ESADE, Ramon Llull University , 2016Conference paper (Other academic)
    Abstract [en]

    Choquet integrals integrate functions with respect to fuzzy measures. From a mathematical point of view these integrals generalize the Lebesgue integrals when the measures are additive. From a point of view of aggregation functions, one of the relevant aspects is that they generalize the weighted mean and the OWA. Choquet integrals have been successfully used in decision making problems when there are interactions between criteria. In this setting we can learn or identify the measures from a set of decisions. This fact seems to indicate that we can consider data as generated from distributions based on the Choquet integral. We will present some results on these types of distributions and on their generalizations.  

  • 44.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Data Privacy: Foundations, New Developments and the Big Data Challenge2017Book (Other academic)
  • 45.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Derivation of Priorities and Weights for Set-Valued Matrices Using the Geometric Mean Approach2015In: Applied Artificial Intelligence, ISSN 0883-9514, E-ISSN 1087-6545, Vol. 29, no 5, p. 500-513Article in journal (Refereed)
    Abstract [en]

    Priorities are essential in the analytic hierarchy process (AHP). Several approaches have been proposed to derive priorities in the framework of the AHP. Priorities correspond to the weights in the weighted mean as well as in other aggregation operators as the ordered weighted averaging (OWA) operators, and the quasi-arithmetic means.

    Derivation of priorities for the AHP typically starts by eliciting a preference matrix from an expert and then using this matrix to obtain the vector priorities. For consistent matrices, the vector of priorities is unique. Nevertheless, it is usual that the matrix is not consistent. In this case, different methods exist for extracting this vector from the matrix.

    This article introduces a method for this purpose when the cells of the matrix are not a single value but a set of values. That is, we have a set-valued preference matrix. We discuss the relation of this type of matrices and hesitant fuzzy preference relations.

  • 46.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Entropy for non-additive measures in continuous domains2017In: Fuzzy sets and systems (Print), ISSN 0165-0114, E-ISSN 1872-6801, Vol. 324, p. 49-59Article in journal (Refereed)
    Abstract [en]

    In a recent paper we introduced a definition of f-divergence for non-additive measures. In this paper we use this result to give a definition of entropy for non-additive measures in a continuous setting. It is based on the KL divergence for this type of measures. We prove some properties and show that we can use it to find a measure satisfying the principle of minimum discrimination.

  • 47.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    Fuzzy microaggregation for the transparency principle2017In: Journal of Applied Logic, ISSN 1570-8683, E-ISSN 1570-8691, Vol. 23, p. 70-80Article in journal (Refereed)
    Abstract [en]

    Microaggregation has been proven to be an effective method for data protection in the areas of Privacy Preserving Data Mining (PPDM) and Statistical Disclosure Control (SDC). This method consists of applying a clustering method to the data set to be protected, and then replacing each of the data by the cluster representative. In this paper we propose a new method for microaggregation based on fuzzy clustering. This new approach has been defined with the main goal of being nondeterministic on the assignment of cluster centers to the original data, and at the same time being simple in its definition. Being nondeterministic permits us to overcome some of the attacks standard microaggregation suffers. 

  • 48.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    On fuzzy c-means and membership based clustering2015In: Advances in Computational Intelligence: 13th International Work-Conference on Artificial Neural Networks, IWANN 2015, Palma de Mallorca, Spain, June 10-12, 2015: Proceedings, Part I / [ed] Ignacio Rojas, Gonzalo Joya & Andreu Catala, Springer, 2015, p. 597-607Conference paper (Refereed)
    Abstract [en]

    Fuzzyc" role="presentation">c-means is one of the most well known fuzzy clustering algorithms. It is usually solved using an iterative algorithm. This algorithm does not ensure that the solution is the global optimum. In this paper we study the distribution of values of the objective function of fuzzyc" role="presentation">c

    -means.

    We also propose a new fuzzy clustering method related to fuzzy c-means. The method presumes that the shape of the membership function is known and can be calculated from the cluster centers, which are the only results of the clustering algorihm.

  • 49.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre.
    On the selection of m for Fuzzy c-Means2015In: Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology / [ed] José M. Alonso, Humberto Bustince & Marek Reformat, Paris: Atlantis Press , 2015, p. 1571-1577Conference paper (Refereed)
    Abstract [en]

    Fuzzy c-means is a well known fuzzy clustering algorithm. It is an unsupervised clustering algorithmthat permits us to build a fuzzy partition from data. The algorithm depends on a parameter m whichcorresponds to the degree of fuzziness of the solution. Large values of m will blur the classes andall elements tend to belong to all clusters. The solutionsof the optimization problem depend on theparameter m. That is, different selections of m willtypically lead to different partitions. In this paper we study and compare the effect ofthe selection of m obtained from the fuzzy c-means.

  • 50.
    Torra, Vicenç
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. Hamilton Institute, Maynooth University, Maynooth, Ireland.
    Random dictatorship for privacy-preserving social choice2019In: International Journal of Information Security, ISSN 1615-5262, E-ISSN 1615-5270, p. 1-9Article in journal (Refereed)
    Abstract [en]

    Social choice provides methods for collective decisions. They include methods for voting and for aggregating rankings. These methods are used in multiagent systems for similar purposes when decisions are to be made by agents. Votes and rankings are sensitive information. Because of that, privacy mechanisms are needed to avoid the disclosure of sensitive information. Cryptographic techniques can be applied in centralized environments to avoid the disclosure of sensitive information. A trusted third party can then compute the outcome. In distributed environments, we can use a secure multiparty computation approach for implementing a collective decision method. Other privacy models exist. Differential privacy and k-anonymity are two of them. They provide privacy guarantees that are complementary to multiparty computation approaches, and solutions that can be combined with the cryptographic ones, thus providing additional privacy guarantees, e.g., a differentially private multiparty computation model. In this paper, we propose the use of probabilistic social choice methods to achieve differential privacy. We use the method called random dictatorship and prove that under some circumstances differential privacy is satisfied and propose a variation that is always compliant with this privacy model. Our approach can be implemented using a centralized approach and also a decentralized approach. We briefly discuss these implementations.

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