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  • 1.
    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.

  • 2.
    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.

  • 3.
    Torra, Vicenç
    et al.
    University of Skövde, School of Informatics. University of Skövde, The Informatics Research Centre. IIIA-CSIC, Campus UAB s/n, Bellaterra, Catalonia, Spain.
    Narukawa, Yasuo
    Toho Gakuen, Kunitachi, Tokyo, Japan.
    Sugeno, Michio
    ECSC, c/ Gonzalo Gutiérrez Quirós s/n, Mieres, Spain.
    On the f-divergence for non-additive measures2016In: Fuzzy sets and systems (Print), ISSN 0165-0114, E-ISSN 1872-6801, Vol. 292, p. 364-379Article in journal (Refereed)
    Abstract [en]

    The f -divergence evaluates the dissimilarity between two probability distributions defined in terms of the Radon–Nikodym derivative of these two probabilities. The f -divergence generalizes the Hellinger distance and the Kullback–Leibler divergence among other divergence functions. In this paper we define an analogous function for non-additive measures. We discuss them for distorted Lebesgue measures and give examples. Examples focus on the Hellinger distance.

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