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On some extensions for S-decomposable fuzzy measures

Vicenç Torra

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Abstract

Practical applications of fuzzy integrals (Choquet and Sugeno integrals) require the definition of a fuzzy measure. However, when they are defined in a domain of n elements, this definition requires 2/sup n/ parameters. To avoid this large number of parameters, several families of measures have been introduced in the literature. In this work we present a new family that generalises some fuzzy measures but restricted so that the number of parameters is not large.

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Practical applications of fuzzy integrals (Choquet and Sugeno integrals) require the definition of a fuzzy measure. However, when they are defined in a domain of n elements, this definition requires 2/sup n/ parameters. To avoid this large number of parameters, several families of measures have been introduced in the literature. In this work we present a new family that generalises some fuzzy measures but restricted so that the number of parameters is not large.

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Available abstract

Practical applications of fuzzy integrals (Choquet and Sugeno integrals) require the definition of a fuzzy measure. However, when they are defined in a domain of n elements, this definition requires 2/sup n/ parameters. To avoid this large number of parameters, several families of measures have been introduced in the literature. In this work we present a new family that generalises some fuzzy measures but restricted so that the number of parameters is not large.

Key concepts: Fuzzy measure theory, Fuzzy logic, Measure (data warehouse), Mathematics, Fuzzy set, Fuzzy number, Domain (mathematical analysis), Computer science

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