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Displaying similar documents to “Numerical experimentation and comparison of fuzzy integrals.”

Mathematical aspects of the theory of measures of fuzziness.

Doretta Vivona (1996)

Mathware and Soft Computing

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After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.

Evaluations of fuzzy sets based on orderings and measures.

Aldo Ventre, Siegfried Weber (1987)

Stochastica

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Total orderings in the range of fuzzy sets can serve as choice criteria for fuzzy sets, a wide class of orderings based on functions is proposed (section 2). Decomposable measures are taken to measure the items on which the fuzzy sets are given (section 3). Combining the two levels of measurement by means of the integral introduced by the second author we obtain evaluations of fuzzy sets as functionals with appropriate properties, the concepts of energy and fuzziness are included (section...

Twofold integral and multi-step Choquet integral

Yasuo Narukawa, Vicenç Torra (2004)

Kybernetika

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In this work we study some properties of the twofold integral and, in particular, its relation with the 2-step Choquet integral. First, we prove that the Sugeno integral can be represented as a 2-step Choquet integral. Then, we turn into the twofold integral studying some of its properties, establishing relationships between this integral and the Choquet and Sugeno ones and proving that it can be represented in terms of 2-step Choquet integral.

Divergence measure between fuzzy sets using cardinality

Vladimír Kobza (2017)

Kybernetika

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In this paper we extend the concept of measuring difference between two fuzzy subsets defined on a finite universe. The first main section is devoted to the local divergence measures. We propose a divergence measure based on the scalar cardinalities of fuzzy sets with respect to the basic axioms. In the next step we introduce the divergence based on the generating function and the appropriate distances. The other approach to the divergence measure is motivated by class of the rational...

Classes of fuzzy measures and distortion

Ľubica Valášková, Peter Struk (2005)

Kybernetika

Similarity:

Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.