Displaying similar documents to “General Fritz Carlson's type inequality for Sugeno integrals.”

Radon-Nikodym derivatives and conditioning in fuzzy measure theory.

Domenico Candeloro, Sabrina Pucci (1987)

Stochastica

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In the last twenty years many papers have appeared dealing with fuzzy theory. In particular, fuzzy integration theory had its origin in the well-known Thesis of Sugeno [7]. More recently, some authors faced this topic by means of some binary operations (see for instance [3], [8] and references): a fuzzy measure must be additive with respect to one of them, an the integral is to define in a way, which is very similar to the construction of the Lebesgue integral. On the contrary, we are...

The fuzzy metric space based on fuzzy measure

Jialiang Xie, Qingguo Li, Shuili Chen, Huan Huang (2016)

Open Mathematics

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In this paper, we study the relation between a fuzzy measure and a fuzzy metric which is induced by the fuzzy measure. We also discuss some basic properties of the constructed fuzzy metric space. In particular, we show that the nonatom of fuzzy measure space can be characterized in the constructed fuzzy metric space.

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...

Numerical experimentation and comparison of fuzzy integrals.

Manuel Jorge Bolaños, Luis Daniel Hernández, Antonio Salmerón (1996)

Mathware and Soft Computing

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Sugeno and Choquet integrals have been widely studied in the literature from a theoretical viewpoint. However, the behavior of these functionals is known in a general way, but not in practical applications and in particular cases. This paper presents the results of a numerical comparison that attempts to be a basis for a better comprehension and usefulness of both integrals.

Fuzzy sets and small systems

Považan, Jaroslav, Riečan, Beloslav

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Independently with [7] a corresponding fuzzy approach has been developed in [3-5] with applications in measure theory. One of the results the Egoroff theorem has been proved in an abstract form. In [1] a necessary and sufficient condition for holding the Egoroff theorem was presented in the case of a space with a monotone measure. By the help of [2] and [6] we prove a variant of the Egoroff theorem stated in [4].

A Method to Construct an Extension of Fuzzy Information Granularity Based on Fuzzy Distance

Thien, Nguyen Van, Demetrovics, Janos, Thi, Vu Duc, Giang, Nguyen Long, Son, Nguyen Nhu (2016)

Serdica Journal of Computing

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In fuzzy granular computing, a fuzzy granular structure is the collection of fuzzy information granules and fuzzy information granularity is used to measure the granulation degree of a fuzzy granular structure. In general, the fuzzy information granularity characterizes discernibility ability among fuzzy information granules in a fuzzy granular structure. In recent years, researchers have proposed some concepts of fuzzy information granularity based on partial order relations. However,...