Displaying similar documents to “Fuzzy orness measure and new orness axioms”

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...

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].

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.

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.

Aggregation operators and fuzzy measures on hypographs

Doretta Vivona, Maria Divari (2002)

Kybernetika

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In a fuzzy measure space we study aggregation operators by means of the hypographs of the measurable functions. We extend the fuzzy measures associated to these operators to more general fuzzy measures and we study their properties.

Classes of fuzzy measures and distortion

Ľubica Valášková, Peter Struk (2005)

Kybernetika

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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.