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Fuzzy measures defined by addition of fuzzy measures
2016 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), 2016Given a measurable space (X, A) and two fuzzy measures μ 1 and μ2 defined on A, the addition of μ 1 and μ2 determines another set function on A. Such a new set function is a fuzzy measure, too. We shall discuss the relation between the new fuzzy measure and the original fuzzy measures. We shall see that the new fuzzy measure preserves some structural
Xiaoli Hu +3 more
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A possibility measure is not a fuzzy measure
Fuzzy Sets and Systems, 1982In the case of metric spaces without isolated points the authors show that every possibility measure with a continuous non vanishing 'density' is not a fuzzy measure. This result is not very surprising, but it corrects a claim mentioned by the way in the literature.
Puri, Madan L., Ralescu, Dan
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Fuzzy Sets and Systems, 1998
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Congxin Wu +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Congxin Wu +3 more
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The Fuzziness Measure in Fuzzy Rough Sets
2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery, 2008The paper studies the fuzziness measure in fuzzy rough sets. By making use of the support set of fuzzy sets, a rough membership function for fuzzy sets based on fuzzy relation is introduced. Simultaneously, a fuzziness measure of fuzzy rough sets from total mean fuzzy degree is proposed.
Yue-Jin Lv +2 more
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Fuzzy Sets and Systems, 1989
We present a characterization of a fuzzy entropy which is formally analogous to the information theoretical Shannon entropy.
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We present a characterization of a fuzzy entropy which is formally analogous to the information theoretical Shannon entropy.
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IEEE Transactions on Fuzzy Systems, 1994
First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes.
Nikhil R. Pal, James C. Bezdek
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First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes.
Nikhil R. Pal, James C. Bezdek
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International Journal of Intelligent Systems, 2005
Summary: Coherence measures are a tool to compare those fuzzy sets that are sensitive to their own similarity as well as to their fuzzy nature. In this article we find three generalizations of the definition of coherence measures: a first one for any fuzzy set, a second one for any definition of strong negation, and a final one for an extension in ...
Alejandro Sancho-Royo, José L. Verdegay
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Summary: Coherence measures are a tool to compare those fuzzy sets that are sensitive to their own similarity as well as to their fuzzy nature. In this article we find three generalizations of the definition of coherence measures: a first one for any fuzzy set, a second one for any definition of strong negation, and a final one for an extension in ...
Alejandro Sancho-Royo, José L. Verdegay
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On the Fuzzy Measures and the Measures of Fuzziness for L-Fuzzy Sets
IFAC Proceedings Volumes, 1983Abstract This paper is based on the results of De Luca and Termini [1.2] and Wang (6,7,8). It includes the following three parts, (l) We extend the fuzzy integrals taking value in the unit inteval (0,1) to a fuzzy integrals taking value in a lattice.
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On Viewing Fuzzy Measures as Fuzzy Subsets
IEEE Transactions on Fuzzy Systems, 2016We introduce the concept of a fuzzy measure, discuss some of their basic properties and look at some notable examples. We introduce a correspondence between a fuzzy measure on X and a fuzzy subset over the power set of X. These fuzzy subsets are required to have special properties on the space 2X and we refer to these as measure type fuzzy sets.
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Fuzzy morphology and fuzzy convexity measures
Proceedings of 13th International Conference on Pattern Recognition, 1996This study results in a very general class of approximate convex measures for objects on grey-tone images. These measures are referred to as convexity indicators. They are based on fuzzy set theory, more precisely, on the fuzzy inclusion indicators defined by Sinha and Dougherty (1993). Consideration is given to the fuzzy morphological operations which
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