Results 261 to 270 of about 314,649 (305)

Fuzzy similarity measures and measurement theory

2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2019
We consider objects associated with a fuzzy set-based representation. By using a classic method of measurement introduced by Tversky, we establish necessary and sufficient conditions for the existence of a particular class of fuzzy similarity measures, agreeing with an ordering relation among pairs of objects which express the idea that two objects are
Coletti, Giulianella, Bouchon-Meunier, Bernadette   +1 more
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Fuzzy Measures and Measures of Fuzziness

1985
In order to prevent confusion about fuzzy measures and measures of fuzziness, we shall first briefly describe the meaning and features of fuzzy measures. In the early 1970s, Sugeno defined a fuzzy measure as follows [Sugeno 1977]: 𝓑 is a Borel field of the arbitrary set (universe) X.
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Fuzzy-valued fuzzy measures and generalized fuzzy integrals

Fuzzy Sets and Systems, 1998
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Caimei Guo, Deli Zhang, Congxin Wu
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Fuzzy confirmation measures

Fuzzy Sets and Systems, 2008
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Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations

International Journal of Intelligent Systems, 2006
Summary: The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of ...
Wenyi Zeng, Hongxing Li 0004
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Measures of Observables and Measures of Fuzziness

2012
The key aims of modern scientific work have generally been to find relationships between observed phenomena, construct mathematical formulas that describe these relationships, take measurements of the observables, and define axioms using terms that are as exact as possible.
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Measuring the Fuzziness of Sets

Journal of Cybernetics, 1974
Set theory begins to be useful when there is some natural criterion for defining belonging to a set. Sets of objects without properties are uninteresting. Elements are assigned to sets because they share properties or conform to a rule. A set of elements is said to be fuzzy when we allow some elements to belong to the set unequally or more strongly ...
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Entropy of Fuzzy Measure

2010
A definition for the entropy of fuzzy measures defined on set systems is proposed. The underlying set is not necessarily the whole power set, but satisfy a condition of regularity. This definition encompasses the classical definition of Shannon for probability measures, as well as the definition of Marichal et al.
Aoi Honda, Michel Grabisch
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On the weak convergence of sequences of fuzzy measures and metric of fuzzy measures

Fuzzy Sets and Systems, 2000
A fuzzy measure is considered on the \(\sigma\)-algebra \({\mathcal A}\) of Borel subsets of a metric space (i.e., \(\mu:{\mathcal A}\to [0,\infty]\), \(\mu(\emptyset)= 0\), \(\mu\) monotone and continuous from above and from below) together with the Sugeno integral \[ \int_A f d\mu= \bigvee_{\alpha\geq 0} [\alpha\wedge \mu(A\cap \{f\geq \alpha\})]. \]
Guijun Wang, Xiaoping Li
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Fuzzy logic in measurements

Fuzzy Sets and Systems, 1998
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