Results 271 to 280 of about 3,363 (306)

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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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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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fuzzy number fuzzy measures and fuzzy integrals. (II). Fuzzy integrals of fuzzy-valued functions with respect to fuzzy number fuzzy measures on fuzzy sets

Fuzzy Sets and Systems, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Congxin Wu, Deli Zhang, Bokan Zhang, Caimei Guo   +3 more
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On the entropy of fuzzy measures

IEEE Transactions on Fuzzy Systems, 2000
Fuzzy measures provides a structure for modeling the knowledge available about variables whose values are unknown and uncertain. A large class of different types of uncertainty can be represented in this framework. In this work, we provide a measure of entropy that can be used to calculate the amount of uncertainty associated with a fuzzy measure.
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Measures of fuzziness of fuzzy events

Fuzzy Sets and Systems, 1987
We prove some new results on two families of fuzzy integrals defined in a previous paper, and by means of them we obtain entropy measures of fuzzy sets (not necessarily finite) which contain as particular cases the measures of Batle and Trillas, and Weber.
Suárez García, Fermín, Gil Álvarez, Pedro   +1 more
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Fuzzy measures and coherent join measures

International Journal of Intelligent Systems, 2011
In assigning weights and scores in a decision problem usually we assume that they are finitely additive normalized measures, i.e., from the formal point of view, finitely additive probabilities. The normalization requirement sometimes appears as an actual restriction.
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