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Fuzzy Sets and Systems, 1994
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CUTELLO, Vincenzo, MONTERO J.
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CUTELLO, Vincenzo, MONTERO J.
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Bulletin of the Kyushu Institute of Technology. Pure and applied mathematics, 1999
Let \({\mathcal B}\) be a \(\sigma\)-algebra on \(X\). An increasing function \(\mu:{\mathcal B}\to [0,1]\) with \(\mu(\emptyset)= 0\) and \(\mu(X)= 1\) is called a fuzzy measure. The authors study the question when for two fuzzy measures \(\mu\) and \(\nu\) on \({\mathcal B}\) there is an increasing function \(f: [0,1]\to [0,1]\) such that \(\nu= \mu ...
Honda, Aoi, Okazaki, Yoshiaki
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Let \({\mathcal B}\) be a \(\sigma\)-algebra on \(X\). An increasing function \(\mu:{\mathcal B}\to [0,1]\) with \(\mu(\emptyset)= 0\) and \(\mu(X)= 1\) is called a fuzzy measure. The authors study the question when for two fuzzy measures \(\mu\) and \(\nu\) on \({\mathcal B}\) there is an increasing function \(f: [0,1]\to [0,1]\) such that \(\nu= \mu ...
Honda, Aoi, Okazaki, Yoshiaki
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Fuzzy Sets and Systems, 2005
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Fuzzy Measures and Measures of Fuzziness
1985In 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 similarity measures and measurement theory
2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2019We 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 +1 more
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Bulletin of the Kyushu Institute of Technology. Pure and applied mathematics, 2001
By a fuzzy measure any monotone function \(g: B\to [0,1]\) (defined on the \(\sigma\)-algebra \(B\) of all Borel subsets of a completely regular Hausdorff topological space) is understood. Various definitions of supports of \(g\) are presented and some relations among them are explained.
Honda, Aoi, Okazaki, Yoshiaki
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By a fuzzy measure any monotone function \(g: B\to [0,1]\) (defined on the \(\sigma\)-algebra \(B\) of all Borel subsets of a completely regular Hausdorff topological space) is understood. Various definitions of supports of \(g\) are presented and some relations among them are explained.
Honda, Aoi, Okazaki, Yoshiaki
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Fuzzy-valued fuzzy measures and generalized fuzzy integrals
Fuzzy Sets and Systems, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Caimei Guo, Deli Zhang, Congxin Wu
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Measures of Observables and Measures of Fuzziness
2012The 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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On the weak convergence of sequences of fuzzy measures and metric of fuzzy measures
Fuzzy Sets and Systems, 2000A 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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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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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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