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Fuzzy sets in the theory of measurement of incompatible observables
Foundations of Physics, 1974The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it.
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Radon-Nikodým derivatives and conditioning in fuzzy measure theory
1987Let (X,\({\mathcal F},g)\) be a fuzzy measure space, as defined by \textit{M. Sugeno} in his Thesis (1974). Given any measurable function f: \(X\to {\mathbb{R}}^+_ 0\), and any set \(A\in {\mathcal F}\), the fuzzy integral of f over A, with respect to g, is the following number: \[ \int_{A}f\cdot g=\sup_{\alpha \geq 0}[\alpha \wedge g(A\cap F_{\alpha})]
CANDELORO, Domenico, PUCCI S.
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Three-Way Group Conflict Analysis Based on Pythagorean Fuzzy Set Theory
IEEE Transactions on Fuzzy Systems, 2020Hamido Fujita +2 more
exaly
Fuzzy Measure Theory [Book Reviews]
IEEE Transactions on Fuzzy Systems, 1995openaire +2 more sources
Mathematical aspects of the theory of the measures of fuzziness
1996After recalling concept of fuzziness measure, we define some fuzziness measures though 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 intergrals.
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The ⁎-fuzzy Lebesgue-Radon-Nikodym theorem and differentiation in fuzzy measure theory
Fuzzy Sets and SystemsAbbas Ghaffari, Reza Chaharpashlou
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