Probability measures of Fuzzy events
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Cites background or result from "Probability measures of Fuzzy event..."
...As shown in [ 48 ], such an event may be characterized as a fuzzy subset, A, of the sample space Q, with tiA , the membership function of A, being a measurable function....
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...The limitations imposed by the assumption that A is well-defined may be removed, at least in part, by allowing A to be a fuzzy event, as was done in [ 48 ]....
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...Let pA (ui) be the grade of membership of ui in A. Then, if the Pi are conventional numerical probabilities pi, 0 dp, Q 1, then the probability of A, P(A), is defined as (see [ 48 ] ; h + = arithmetic sum)...
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Cites background from "Probability measures of Fuzzy event..."
...P(A) = J'(x)dP = In Zadeh [1968] the similarity of the probability of fuzzy events and the probability of crisp events is illustrated....
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...They have been studied by a number of authors, in particular by Zadeh [1965, 1971], Kaufmann [1975], and Rosenfeld [1975]. Applications of fuzzy relations are widespread and important....
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...They have been studied by a number of authors, in particular by Zadeh [1965, 1971], Kaufmann [1975], and Rosenfeld [1975]....
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Cites background from "Probability measures of Fuzzy event..."
...1) and let the question be "What is the probability of throwing a large number?" According to Zadeh [234], the probability P( £) is computed as 1 P(£) = LP(u;) · Jliarge(u;) = -(1 + 0....
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"Probability measures of Fuzzy event..." refers background in this paper
...Equation (3) equates the probability of an event A with the expectation of the characteristic function of A....
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...(5) Thus, as in (3), the probability of a fuzzy event is the expectation of its membership function....
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