Deriving expected values from probabilities of fuzzy subsets

Deriving expected values from probabilities of fuzzy subsets

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Article ID: iaor1993608
Country: Netherlands
Volume: 50
Issue: 2
Start Page Number: 199
End Page Number: 210
Publication Date: Jan 1991
Journal: European Journal of Operational Research
Authors: ,
Keywords: artificial intelligence: expert systems
Abstract:

The problem of determinig the expected value of a variable V on the basis of a fuzzy evidence of the type ‘Pr(V is A) is Q’ is considered. It is shown that if the set X of possible values of V is finite, X={x1,...,xn}, and the membership function of the fuzzy probability Q is upper semi-continuous then the problem may be reduced to the analysis of a certain linear programming problem. Since this problem is of a special form it is possible to develop solution algorithms which are more effective than classical methods known in linear programming. There are presented two algorithms. Using the first algorithm one may obtain the r-cut of the fuzzy expected value for any fixed r∈(0,1]. With the help of the second algorithm one may obtain the r-cuts of the fuzzy expected value for all r∈(0,1]. The presented approach is an essential improvement of the method proposed before that by Yager.

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