Elsevier

Fuzzy Sets and Systems

Volume 86, Issue 2, 1 March 1997, Pages 223-234
Fuzzy Sets and Systems

The random set and the cutting of random fuzzy sets

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Abstract

In this paper, we shall examine the procedure how a random set is realized. We consider three cases. The first case is the ideal case where random set comes as the random α-cut of a given fuzzy set; the second case is that the random set comes as the α-cut of a random fuzzy set for a given cutting level α ϵ [0,1]; the third case is that the random set comes as the random α-cut of a random set. Our study shows that the expected fuzzy set of a random set is strongly affected by the distribution of the random threshold α.

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