Fuzzy sets as a basis for a theory of possibility
Fuzzy Sets and Systems
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Fuzzy numbers have heretofore been conceived simply as convex fuzzy subsets of the real line, especially in the context of possibility theory. This paper proposes an alternative interpretation of fuzzy numbers: fuzzy confidence intervals. This number concept is particularly appropriate to problems of optimization with a fuzzy objective function or fuzzy constraints, and it is clearly free of some ambiguities or contradictions in possibility theory. The membership indices are not assumed to be numerical. Numerical examples of the construction of fuzzy confidence intervals from uncertain hypotheses are given.