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A parametric total order on fuzzy numbers and a fuzzy shortest route problem. (English) Zbl 0818.90136
Summary: A parametric total order relation is introduced in the form of a certain modification of the “fuzzy max” order on the class of fuzzy numbers generated by a shape function. By the parametric relation, fuzzy numbers unordered with respect to the fuzzy max order can be ordered according either to their value of center or the size of ambiguity. A fuzzy shortest route problem in which arc distances are given by fuzzy numbers is discussed under the criterion of the parametric total order, and solved by the dynamic programming approach. A method is proposed to find all of fuzzy routes minimal in the sense of the fuzzy max order.
MSC:
90C70Fuzzy programming
03E72Fuzzy set theory
90C39Dynamic programming