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Fuzzy geometric programming. I. (English) Zbl 0804.90135

Summary: First, the concepts of fuzzy valuation convex (or concave) function and fuzzy convex-geometric programming problem are based on a fuzzy valuation set in this paper. Secondly, fuzzy posynomial geometric programming and its dual-form properties concerned are discussed by means of a fuzzy geometric inequality and of a fuzzy dual theory. Lastly, direct and dual algorithms of fuzzy posynomial geometric programming are respectively deduced by the aid of a fuzzy fixed-point theorem and the notion of \(\alpha\), \(\beta\)-cut.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C30 Nonlinear programming
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