Fuzzy geometric programming (I)

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 α,β-cut.