Interactive fuzzy programming for two-level nonconvex nonlinear programming problems through genetic algorithms

Abstract

In this paper, we present interactive fuzzy programming through genetic algorithms, which are reported their effectiveness to solving nonconvex nonlinear programming problems, for multi-level nonconvex nonlinear programming problems. In the proposed method, fuzzy goals for objective function of each decision maker and a ratio of satisfactory degrees of decision makers at adjacent two levels are introduced to take the vague or fuzzy nature of human judgments into account, and mathematical programming problems for obtaining satisfactory solutions concerned in some groups within all the decision makers are successively solved to lead to a global satisfactory solution such that the decision makers at relatively upper levels are esteemed and the satisfactory degree of each decision maker balances with those of the others. Finally, a numerical example is given to illustrate an interactive process in the proposed method for deriving a satisfactory solution.