부산대학교 도서관

It is natural to consider that possible values of parameters of mathematical programming problems are only ambiguously known to experts. From this point of view, in this paper, we formulate two-level nonconvex nonlinear programming problems with fuzzy parameters and present interactive fuzzy programming through genetic algorithms for the problems. Recently, the genetic algorithms attract a great deal of considerable attention as methods for optimization, adaptation and learning, and it has been shown that they effectively work in nonconvex nonlinear programming problems. In our interactive method, after determining the fuzzy goals of the decision makers at both levels, through genetic algorithms, a satisfactory solution is efficiently derived by updating the minimal satisfactory level of decision makers at the upper level with considerations of overall satisfactory balance between both levels. An illustrative numerical example for two-level nonconvex nonlinear programming problems with fuzzy parameters is provided to demonstrate the feasibility of the proposed method.