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The Definition of Optimal Solution and an Extended Kuhn-Tucker Approach for Fuzzy Linear Bilevel Programming

Bilevel decision techniques are mainly developed for solving decentralized management problems with decision makers in a hierarchical organization. Organizational bilevel decision-making, such as planning of land-use, transportation and water resource, all may involve uncertain factors. The parameters shown in a bileved programming model, either in the objective functions or constraints, are thus often imprecise, which is called fuzzy parameter bilevel programming (FPBLP) problem. Following our previous work (1, 2), this study first proposes a model of FPBLP. It then gives the definition of optimal solution for an FPBLP problem. Based on the definition and related theorems, this study develops a fuzzy number based Kuhn-Tucher approach to solve the proposed FPBLP problem. Finally, an example further illustrates the power of the fuzzy number based Kuhn-Tucher approach.