Abstract
Bi-level programming is widely used in processing various questions, but it cannot deal with the complex and fuzzy information contained in problems. In order to solve such problems better with intricate and vague information that can be efficiently handled by bifuzzy theory, a bifuzzy–bilevel programming model that sets the parameters to bifuzzy variables is proposed in this paper, which can process complex realistic data more accurately and improve the feasibility and validity of bi-level programming models. To ensure the solvability of the model, the equivalent form of the bifuzzy–bilevel programming model is obtained by utilizing the expected value operator. According to the linear and nonlinear characteristics of the model, the Karush–Kuhn–Tucker condition and particle swarm optimization algorithm are employed to handle the problem, respectively. Finally, by taking the distribution center location problem of the supplier as an example, the bifuzzy–bilevel programming model is applied in practice to balance highly intricate customer demands and corporate cost minimization, obtaining the feasible solution of functions at the upper and lower levels, and the bifuzzy information in the problem can also be processed well, which proves the effectiveness of the proposed methodology.
Highlights
Bi-level programming is widely used in processing various questions, but it cannot deal with the complex and fuzzy information contained in problems
To solve optimization problems with double uncertainty, the bifuzzy variable, which belongs to the latter case [13], was proposed by Liu [14] to represent the function from a possibility space to the set of fuzzy variables
We study the combined application and solution of bifuzzy variables and bi-level programming with the aim of solving the problems with bifuzzy information in practice
Summary
Bi-level programming was first proposed in the study of market competition in unbalanced economies. Emam [2] proposed a bi-level programming method involving a fuzzy approach to solve the problems of bi-level integer non-linear programming. To solve optimization problems with double uncertainty, the bifuzzy variable, which belongs to the latter case [13], was proposed by Liu [14] to represent the function from a possibility space to the set of fuzzy variables. We study the combined application and solution of bifuzzy variables and bi-level programming with the aim of solving the problems with bifuzzy information in practice. The application scope of bifuzzy theory is extended, and the proposed method can solve bi-level programming problems with bifuzzy parameters. The expected value operator of bifuzzy variables is first applied to the upper and lower level models of the bi-level programming, and a bifuzzy–bilevel programming model is proposed.
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