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Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

机译：用偏差度测度和秩函数法求解完全模糊的双层线性规划问题

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摘要

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.
机译：本文涉及一类完全模糊的双层线性规划问题，其中目标函数和约束的所有系数和决策变量均为模糊数。提出了一种基于偏差度测度和排序函数的新方法来解决这些问题。我们首先介绍一个完全模糊的双层线性规划问题的可行区域和模糊最优解的概念。为了获得该问题的模糊最优解，我们采用偏差度度量方法来处理模糊约束，并使用模糊数的排序函数方法对上下级模糊目标函数进行排序。然后，可以将完全模糊的双层线性规划问题转化为确定性的双层规划问题。考虑到提高目标函数值和减小允许偏差度之间的总体平衡，提出了寻找模糊最优解的计算程序。最后，提供了一个数值示例来说明所提出的方法。结果表明，与现有方法相比，该方法具有更好的最优解。

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  • 来源
    《Mathematical Problems in Engineering》 |2016年第4期|7069804.1-7069804.11|共11页
  • 作者

    Ren Aihong;

  • 作者单位

    Baoji Univ Arts & Sci, Dept Math, Baoji 721013, Peoples R China;

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