有约束多目标模糊指派问题的改进算法

对有约束多目标模糊指派问题的算法进行了改进，提出借助于运输问题的表上作业法的思想，用最大差额法和列差额法来求解工程指派问题。对工程数小于、等于或大于位置数的情形均可求解，且不用考虑最大化与最小化之间的转化问题，算法简便、实用；并探讨了如何利用非线性隶属函数将指标矩阵转化为模糊关系综合评价矩阵．使多目标工程选址问题的求解更趋合理。

An Improved Algorithm for Solving Fuzzy Assignment Problem with Multi-Objective Constraints

The existing fuzzy Hungary method for solving assignment problem with multi-objective constraints is complicated. An improved algorithm based on the idea of table-working is presented to overcome the shortcoming. It integrated the methods of maximal row margin, maximal column margin, local judgment and nonlinear membership transformer. In our algorithm, synthetic evaluation matrix is resolved by combining the method of maximal row margin (or maximal column margin) with formula of local judgment; the attribute value matrix can be transformed into fuzzy relationship synthetic matrix by the nonlinear fuzzy membership functions according to profit objective, cost objective, fixed objective, deviating objective, and interval objective. The following examples are given to verify this algorithm: (1) the application of maximal row margin and local judgment when the number of projects is less or equal to the number of positions. (2) the application of maximal column margin and local judgment when the number of projects is more than the number of positions. Our new algorithm is applicable to any combination of the number of projects and positions, and is more simple, practical, and reasonable.