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 integrates 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 algorithm is applicable to any combination of the number of projects and positions, and is more simple, practical, and reasonable.