A novel approach for the solution of generalised fuzzy assignment problem

摘要

In engineering and other fields, generalised assignment problem plays a vital role. It has widespread applications in routing problems, knapsack problems and other complicated models. In real world problems, the available data may not be known with certainty. Hence to model and solve practical problems, we must deal with uncertainty and vagueness. Fuzzy sets play a vital role to tackle these uncertainty and vagueness. The generalised fuzzy assignment problem became popular and has gained its importance too. In this paper, we consider a generalised fuzzy assignment problem which has restrictions both on tasks and on persons with respect to his/her efficiency/qualification. We propose a unique approach for the solution of generalised fuzzy assignment problem with restrictions without converting the problem to a corresponding crisp form. Costs for handling j~(th)task by the i~(th)person are taken to be trapezoidal fuzzy numbers. The trapezoidal fuzzy numbers are first represented in its parametric form. In view of the decision maker's preference, a new ranking method and arithmetic operations are used to bring a desirable solution. A numerical example is given to illustrate the proposed method.