Solution of a class of Intuitionistic Fuzzy Assignment Problem by using similarity measures

摘要

In this paper, we set mathematical models of the assignment problem with restriction on person cost depending on efficiency/qualification and restriction on job cost where both the costs are considered as intuitionistic fuzzy numbers. Restriction of qualification is in the form of the maximum intuitionistic fuzzy cost which can be offered to a person depending on his/her efficiency/qualification. Further restrictions on the intuitionistic fuzzy cost which can be spent for doing a particular job makes the problem of Intuitionistic Fuzzy Assignment Problem with Restrictions (IFAPR) more realistic than the problems found in the literature so far. Consideration of Intuitionistic Fuzzy Numbers (IFNs) for representing the costs makes the problem more general in the sense that it considers both the degree of acceptance and the degree of rejection. A heuristic method has been constructed for showing the existence of the solution so that both the constraints are satisfied. The methodology for solving the problem consists of two algorithms. The concept of relative degree of similarity measures to the Positive Ideal Intuitionistic Fuzzy Solution (PIIFS) has been applied under Atanassov’s intuitionistic fuzzy environment. A well established intuitionistic fuzzy ranking method has been used here for comparing the IFNs using their score functions and the accuracy degrees. Mathematical model of the problem has been established. Numerical examples show the effectiveness of this method.