Solving Fuzzy Assignment Problem using Ranking of Generalized Trapezoidal Fuzzy Numbers

Abstract

Background/Objectives: The fuzzy optimal solution is totally based on ranking or comparing fuzzy numbers. Ranking fuzzy numbers play an vital role in decision making problems, data analysis and socio economics systems. The aim is to optimize the total cost of assigning all the jobs to the available persons. Ranking fuzzy number offers an powerful tool for handling fuzzy assignment problems. Methods/Statistical analysis: In this paper we used Hungarian method for solving fuzzy assignment problems using generalized trapezoidal fuzzy numbers. By using the ranking procedure we convert the fuzzy assignment problem to a crisp value assignment problem which then can be solved using Hungarian Method to find the fuzzy optimal solution. We presented the method which is not only simple in calculation but also gives better approximation and satisfactory results which is illustrated through the numerical examples. Findings: We propose a new ranking method which discriminates the fuzzy numbers where as few of the existing method fails to discriminates the fuzzy numbers. This method ranks all types of fuzzy numbers i.e. normal and generalized fuzzy numbers. Both triangular and trapezoidal fuzzy numbers). It is evident from the numerical examples that the proposed ranking measure for a fuzzy assignment problem is easy to compute and cost effective and gives much more optimal value. Applications/Improvements: The proposed ranking procedure can be applied in various decision making problems. This ranking method could also be used to solve other types of problems like game theory, project schedules, transportation problems.