Title: A novel approach for the solution of generalised fuzzy assignment problem

Authors: E. Melita Vinoliah; K. Ganesan

Addresses: Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai – 603203, India ' Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai – 603203, India

Abstract: 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 jth task by the ith 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.

Keywords: generalised fuzzy; assignment problem; trapezoidal fuzzy numbers; fuzzy arithmetic; fuzzy ranking; extremum difference method; judging matrix; uncertainty and vagueness; generalised assignment problem; multilevel fuzzy generalised assignment problem.

DOI: 10.1504/IJICA.2021.116655

International Journal of Innovative Computing and Applications, 2021 Vol.12 No.4, pp.189 - 194

Received: 07 Nov 2019
Accepted: 24 Feb 2020

Published online: 10 Jun 2021 *

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