Computing a fuzzy shortest path in a network with mixed fuzzy arc lengths using α-cuts

Authors:
Ali Tajdin;Iraj Mahdavi;Nezam Mahdavi-Amiri;Bahram Sadeghpour-Gildeh
Affiliations:
Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran;Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran;Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran;Department of Mathematics and Statistics, Mazandaran University, Babolsar, Iran
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

We are concerned with the design of a model and an algorithm for computing a shortest path in a network having various types of fuzzy arc lengths. First, we develop a new technique for the addition of various fuzzy numbers in a path using @a-cuts by proposing a linear least squares model to obtain membership functions for the considered additions. Then, using a recently proposed distance function for comparison of fuzzy numbers, we present a dynamic programming method for finding a shortest path in the network. Examples are worked out to illustrate the applicability of the proposed model.