Title: From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review

Authors: Thanh Nguyen

Addresses: Centre for Intelligent Systems Research (CISR), Deakin University, Waurn Ponds, Victoria, Australia

Abstract: Solving fuzzy linear programming (FLP) requires the employment of a consistent ranking of fuzzy numbers. Ineffective fuzzy number ranking would lead to a flawed and erroneous solving approach. This paper presents a comprehensive and extensive review on fuzzy number ranking methods. Ranking techniques are categorised into six classes based on their characteristics. They include centroid methods, distance methods, area methods, lexicographical methods, methods based on decision maker's viewpoint, and methods based on left and right spreads. A survey on solving approaches to FLP is also reported. We then point out errors in several existing methods that are relevant to the ranking of fuzzy numbers and thence suggest an effective method to solve FLP. Consequently, FLP problems are converted into non-fuzzy single (or multiple) objective linear programming based on a consistent centroid-based ranking of fuzzy numbers. Solutions of FLP are then obtained by solving corresponding crisp single (or multiple) objective programming problems by conventional methods.

Keywords: review; fuzzy number ranking; fuzzy numbers; fuzzy linear programming; FLP; fuzzy MOLP; multiobjective linear programming; FMOLP; fuzzy number centroid.

DOI: 10.1504/IJCSM.2014.064871

International Journal of Computing Science and Mathematics, 2014 Vol.5 No.3, pp.219 - 235

Received: 28 Apr 2014
Accepted: 21 Jul 2014
Published online: 27 Sep 2014 *

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