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

journal contribution
posted on 2014-09-01, 00:00 authored by Thanh Thi NguyenThanh Thi Nguyen
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.

History

Journal

International journal of computing science and mathematics

Volume

5

Issue

3

Pagination

219 - 235

Publisher

Inderscience Enterprises

Location

Olney, Eng.

ISSN

1752-5055

eISSN

1752-5063

Language

eng

Publication classification

C Journal article; C1 Refereed article in a scholarly journal

Copyright notice

2014, Inderscience Enterprises