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

Nguyen,T 2014, From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review, International journal of computing science and mathematics, vol. 5, no. 3, pp. 219-235, doi: 10.1504/IJCSM.2014.064871.

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Title From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review
Author(s) Nguyen,TORCID iD for Nguyen,T
Journal name International journal of computing science and mathematics
Volume number 5
Issue number 3
Start page 219
End page 235
Total pages 17
Publisher Inderscience Enterprises
Place of publication Olney, Eng.
Publication date 2014-09
ISSN 1752-5055
Keyword(s) FLP
Fuzzy linear programming
Fuzzy multiobjective linear programming
Fuzzy number centroid
Ranking fuzzy numbers
Summary 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.
Language eng
DOI 10.1504/IJCSM.2014.064871
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
010206 Operations Research
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2014, Inderscience Enterprises
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