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From ranking fuzzy numbers to solving fuzzy linear programming: a comprehensive review
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 mathematicsVolume
5Issue
3Pagination
219 - 235Publisher
Inderscience EnterprisesLocation
Olney, Eng.Publisher DOI
ISSN
1752-5055eISSN
1752-5063Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2014, Inderscience EnterprisesUsage metrics
Keywords
FLPFMOLPFuzzy linear programmingFuzzy multiobjective linear programmingFuzzy number centroidRanking fuzzy numbersReviewScience & TechnologyTechnologyEngineering, MultidisciplinaryEngineering2-PHASE APPROACHAPPROXIMATE ALGORITHMDECISION-MAKINGOPTIMIZATIONCENTROIDSINDEXAREAComputation Theory and Mathematics
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