Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method

This paper proposes a method for solving fuzzy multi-objective linear programming (FMOLP) problems where all the coefficients are triangular fuzzy numbers and all the constraints are fuzzy equality or inequality. Using the deviation degree measures and weighted max–min method, the FMOLP problem is t...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 37; no. 10-11; pp. 6855 - 6869
Main Authors: Cheng, Haifang, Huang, Weilai, Zhou, Quan, Cai, Jianhu
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2013
Subjects:
Deviation
Deviation degree
Fuzzy
Fuzzy constraints
Fuzzy logic
Fuzzy multi-objective linear programming
Fuzzy set theory
Fuzzy systems
Linear programming
Mathematical analysis
Mathematical models
Triangular fuzzy numbers
Weighted max–min method
Triangular fuzzy numbers
Weighted max–min method
Deviation degree
Fuzzy multi-objective linear programming
Fuzzy constraints
ISSN:0307-904X
Online Access:Get full text
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Summary:This paper proposes a method for solving fuzzy multi-objective linear programming (FMOLP) problems where all the coefficients are triangular fuzzy numbers and all the constraints are fuzzy equality or inequality. Using the deviation degree measures and weighted max–min method, the FMOLP problem is transformed into crisp linear programming (CLP) problem. If decision makers fix the values of deviation degrees of two side fuzzy numbers in each constraint, then the δ-pareto-optimal solution of the FMOLP problems can be obtained by solving the CLP problem. The bigger the values of the deviation degrees are, the better the objectives function values will be. So we also propose an algorithm to find a balance-pareto-optimal solution between two goals in conflict: to improve the objectives function values and to decrease the values of the deviation degrees. Finally, to illustrate our method, we solve a numerical example.
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ISSN:0307-904X
DOI:10.1016/j.apm.2013.01.048