Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming

This paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving...

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Veröffentlicht in:International journal of fuzzy systems Jg. 20; H. 2; S. 488 - 499
Hauptverfasser: Sharma, Uday, Aggarwal, Shashi
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2018
Springer Nature B.V
Schlagworte:
Algorithms
Approximation
Artificial Intelligence
Computational Intelligence
Engineering
Fuzzy sets
Fuzzy systems
Linear programming
Management Science
Multiple objective analysis
Operations Research
Set theory
Slack variables
flat fuzzy numbers
Nearest interval approximation of fuzzy numbers
MSC 90C05
MSC 90C29
Centre and width of the closed interval
MSC 90C70
ISSN:1562-2479, 2199-3211
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Zusammenfassung:This paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem. Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared.
Bibliographie:ObjectType-Article-1
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ISSN:1562-2479
2199-3211
DOI:10.1007/s40815-017-0336-8