Iterative Solution Process for Multiple Objective Stochastic Linear Programming Problems Under Fuzzy Environment

This article presents one interactive algorithm, and thereby determines the Pareto optimal solution to multi-objective stochastic linear programming (MOSLP) problems in real-life oriented fuzzy environment. Among the various objective functions, there always exists one objective function, referred t...

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Published in:Fuzzy information and engineering Vol. 10; no. 4; pp. 435 - 451
Main Authors: Garai, Arindam, Mandal, Palash, Roy, Tapan Kumar
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.10.2018
Taylor & Francis Group
Subjects:
Algorithms
chance-constrained programming
Decision making
expectation model
Fuzzy logic
fuzzy multi-objective optimisation
Fuzzy sets
Iterative methods
Iterative solution
Linear programming
Main objective function
Optimization
Pareto optimum
stochastic optimisation
trade-off ratio
ISSN:1616-8658, 1616-8666
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Abstract This article presents one interactive algorithm, and thereby determines the Pareto optimal solution to multi-objective stochastic linear programming (MOSLP) problems in real-life oriented fuzzy environment. Among the various objective functions, there always exists one objective function, referred to as the main objective function in this article, to multi-objective models, whose optimal value is most vital to decision-makers. When the optimal value to main objective function meets the pre-determined aspiration level, and the corresponding values to other objective functions are satisfactory in nature, that Pareto optimal solution is acceptable to decision-makers. Again, in several existing interactive fuzzy optimisation methods to MOSLP models, all reference membership levels of expectations to objective functions are considered as a unity. However, this seems to be less rational that the expectation of each conflicting objective function simultaneously attains the individual goal. So, the present article proposes to employ the trade-off ratios of membership functions to analytically determine reference membership levels in a fuzzy environment. Numerical applications further illustrate this algorithm. Finally, conclusions are drawn.
AbstractList This article presents one interactive algorithm, and thereby determines the Pareto optimal solution to multi-objective stochastic linear programming (MOSLP) problems in real-life oriented fuzzy environment. Among the various objective functions, there always exists one objective function, referred to as the main objective function in this article, to multi-objective models, whose optimal value is most vital to decision-makers. When the optimal value to main objective function meets the pre-determined aspiration level, and the corresponding values to other objective functions are satisfactory in nature, that Pareto optimal solution is acceptable to decision-makers. Again, in several existing interactive fuzzy optimisation methods to MOSLP models, all reference membership levels of expectations to objective functions are considered as a unity. However, this seems to be less rational that the expectation of each conflicting objective function simultaneously attains the individual goal. So, the present article proposes to employ the trade-off ratios of membership functions to analytically determine reference membership levels in a fuzzy environment. Numerical applications further illustrate this algorithm. Finally, conclusions are drawn.
Author Mandal, Palash
Garai, Arindam
Roy, Tapan Kumar
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  surname: Roy
  fullname: Roy, Tapan Kumar
  organization: Department of Mathematics, IIEST
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Snippet This article presents one interactive algorithm, and thereby determines the Pareto optimal solution to multi-objective stochastic linear programming (MOSLP)...
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SubjectTerms Algorithms
chance-constrained programming
Decision making
expectation model
Fuzzy logic
fuzzy multi-objective optimisation
Fuzzy sets
Iterative methods
Iterative solution
Linear programming
Main objective function
Optimization
Pareto optimum
stochastic optimisation
trade-off ratio
Title Iterative Solution Process for Multiple Objective Stochastic Linear Programming Problems Under Fuzzy Environment
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