A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems

•We propose a new method for solving nonlinear programming problems.•It integrates the concepts of intuitionistic fuzzy sets and geometric programming.•A two steps approach is employed to determine satisfying solutions to the problem.•The obtained solutions satisfy the conditions of Pareto-optimalit...

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Vydané v:Expert systems with applications Ročník 93; s. 245 - 256
Hlavní autori: Jafarian, E., Razmi, J., Baki, M.F.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Elsevier Ltd 01.03.2018
Elsevier BV
Predmet:
Constraint modelling
Decision making
Fuzzy sets
Geometric programming
Interactive decision making
Intuitionistic fuzzy optimization
Iterative methods
Mathematical programming
Multi-objective nonlinear programming
Multiple objective analysis
Nonlinear programming
Optimization
Problem solving
Intuitionistic fuzzy optimization
Multi-objective nonlinear programming
Interactive decision making
Geometric programming
ISSN:0957-4174, 1873-6793
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Shrnutí:•We propose a new method for solving nonlinear programming problems.•It integrates the concepts of intuitionistic fuzzy sets and geometric programming.•A two steps approach is employed to determine satisfying solutions to the problem.•The obtained solutions satisfy the conditions of Pareto-optimality.•The formulation of the models does not affect the posynomiality of the problem. In this paper, a novel method is proposed to support the process of solving multi-objective nonlinear programming problems subject to strict or flexible constraints. This method assumes that the practical problems are expressed in the form of geometric programming problems. Integrating the concept of intuitionistic fuzzy sets into the solving procedure, a rich structure is provided which can include the inevitable uncertainties into the model regarding different objectives and constraints. Another important feature of the proposed method is that it continuously interacts with the decision maker. Thus, the decision maker could learn about the problem, thereby a compromise solution satisfying his/hers preferences could be obtained. Further, a new two-step geometric programming approach is introduced to determine Pareto-optimal compromise solutions for the problems defined during different iterative steps. Employing the compensatory operator of “weighted geometric mean”, the first step concentrates on finding an intuitionistic fuzzy efficient compromise solution. In the cases where one or more intuitionistic fuzzy objectives are fully achieved, a second geometric programming model is developed to improve the resulting compromise solution. Otherwise, it is concluded that the resulting solution vectors simultaneously satisfy both of the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The models forming the proposed solving method are developed in a way such that, the posynomiality of the defined problem is not affected. This property is of great importance when solving nonlinear programming problems. A numerical example of multi-objective nonlinear programming problem is also used to provide a better understanding of the proposed solving method.
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ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2017.10.030