On Fuzzy Solutions to a Class of Fuzzy Multi-objective Linear Optimization Problems

Stanojević, Bogdana; Stanojević, Miroslav

doi:10.1007/978-3-030-21990-1_4

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Neither Liu and Kao [25] nor Liu [26] reported the shapes of the fuzzy sets of the optimal values of the decision variables. Later on, based on Liu and Kao's solution concept [25], the optimal values of the decision variables were empirically disclosed by a Monte Carlo simulation in [27] to be trapezoidal-like FNs whenever the problem's coefficients were TrFNs. In that way, it was proved that the problems solved by Liu and Kao [25] belong to the class of problems that can be modeled using fuzzy decision variables with a priori unknown shapes (see FUS in Figure 1).…”

Section: Fuzzy Transportation Problemsmentioning

confidence: 99%

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Stanojević

Nădăban

2021

Mathematics

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Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

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Section: Fuzzy Transportation Problemsmentioning

confidence: 99%

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Stanojević

Nădăban

2021

Mathematics

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Intuitionistic Fuzzy Sets and Dynamic Programming for Multi-objective Non-linear Programming Problems

Rizk‐Allah

Abo-Sinna

Hassanien

2021

Int. J. Fuzzy Syst.

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Multidimensional solution of fuzzy linear programming

Edalatpanah

2023

PeerJ Computer Science

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There are several approaches to address fuzzy linear programming problems (FLPP). However, due to using standard interval arithmetic (SIA), these methods have some limitations and are not complete solutions. This article establishes a new approach to fuzzy linear programming via the theory of horizontal membership functions and the multidimensional relative-distance-measure fuzzy interval arithmetic. Furthermore, we propose a multidimensional solution based on the primal Simplex approach that satisfies any equivalent form of FLPP. The new solutions of FLPP are also compared with the results of existing methods. Some numerical examples have been illustrated to show the efficiency of the proposed method.

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On Fuzzy Solutions to a Class of Fuzzy Multi-objective Linear Optimization Problems

Cited by 3 publications

References 13 publications

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Intuitionistic Fuzzy Sets and Dynamic Programming for Multi-objective Non-linear Programming Problems

Multidimensional solution of fuzzy linear programming

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