A Reply to a Note on the Paper “A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems”

Khan, Iqbal A.; Ahmad, Tahir; Maan, Normah

doi:10.1007/s10957-017-1088-1

Cited by 11 publications

(3 citation statements)

References 5 publications

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“…To illustrate the previous algorithm to compute a compromise fuzzy Pareto solution, let us consider the following fully fuzzy multiobjective programming problem, from another used by Khan et al(28;29), also by Arana-Jiménez (5), Table 3 Steps. Outputs from Algorithm 2 (maximization case) z2 , respectively.…”

Section: Numerical Applicationmentioning

confidence: 99%

On generating fuzzy Pareto solutions in fully fuzzy multiobjective linear programmingviaa compromise method

Arana‐Jiménez

2022

RAIRO-Oper. Res.

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In the present paper, it is unified and extended recent contributions on fully fuzzy multiobjective linear programming, and it is proposed a new method for obtaining fuzzy Pareto solutions of a fully fuzzy multiobjective linear programming problem. For its formulation, triangular fuzzy numbers and variables are combined with fuzzy partial orders and fuzzy arithmetic, and no ranking functions are required. By means of solving related crisp multiobjective linear problems, it is provided algorithms to generate fuzzy Pareto solutions; in particular, to generate compromise fuzzy Pareto solutions, what is a novelty in this field.

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Section: Numerical Applicationmentioning

confidence: 99%

On generating fuzzy Pareto solutions in fully fuzzy multiobjective linear programmingviaa compromise method

Arana‐Jiménez

2022

RAIRO-Oper. Res.

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“…This method was corrected by Najafi and Edalatpanah to make the model well in general, since the original method in Kumar et al can provide infeasible (not nonnegative) optimal solutions. Khan et al deal with FFLP with inequalities, and they also compare the objective function values via ranking functions (see also Bhardwaj and Kumar and Khan et al). Chakraborty et al have updated and applied methods for finding a fuzzy optimal solution to fuzzy transportation problems.…”

Section: Introductionmentioning

confidence: 99%

Nondominated solutions in a fully fuzzy linear programming problem

Arana‐Jiménez

2018

Math Methods in App Sciences

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In this work, a new method is presented for locating fuzzy optimal (nondominated) solutions of a fully fuzzy linear programming problem with inequality constraints and triangular fuzzy numbers, not necessarily symmetric, without ranking functions, by means of solving a multiobjective linear problem. An equivalence is proved between the set of nondominated solutions of the fully fuzzy linear programming problem and the set of weakly efficient solutions of the considered and related multiobjective linear problem. An algorithm is provided to generate nondominated solutions of a fully fuzzy linear programming problem, as well as an example to illustrate it.

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“…A new method for finding the fuzzy optimal solution of (FFLP) problems with equality constraints, with triangular fuzzy numbers involved, although they use ranking function (see [4], and the references there in) to compare the objective function values. In this way, Khan et al [34] deal with (FFLP) with inequalities, and they also compare the objective function values via ranking functions (see also [8,35]). Das and Göçken [13] apply a ranking method for the reviewer assignment problem.…”

Section: Introductionmentioning

confidence: 99%

On a fully fuzzy framework for minimax mixed integer linear programming

Arana‐Jiménez¹,

Blanco²

2018

Preprint

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In this work, we present a modeling framework for minimax mixed 0-1 fuzzy linear problems. It is based on extending the usual rewriting of crisp minimax problems via auxiliary variables to model the maximum of a finite set of fuzzy linear functions. We establish that the considered problem can be equivalently formulated as a multiple objective mixed integer programming problem. The framework is applied to a fully fuzzy version of the capacitated center facility location problem.

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A Reply to a Note on the Paper “A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems”

Cited by 11 publications

References 5 publications

On generating fuzzy Pareto solutions in fully fuzzy multiobjective linear programmingviaa compromise method

On generating fuzzy Pareto solutions in fully fuzzy multiobjective linear programmingviaa compromise method

Nondominated solutions in a fully fuzzy linear programming problem

On a fully fuzzy framework for minimax mixed integer linear programming

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