Mottaghi et al. (Int J fuzzy Syst 17:236-245, 2015) proposed some results by considering a pair of fuzzy linear programming problems as a primal-dual pair. In this paper, it is pointed out that the pair of fuzzy linea...
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Mottaghi et al. (Int J fuzzy Syst 17:236-245, 2015) proposed some results by considering a pair of fuzzy linear programming problems as a primal-dual pair. In this paper, it is pointed out that the pair of fuzzy linear programming problems, considered by Mottaghi et al. as a primal-dual pair, is not a primal-dual pair. Hence, all the results, proposed by Mottaghi et al. by considering the pair of fuzzy linear programming problems as a primal-dual pair, are not valid.
To solve a fuzzylinear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy number...
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To solve a fuzzylinear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, it is not necessary to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search algorithm for solving fuzzy number linearprogrammingproblems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programmingproblems. In several methods, a fuzzy optimization problem is converted to a crisp problem but in our proposed method, using our modified Kerre's method, the fuzzy optimization problem is solved directly, without changing it to a crisp program. We provide examples to compare the performance of our proposed algorithm to other available methods. We show the effectiveness of our proposed algorithm by using the nonparametric statistical sign test.
We want to solve fuzzy linear programming problems with fuzzy coefficients in the objective function using a new variable neighborhood search algorithm. In our proposed algorithm, the local search is defined based on ...
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ISBN:
(纸本)9781538628362
We want to solve fuzzy linear programming problems with fuzzy coefficients in the objective function using a new variable neighborhood search algorithm. In our proposed algorithm, the local search is defined based on descent directions. We make use of our recently proposed modified Kerre's method for finding descent directions. The fuzzy optimization problem is solved directly, without changing it to a crisp program. We show the effectiveness of our proposed method in comparison with some available methods by using a non-parametric statistical sign test. The objective function values obtained by our proposed method turn to be more accurate the ones obtained by other methods.
There are several methods, in the literature, for solving fuzzy variable linearprogrammingproblems (fuzzylinearprogramming in which the right-hand-side vectors and decision variables are represented by trapezoidal...
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There are several methods, in the literature, for solving fuzzy variable linearprogrammingproblems (fuzzylinearprogramming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linearprogrammingproblems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linearprogrammingproblems occurring in real-life situations.
Data envelopment analysis (DEA) is a non-parametric technique to measure the relative efficiencies of a set of decision making units (DMUs) with common crisp inputs and outputs. Input and output data of DMUs often flu...
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Data envelopment analysis (DEA) is a non-parametric technique to measure the relative efficiencies of a set of decision making units (DMUs) with common crisp inputs and outputs. Input and output data of DMUs often fluctuate. These fluctuating data can be represented as linguistic variable characterized by fuzzy numbers. This paper attempts to extend the traditional DEA model to a fuzzy framework, thus proposing a fuzzy DEA model based on a-cut approach to deal with the efficiency measuring and ranking problem with the given fuzzy input and output data. Finally, a numerical example is presented to illustrate the fuzzy DEA model. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for management. By extending to fuzzy environment, the DEA approach is made more powerful for application.
The fuzzy set theory is being applied massively in many fields these days. One of these is linearprogrammingproblems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variab...
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The fuzzy set theory is being applied massively in many fields these days. One of these is linearprogrammingproblems. Kheirfam and Hasani (Sensitivity analysis for fuzzy linear programming problems with fuzzy variables, Advanced Modeling and Optimization, 12 (2010) 257-272), proposed a method for the sensitivity analysis for fuzzylinearprogramming (FLP) problems with fuzzy variables. There are some important cases that are not considered by Kheir- fam and Hasani. In this paper, those cases are considered and numerical examples are solved.
We examine a linearprogrammingproblem formulation in which the constraint coefficients are not precisely given in the work. We investigate the possibility of applying GAs to solve this kind of fuzzylinear programmi...
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We examine a linearprogrammingproblem formulation in which the constraint coefficients are not precisely given in the work. We investigate the possibility of applying GAs to solve this kind of fuzzy linear programming problem without defining membership functions for fuzzy numbers, using the extension principle, interval arithmetic, and alpha-cut operations for fuzzy computations, and using a penalty method for constraint violations. The proposed approach simulates every fuzzy number by distributing it into certain partition points. GAs are then used to evolve the values in each partition point. As a result, the final values represent the membership grade of that fuzzy number. After calculating the estimated values of each uncertain coefficient, we obtain a defuzzified linearprogrammingproblem. The crisp problem can then be solved using the following GA stage. The empirical results show that the proposed approach can obtain very good solutions within the given bounds for each fuzzy coefficient, thereby accomplishing flexible linearprogramming.
A dual for linearprogrammingproblems of a two person zero sum constrained matrix game with fuzzy payoffs is introduced and it is proved that such a game is equivalent to a primal-dual pair of certain fuzzylinear pr...
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ISBN:
(纸本)9781424417339
A dual for linearprogrammingproblems of a two person zero sum constrained matrix game with fuzzy payoffs is introduced and it is proved that such a game is equivalent to a primal-dual pair of certain fuzzy linear programming problems. It's solution is the focus of discussion in the future.
This paper connects finitely many indepen- dent fuzzy sets in an axiomatic possibility measure with possibility-based fuzzylinearprogramming prob- lems.
This paper connects finitely many indepen- dent fuzzy sets in an axiomatic possibility measure with possibility-based fuzzylinearprogramming prob- lems.
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