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To the best of author's knowledge, only one approach is proposed in the literature to solve fuzzy linear fractional minimal cost flow problems (minimal cost flow problems in which each known arc cost is represented either by a triangular fuzzy number or a trapezoidal fuzzy number). In this paper, the mathematical incorrect assumptions, considered in the existing approach to solve fuzzy linear fractional minimal cost flow problems, are pointed out. Also, by generalizing an existing approach for solving fuzzy linear fractional programming problems, an approach (named as Mehar approach) is proposed to solve fuzzy linear fractional minimal cost flow problems. Furthermore, two numerical examples are solved to illustrate the proposed Mehar approach. [ABSTRACT FROM AUTHOR]

Abdel-Basset et al. (Neural Computing and Applications, 2018, https://doi.org/10.1007/s00521-018-3404-6) proposed methods for solving different types of neutrosophic linear programming problems (NLPPs) (NLPPs in which some/all the parameters are represented as trapezoidal neutrosophic numbers (TrNNs)). Abdel-Basset et al. also pointed out that as a trapezoidal fuzzy number is a special case of trapezoidal neutrosophic number. Therefore, the fuzzy linear programming problems which can be solved by the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33) can also be solved by thier proposed method. In addition to that, to show the advantages of their proposed method over the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33), Abdel-Basset et al. solved the same fuzzy linear programming problems by their proposed method as well as the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33) and shown that the results, obtained on applying by their proposed method are better than the results, obtained on applying the existing methods (Ganesan and Veermani, Ann Oper Res, 2006, 143 : 305-315; Ebrahimnejad and Tavana, Appl Math Model, 2014, 38 : 4388-4395; Kumar et al., 2011, Appl Math Model, 35 : 817-823; Satti et al., Int J Decis Sci, 7 : 312-33). After a deep study of Abdel-Basset et al. 's method, it is observed that Abdel-Basset et al. have considered several mathematical incorrect assumptions in their proposed method and hence, it is scientifically incorrect to use Abdel-Basset et al. 's method in its present form. The aim of this paper is to make the researchers aware about the mathematical incorrect assumptions, considered by Abdel-Basset et al. in their proposed method, as well as to suggest the required modifications in Abdel-Basset et al. 's method. [ABSTRACT FROM AUTHOR]

Bhardwaj and Kumar (J. Optim. Theory Appl. 163(2), 685-696 (2014)) pointed out that Khan et al. (J. Optim. Theory Appl. 159(2), 536-546 (2013)) have assumed some mathematical incorrect assumptions in their proposed method for solving fully fuzzy linear programming problems (FFLPPs). However, Khan et al. (J. Optim. Theory Appl. 173(1), 353-356 (2017)) replied that their proposed method is valid and no mathematical incorrect assumptions have been considered. The aim of this commentary is to make the researchers aware that Khan et al. (J. Optim. Theory Appl. 173(1), 353-356 (2017)) are misleading the others. In actual case, Khan et al. (J. Optim. Theory Appl. 159(2), 536-546 (2013)) have considered mathematical incorrect assumptions in their proposed method due to which some of the elements of the optimal simplex table, obtained by Khan et al. (J. Optim. Theory Appl. 159(2), 536-546 (2013)), are not triangular fuzzy numbers. [ABSTRACT FROM AUTHOR]

There are very few methods in literature to deal with fully fuzzy linear fractional programming (FFLFP) problems. In this paper, it is pointed out that in the existing methods (Journal of Applied Mathematics and Computing, 27 (2008), 227-242; Yugoslav Journal of Operations Research, 22 (2012), 41-50) for solving FFLFP problems, an inappropriate ranking property is used which may lead to the erroneous results. To resolve the flaw of the existing methods, a new method is proposed for solving FFLFP problems, and is illustrated with the help of a numerical problem. [ABSTRACT FROM AUTHOR]

Suresh et al. (Solving intuitionistic fuzzy linear programming problems by ranking function, Journal of Intelligent and Fuzzy Systems, 27, 3081-3087, 2014) proposed the ranking function for comparing triangular intuitionistic fuzzy numbers (TIFNs) and applied this ranking function to solve different types of intuitionistic fuzzy linear programming problems (IFLPPs). In this note, it is pointed out that the ranking function proposed by authors is not valid. Hence, the results of intuitionistic fuzzy linear programming problems, obtained by using this ranking function, are also not valid. Further, the exact ranking function is obtained by modifying existing ranking function and using the exact ranking function, the exact results of intuitionistic fuzzy linear programming problems considered by Suresh et al., are obtained. [ABSTRACT FROM AUTHOR]

Li and Yang [D.F. Li and J. Yang, A difference-index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers, Journal of Applied Mathematics 2013 (2013), 1-10] pointed out that there is no method in the literature for solving such bimatrix games in which payoffs are represented by intuitionistic fuzzy numbers and proposed a method for the same. In this paper, it is pointed out that Li and Yang have considered some mathematical incorrect assumptions in their proposed method. For resolving the shortcomings of Li and Yang's method, a new method (named as Mehar method) is proposed. Also, the exact optimal solution of the numerical problem, solved by Li and Yang by their proposed method, is obtained by the proposed Mehar method. [ABSTRACT FROM AUTHOR]

Ezzati et al. (2013) proposed a method for comparing triangular fuzzy numbers and using it, propose a new algorithm to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints. Ezzati et al. also claimed that the fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints can also be obtained by the same algorithm by transforming it into fully fuzzy linear programming problems with equality constraints. In this note, it is proved that the fully fuzzy linear programming problems with inequality constraints cannot be transformed into fully fuzzy linear programming problems with equality constraints and hence, the algorithm, proposed by Ezzati et al. to find the fuzzy optimal solution of fully fuzzy linear programming problems with equality constraints, cannot be used for finding the fuzzy optimal solution of fully fuzzy linear programming problems with inequality constraints. [ABSTRACT FROM AUTHOR]

Several authors have proposed different methods for solving fuzzy minimum cost flow (MCF) problems. In this paper, some single and multi-objective fuzzy MCF problems are chosen which cannot be solved by using any of the existing methods and a new method is proposed for solving such type of problems. The main advantage of the proposed method over existing methods is that the fuzzy MCF problems which can be solved by using the existing methods can also be solved by the proposed method. But, there exist several fuzzy MCF problems which can be solved only by using the proposed method i.e., it is not possible to solve these problems by using the existing methods. To illustrate the proposed method and also to show the advantages of the proposed method over existing methods some single and multi-objective fuzzy MCF problems which cannot be solved by using the existing methods are solved by using the proposed method and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems with mixed constraints. By using the proposed method the fuzzy optimal solution of FFLP problems with mixed constraints occurring in real life situations can be easily obtained. To illustrate the proposed method a numerical example is solved. The proposed method can be easily applied to find the fuzzy optimal solution of FFLP problems occurring in real life situations. [ABSTRACT FROM AUTHOR]

The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method) is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems. [ABSTRACT FROM AUTHOR]

In this paper limitations of an existing method (M. Otadi and M. Mosleh, Solving fully fuzzy matrix equations, Applied Mathematical Modelling 2012) are pointed out and to overcome these limitations a new method is proposed. To illustrate the proposed method numerical examples are solved and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

Abstract: To the best of our knowledge, there is no method in literature for solving such fully fuzzy linear programming (FLP) problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers. Also, to propose such a method, there is need to find the product of unrestricted L-R flat fuzzy numbers. However, there is no method in the literature to find the product of unrestricted L-R flat fuzzy numbers. In this paper, firstly the product of unrestricted L-R flat fuzzy numbers is proposed and then with the help of proposed product, a new method (named as Mehar’s method) is proposed for solving fully FLP problems. It is also shown that the fully FLP problems which can be solved by the existing methods can also be solved by the Mehar’s method. However, such fully FLP problems in which some or all the parameters are represented by unrestricted L-R flat fuzzy numbers can be solved by Mehar’s method but can not be solved by any of the existing methods. [Copyright &y& Elsevier]

Abstract: In published works on fuzzy linear programming there are only few papers dealing with stability or sensitivity analysis in fuzzy mathematical programming. To the best of our knowledge, till now there is no method in the literature to deal with the sensitivity analysis of such fuzzy linear programming problems in which all the parameters are represented by LR flat fuzzy numbers. In this paper, a new method, named as Mehar’s method, is proposed for the same. To show the advantages of proposed method over existing methods, some fuzzy sensitivity analysis problems which may or may not be solved by the existing methods are solved by using the proposed method. [Copyright &y& Elsevier]

To the best of our knowledge, there is no method in the literature for solving such fuzzy transportation problems in which the different cost parameters are represented by different type of LR flat fuzzy numbers. In this paper, a new method is proposed for solving similar type of fuzzy transportation problems. To illustrate the proposed method and also to show the advantages of the proposed method some fuzzy transportation problems which can not be solved by using any of the existing method are solved. Also, it is shown that the fuzzy transportation problems which can be solved by the existing methods can also be solved by using the proposed method and the same results are obtained. [ABSTRACT FROM AUTHOR]