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We present a new model and a new approach for solving fuzzy linear programming (FLP) problems with various utilities for the satisfaction of the fuzzy constraints. The model, constructed as a multi-objective linear programming problem, provides flexibility for the decision maker (DM), and allows for the assignment of distinct weights to the constraints and the objective function. The desired solution is obtained by solving a crisp problem controlled by a parameter. We establish the validity of the proposed model and study the effect of the control parameter on the solution. We also illustrate the efficiency of the model and present three algorithms for solving the FLP problem, the first of... 

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, α-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently,... 

Recently, Ghanbari et al. (IEEE Transactions on Fuzzy Systems 27:1286–1294, 2019) have proposed modified Kerre’s method for comparison of LR fuzzy numbers. Here, we make use of the modified Kerre’s method to solve fuzzy linear programming problems with LR coefficients. In an approach to solve a fuzzy linear program with fuzzy LR coefficients, a bi-objective optimization problem is formulated. For the associated bi-objective optimization problem, we present a time variant multi-objective particle swarm optimization (TV-MOPSO) algorithm to compute the Pareto front, a set containing a large number of solutions. Contrary to methods that change the fuzzy optimization problem to a crisp problem by... 

Recently, Ghanbari et al. (IEEE Transactions on Fuzzy Systems 27:1286–1294, 2019) have proposed modified Kerre’s method for comparison of LR fuzzy numbers. Here, we make use of the modified Kerre’s method to solve fuzzy linear programming problems with LR coefficients. In an approach to solve a fuzzy linear program with fuzzy LR coefficients, a bi-objective optimization problem is formulated. For the associated bi-objective optimization problem, we present a time variant multi-objective particle swarm optimization (TV-MOPSO) algorithm to compute the Pareto front, a set containing a large number of solutions. Contrary to methods that change the fuzzy optimization problem to a crisp problem by... 

In this paper, a fuzzy comparison of fuzzy numbers is defined and a slack-based measure (SBM model) in data envelopment analysis (DEA) is extended to be a fuzzy DEA model, using it. Proposed measure is employed for evaluation and ranking of all decision making units, using a fuzzy concept called fuzzy profit. Also, it is shown that the introduced model is convenient for using weights restrictions. Furthermore, we compare the results of proposed model with Guo and Tanaka's results [Fuzzy Sets Syst. 119 (2001) 149] by representing a numerical example introduced by them. © 2003 Elsevier Inc. All rights reserved  

To solve a fuzzy linear 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, we do not need to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search (VNS) algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a... 

In this paper, we present a fuzzy goal programming model for Transportation Planning Decisions (TPD) problem. In real-world applications of the transportation planning decisions problems with multi-objective, input data or related parameters are majority vague/fuzzy. It is hard for decision maker(s) to determine the goal value of each objective precisely as the goal values are imprecise. We consider three methods in the research for solving TPD problem under fuzziness, first method is interactive fuzzy goal programming (IFGP), that this approach aim minimizing the worst upper bound to determine an reasonable solution which is end to the best lower bound of each objective function. Second... 

In this paper, we propose a two-phase approach to find the optimal solutions of a class of fuzzy linear programming problems called fully fuzzified linear programming (FFLP), where all decision parameters and variables are fuzzy numbers. Our approach is constructed on the basis of comparison of mean and standard deviation of fuzzy numbers. In this approach, the first phase maximizes the possibilistic mean value of fuzzy objective function and obtains a set of feasible solutions. The second phase minimizes the standard deviation of the original fuzzy objective function, by considering all basic feasible solutions obtained at the end of the first phase. The advantage of the proposed approach... 

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. © 2018 IEEE  

To solve a fuzzy linear 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 linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a... 

Even though there have been so many articles and studies that focused on the supplier selection problem, a few of them considered the major decisions related to supplier selection. In this paper, the supplier selection problem is studied under a novel fuzzy approach in multiple sourcing conditions to select appropriate supplier in group decision-making environment regarding multiple sources. The use of the model is suitable in evaluating situations that involve subjectivity, vagueness and imprecise information. The group data have been used in multiple criteria decision making with multiple objective supplier selection. Trapezoidal fuzzy numbers are applied to evaluate the weights of...