A new method for solving fully fuzzy linear programming problems (original) (raw)
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Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution
This paper discusses full fuzzy linear programming (FFLP) problems of which all parameters and variable are triangular fuzzy numbers. We use the concept of the symmetric triangular fuzzy number and introduce an approach to defuzzify a general fuzzy quantity. For such a problem, first, the fuzzy triangular number is approximated to its nearest symmetric triangular number, with the assumption that all decision variables are symmetric triangular. An optimal solution to the above-mentioned problem is a symmetric fuzzy solution. Every FLP models turned into two crisp complex linear problems; first a problem is designed in which the center objective value will be calculated and since the center of a fuzzy number is preferred to (its) margin. With a special ranking on fuzzy numbers, the FFLP transform to multi objective linear programming (MOLP) where all variables and parameters are crisp.
A New Approach for Solving Fully Fuzzy Linear Programming by Using the Lexicography Method
Advances in Fuzzy Systems
The fully fuzzy linear programming (FFLP) problem has many different applications in sciences and engineering, and various methods have been proposed for solving this problem. Recently, some scholars presented two new methods to solve FFLP. In this paper, by considering theL-Rfuzzy numbers and the lexicography method in conjunction with crisp linear programming, we design a new model for solving FFLP. The proposed scheme presented promising results from the aspects of performance and computing efficiency. Moreover, comparison between the new model and two mentioned methods for the studied problem shows a remarkable agreement and reveals that the new model is more reliable in the point of view of optimality.
Mehar method for finding exact fuzzy optimal solution of fully fuzzy linear programming problems
International Journal of Mathematics and Systems Science, 2018
There are several methods in the literature to find the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems. However, in all these methods, it is assumed that the product of two trapezoidal (triangular) fuzzy numbers will also be a trapezoidal (triangular) fuzzy number. Fan et al. (“Generalized fuzzy linear programming for decision making under uncertainty: Feasibility of fuzzy solutions and solving approach”, Information Sciences, Vol. 241, pp. 12–27, 2013) proposed a method for finding the fuzzy optimal solution of FFLP problems without considering this assumption. In this paper, it is shown that the method proposed by Fan et al. (2013) suffer from errors and to overcome these errors, a new method (named as Mehar method) is proposed for solving FFLP problems by modifying the method proposed by Fan et al. (2013) . To illustrate the proposed method, some numerical problems are solved.
New method for solving fuzzy linear programming problem
This study investigates possibilistic linear programming and offer a new method to achieve optimal value of the necessary degree of constraints for Decision Maker in fuzzy linear programming with fuzzy technological coefficients and solve problem by this value. In the proposed algorithm, fuzzy decision set algorithm have been used that is based on the definition of fuzzy decision. Yet in possibilistic programming problem there were not any method to establish optimum value of necessary degree. When possibilistic linear programming is used for solving fuzzy linear pro- gramming problem with fuzzy technological coefficients, the decision maker must establish necessary degree of constraints, there is a need for a method which is able to achieve optimal value of necessary degree and solve the problem.
Using Min-max Method to Solve a Full Fuzzy Linear Programming
2011
In this paper, we propose a new procedure to solve a full fuzzy linear programming such that all parameters and variables in the model are triangular fuzzy numbers. First, we approximate all fuzzy numbers by the nearest symmetric triangular fuzzy numbers. Then, using arithmetic of fuzzy numbers, we have a multiobjective linear programming (MOLP) where the center and margin of fuzzy numbers are considered as objective functions in our MOLP. Also, all parameters and variables in this MOLP are crisp. After that, MOLP is solved by min-max method. We prefer min-max method to lexicography method proposed by Hosseinzadeh et al. (2009), due to the fact that min-max method considers the center and margin of fuzzy number simultaneously, while lexicography method prefers the center of a fuzzy number to its margin. Finally, Numerical examples show that the solution of full fuzzy linear programming using min-max method has less margin than lexicography method.
Alexandria Engineering Journal
Several methods currently exist for solving fuzzy linear programming problems under nonnegative fuzzy variables and restricted fuzzy coefficients. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear programming (FFLP) with unrestricted fuzzy coefficients and fuzzy variables. In this paper a new efficient method for FFLP has been proposed, in order to obtain the fuzzy optimal solution with unrestricted variables and parameters. This proposed method is based on crisp nonlinear programming and has a simple structure. To show the efficiency of our proposed method some numerical examples have been illustrated.
A novel approach to find the entire feasible solutions on fuzzy linear programming problem
Journal of Mathematical and Computational Science, 2013
In this paper, a new method for fuzzy variable linear programming problem is proposed. The optimal solution of the fuzzy variable linear programming problem is derived after finding the feasible solution. A new algorithm is discussed to transfer the infeasible/feasible solution to feasible/optimal solution is also verified.
Mathematics, 2021
Recently, new methods have been recommended to solve fully fuzzy linear programming (FFLP) issues. Likewise, the present study examines a new approach to solve FFLP issues through fuzzy decision parameters and variables using triangular fuzzy numbers. The strategy, which is based on alpha-cut theory and modified triangular fuzzy numbers, is suggested to obtain the optimal fully fuzzy solution for real-world problems. In this method, the problem is considered as a fully fuzzy problem and then is solved by applying the new definition presented for the triangular fuzzy number to optimize decision variables and the objective function. Several numerical examples are solved to illustrate the above method.
Fuzzy linear programming problems: models and solutions
Soft Computing, 2019
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, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.