A New Approach for Solving Fully Fuzzy Linear Programming by Using the Lexicography Method (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.
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Lotfi et al. [Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Modell. 33 (2009) 3151-3156] pointed out that there is no method in literature for finding the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints. In this paper, a new method is proposed to find the fuzzy optimal solution of same type of fuzzy linear programming problems. It is easy to apply the proposed method compare to the existing method for solving the FFLP problems with equality constraints occurring in real life situations. To illustrate the proposed method numerical examples are solved and the obtained results are discussed.
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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.
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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.
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Fuzzy Linear Programming models and methods has been one of the most and well studied topics inside the broad area of Soft Computing. Its applications as well as practical realizations can be found in all the real world areas. In this paper a basic introduction to the main models and methods in fuzzy mathematical programming, with special emphasis on those developed by the authors, is presented. As a whole, Linear Programming problems with fuzzy costs, fuzzy constraints and fuzzy coefficients in the technological matrix are analyzed. Finally, future research and development lines are also pointed out by focusing on fuzzy sets based heuristic algorithms.
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Fuzzy linear programming problems have an essential role in fuzzy modeling, which can formulate uncertainty in actual environment In this paper we present methods to solve (i) the fuzzy linear programming problem in which the coefficients of objective function are trapezoidal fuzzy numbers, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers, and (ii) the fuzzy linear programming problem in which the variables are trapezoidal fuzzy variables, the coefficients of objective function and right hand side of the constraints are trapezoidal fuzzy numbers, (iii) the fuzzy linear programming problem in which the coefficients of objective function, the coefficients of the constraints, right hand side of the constraints are triangular fuzzy numbers. Here we use α –cut and ranking functions for ordering the triangular fuzzy numbers and trapezoidal fuzzy numbers. Finally numerical examples are provided to illustrate the various methods of the fuz...