TAILIEUCHUNG - Solving fuzzy linear programming problems with linear membership functions

In this paper, we concentrate on two kinds of fuzzy linear programming problems: Linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. | Turk J Math 26 (2002) , 375 – 396. ¨ ITAK ˙ c TUB Solving Fuzzy Linear Programming Problems with Linear Membership Functions Rafail N. Gasimov, K¨ ur¸sat Yenilmez Abstract In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. We propose here the “modified subgradient method” and use it for solving these problems. We also compare the new proposed method with well known “fuzzy decisive set method”. Finally, we give illustrative examples and their numerical solutions. Key Words: Fuzzy linear programming; fuzzy number; modified subgradient method; fuzzy decisive set method. 1. Introduction In fuzzy decision making problems, the concept of maximizing decision was proposed by Bellman and Zadeh [2]. This concept was adopted to problems of mathematical programming by Tanaka et al. [13]. Zimmermann [14] presented a fuzzy approach to multiobjective linear programming problems. He also studied the duality relations in fuzzy linear programming. Fuzzy linear programming problem with fuzzy coefficients was formulated by Negoita [8] and called robust programming. Dubois and Prade [3] investigated linear fuzzy constraints. Tanaka and Asai [12] also proposed a formulation of fuzzy linear programming with fuzzy constraints and gave a method for its solution which bases on inequality relations between fuzzy numbers. Shaocheng [11] considered 2000 Mathematical Subject Classification: 90C70, 90C26. 375 ˙ GASIMOV, YENILMEZ the fuzzy linear programming problem with fuzzy constraints and .

• Toán học
• Fuzzy linear programming
• Fuzzy number
• Modified subgradient method
• Fuzzy decisive set method
• Fuzzy technological coefficients
• Linear programming
• Triangular fuzzy number
• Trapezoidal fuzzy number
• Multi choice programming
• Fuzzy programming
• Fractional programming
• Centroid of triangle
• Fully fuzzified linear fractional programming
• Fuzzy Goal Programming
• α Cut Analysis
• Supply Chain Master Planning
• Possibilistic Linear Programming
• Fuzzy multi objective linear model
• Reverse logistic chain
• Electrical and electronic waste
• Linear relaxation
• Economy and environmental protection
• Multi objective bi level linear programming problems
• Partial information of preference
• Fuzzy environment
• Parametric linear programming problems
• Parametric space
• Optimal decision
• Economic order quantity
• Fuzzy Non Linear Programming Technique
• Real inventory problems
• Probabilistic models
• Penalty method
• Stochastic methods
• Optimization methods
• Inventory model
• Stock dependent demand
• Fuzzy stochastic programming
• Illustrated numerically
• Multi objective matrix game
• Fuzzy goal
• Max min solution
• Optimization problem
• Linear programming problem