Abstract
This article’s goal is to support the existence of the dual in a Linear Fuzzy Real environment and focus on its application to Linear fuzzy program problems. This concept will apply to linear fuzzy programming problems that contain fuzzy constraints with a crisp objective function, crisp constraints with a fuzzy objective function, or fuzzy constraints with a fuzzy objective function. It is also proposed here that optimizing fuzzy constraints and objectives of the dual linear program that consist of a triplet and are much like triangular fuzzy numbers, but differ in that they are a hybrid fuzzy number that contains characteristics that are both fuzzy and crisp.
Highlights
An idea in decision making is to maximize gains and minimize
Fuzzy linear programming problem with fuzzy coefficients was formulated by Negoita [6]
Tankaka and Asai [8] proposed a formulation of fuzzy linear programming with fuzzy constraints and gave a method for its solution
Summary
An idea in decision making is to maximize gains and minimize. This applies to the world of fuzzy decision making. Fuzzy set were initially introduced by Bellman and Zadeh [1] This concept was adopted to mathematical programming by Tanaka et al [9]. Tankaka and Asai [8] proposed a formulation of fuzzy linear programming with fuzzy constraints and gave a method for its solution. Linear Fuzzy Real numbers were used by Monk [3] and Prevo [7] in the study of fuzzy random variables and used to optimize the primal problems of linear programs with fuzzy constraints[8]. The solution of a linear programing problem may be easier to obtain through the dual than through the primal problem.
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