Abstract
In this paper, we concentrate on three kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients, linear programming problems with fuzzy right-hand sides 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. Finally, we give illustrative examples and their numerical solutions.
Highlights
In fuzzy decision making problems, the concept of maximizing decision was proposed by Bellman and Zadeh [2]
From the beginning of the theory, three periods in its development can be recognized: 1. The period between 1965 - 1977. This period is known as the academic phase, which is characterized by the development of fundamentals of Fuzzy Set Theory, and speculations about possible prospective applications of the theory
The outcome was a small number of publications of a predominantly theoretical nature, by a small number of contributors, primarily from the academic community
Summary
In fuzzy decision making problems, the concept of maximizing decision was proposed by Bellman and Zadeh [2]. Shaocheng [11] considered the fuzzy linear programming problem with fuzzy constraints and defuzzificated it by first determining an upper bound for the objective function. Further he solved the so-obtained crisp problem by the fuzzy decisive set method introduced by Sakawa and Yana [10]. We combine solution methods of Asai and Shaocheng, We first consider linear programming problems with fuzzy right-hand sides.
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