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the Fuzzy Optimal Profit Problem

**Feng-Tse Lin and Jing-Shing Yao ^{*}**

Department of Applied Mathematics

Chinese Cultiure University

Taipei, 111 Taiwan

E-mail: ftlin@staff.pccu.edu.tw

National Taiwan University

Taipei, 106 Taiwan

This study investigated the application of genetic algorithms for solving a fuzzy optimization problem that arises in business and economics. In this problem, a fuzzy price is determined using a linear or a quadratic fuzzy demand function as well as a linear cost function. The objective is to find the optimal fuzzy profit, which is derived from the fuzzy price and the fuzzy cost. The traditional methods for solving this problem are (1) using the extension principle, and (2) using the interval arithmetic and a-cuts. However, we argue that the traditional methods for solving this problem are too restrictive to produce an optimal solution, and that an alternative approach is possibly needed. We use genetic algorithms to obtain an approximate solution for this fuzzy optimal profit problem without using the membership functions. We not only give empirical examples to show the effectiveness of this approach, but also give theoretical proofs to validate the correctness of the algorithm. We conclude that genetic algorithms can produce good approximate solutions when applied to solve fuzzy optimization problems.

*Keywords:* genetic algorithms, fuzzy sets, fuzzy numbers, fuzzy optimization profit problem, fuzzy demand

Retrieve PDF document (**200207_07.pdf**)

Received August 9, 2001; revised October 15, 2001; accepted January 9, 2002.

Communicated by Chuen-Tsai Sun.