document: Applying genetic algorithms to solve the fuzzy optimal profit problem This study investigated the application of genetic algorithms in 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 fuzzy cost . Traditional methods for solving this problem are -LRB- 1 -RRB- the extension principle , and -LRB- 2 -RRB- using interval arithmetic and alpha - cuts . However , we argue that 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 membership functions . We not only give empirical examples to show the effectiveness of this approach , but also give theoretical proofs to validate correctness of the algorithm . We conclude that genetic algorithms can produce good approximate solutions when applied to solve fuzzy optimization problems
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extractive_keyphrases: genetic algorithms fuzzy optimization problem fuzzy optimal profit problem economics business fuzzy price quadratic fuzzy demand function linear cost function approximate solution theoretical proofs
abstractive_keyphrases: linear fuzzy demand function algorithm correctness validation