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FUZZY PROFIT FOR LINEAR DEMAND FUNCTIONS USING POLYGONAL FUZZY NUMBERS

I. Ozcan, S. Aytar

Abstract

Let the linear demand function be ??0(??)=??0???0??,0??????0??0, where ??0,??0>0 and ??0(??) is the unit price with respect to the demand quantity ??.Then the revenue function is ??0(??)=??0?????0??2 where 0??????0??0 . Consider the cost function ??0(??)=??0+??0?? where 0???, ??0>0 and 0<??0<??0. Then we obtain profit function as ??0(??)=??0(??)???0(??)=??0?????0??2???0???0?? where 0??????0??0 . Yao and Lin [Yao J.-S., Lin D.-C., Optimal fuzzy profit for price in fuzzy sense, Fuzzy Sets and Systems 111, 455-464 2000.] fuzzified demand function using the triangular fuzzy numbers. In this paper, fuzzifying the constants a? and b? of linear demand function we calculate optimal profit. Here we use polygonal fuzzy numbers for fuzzification. Polygonal fuzzy number is a generalization of triangular fuzzy number. This type of fuzzy number was introduced by Baez et al. [A.D. Baez-Sanchez, A.C. Moretti, M.A. Rojas-Medar, On polygonal fuzzy sets and numbers, Fuzzy Sets and Systems, 209, 54-65, 2012.]. In this work we use the graded mean defuzzification method for defuzzification. Finally, we give a numerical example which shows that our polygonal fuzzy model gives more optimum results than the triangular fuzzy model.

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DOI resolver: doi.org/10.5593/SWS.ISCSS.2019.2/S05.103

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