Scholarly record
FUZZY PROFIT FOR LINEAR DEMAND FUNCTIONS USING POLYGONAL FUZZY NUMBERS
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.
Publication Impact Profile
Publication details
References8
Báez-Sánchez A.D., Moretti A.C., Rojas-Medar M.A., On polygonal fuzzy sets and numbers, Fuzzy Sets and Systems, 209, 54-65, 2012.
Chang S.S.L., Zadeh L.A., On fuzzy mapping and control. IEEE Transactions on Systems Man and Cybernetics, 2, 30-34, 1972.
Chang S.-C., Yao J.-S., Optimal revenue for demand function in fuzzy sense, Fuzzy Sets and Systems, 111, 419-431, 2000.
Chen S. H., and Hsieh C. H., Graded mean integration representation of generalized fuzzy number, Journal of the Chinese Fuzzy System Association, 5(2), 1-7, 1999.
Lin D.-C., Optimal profit for fuzzy demand in the fuzzy sense, Journal of Interdisciplinary Mathematics, 8:3, 301-326, 2005.
Liu P., Li H., Fuzzy neural network theory and application, World Scientific, Singapore 2004.
Özcan İ., Application of polygonal fuzzy numbers to the basic economic order quantity model, MSc thesis, Suleyman Demirel University, Turkey, 2019.
Yao J.-S., Lin D.-C., Optimal fuzzy profit for price in fuzzy sense, Fuzzy Sets and Systems, 111, 455-464, 2000.
View or Download full articleAccess options
SWS access login
Login as SWS Scientific CommitteeLogin as SWS Scientific PartnerLogin as SWS AuthorAuthors and approved SWS contributors will read and export their own linked papers after identity matching by SWS profile, email and SGEM GlobalID.
For librarian assistance: [email protected]
Purchase Instant Access
- Article can be downloaded after successful payment.
- Article may be used according to SWS library access terms.
- Article cannot be redistributed.
