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CONSUMER SURPLUS OF THE QUADRATIC DEMAND FUNCTION AND PRODUCER SURPLUS OF THE QUADRATIC SUPPLY FUNCTION BY FUZZIFYING POLYGONAL FUZZY NUMBERS AND DEFUZZIFYING GRADED MEAN

I. Ozcan, S. Aytar

First published: 2019https://doi.org/10.5593/SWS.ISCSS.2019.2/S04.008View metrics

Abstract

In this paper, we calculate the consumer surplus of the quadratic demand function p=a?bx1?cx12 and the producer surplus of the quadratic supply function p=d?ex1?gx12 where x is a crisp quantity and a, b, c, d, e, g are polygonal fuzzy numbers. Polygonal fuzzy number is 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 (2012) 54-65.]. For a fixed partition Pm? 0=?0<?1<...<?m=1 of the interval [0,1], A?F(Rn) is called a polygonal fuzzy set associated with partition Pm. ???(0,1] we have that the ?? level set A? satisfies A?=(1??) A?i+?A?i+1 where 0??i<?<?i+1?1 for some i=0,...,m?1 and ?=?(?)=(???i)(?i+1??i)?. Using this type of fuzzy numbers we fuzzify the coefficients instead of quantity in the functions of quadratic demand and quadratic supply. Then we use the graded mean method for defuzzification process. Finally we compare polygonal fuzzy model with the triangular fuzzy model.

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Title
CONSUMER SURPLUS OF THE QUADRATIC DEMAND FUNCTION AND PRODUCER SURPLUS OF THE QUADRATIC SUPPLY FUNCTION BY FUZZIFYING POLYGONAL FUZZY NUMBERS AND DEFUZZIFYING GRADED MEAN
Authors
I. Ozcan, S. Aytar
Proceedings
6th SWS International Scientific Conference on Social Sciences ISCSS 2019
Publisher
STEF92 Technology
Year
2019
Pages
57-64
SWS Citekey
Ozcan201945764
ISSN
2682-9959
ISBN
978-619-7408-92-8
Language
en
Publication type
Proceedings Paper
Keywords
Consumer surplusproducer surpluspolygonal fuzzy numbergraded mean defuzzification method
References14

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