Fuzzy revenue for fuzzy demand quantity based on interval-valued fuzzy sets

Authors:
Jing-Shing Yao;Teng-san Shih
Affiliations:
Department of Mathematics, National Taiwan University, Taipei, Taiwan, China;Department of Applied Mathematics, Chinese Culture University, Hwa Kang Yangminshan, Taipei, Taiwan, China and Graduate Institute of International Business Administration, Chinese Culture Universi ...
Venue:
Computers and Operations Research
Year:
2002

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Abstract

Gorzalezany (Fuzzy Sets and Systems 21 (1987) 1) has mentioned the interval-valued fuzzy sets and its properties. In his paper, we may fuzzify the demand quantity d as D by considering the demand function P(d) = a - bd and revenue function R(d) = ad - bd2. If D is the interval-valued fuzzy set with two triangular fuzzy numbers, we can obtain the fuzzy revenue R(D) = aD - bD2. Therefore, we can find the membership function µR(D)(z) of the interval-valued fuzzy set R(D). We also can find out the estimate of revenue in the fuzzy sense M(x; Δ1, Δ2) by defuzzification of fuzzy revenue R(D). Finally, we compare with the crisp and fuzzy case.