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

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 View the MathML source of the interval-valued fuzzy set R(D). We also can find out the estimate of revenue in the fuzzy sense View the MathML source by defuzzification of fuzzy revenue R(D). Finally, we compare with the crisp and fuzzy case.