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

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− bd 2. If D is the interval-valued fuzzy set with two triangular fuzzy numbers, we can obtain the fuzzy revenue R( D)= aD− bD 2. Therefore, we can find the membership function μ ̄ R(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; Δ 1, Δ 2) by defuzzification of fuzzy revenue R( D). Finally, we compare with the crisp and fuzzy case. Scope and purpose Generally, it is not sure if the demand quantity is fixed for the same unit price in a perfect competitive market. In this paper, we explore the problems of maximum revenue and optimal price in the fuzzy sense with the interval-valued fuzzy set for the merchandise in the perfect competitive market, utilizing the linear demand function and quadratic revenue function. We derive the estimation of revenue in the fuzzy sense with mathematical formulas, and illustrate the results by numerical examples.