Modeling pricing decision problem based on interval type-2 fuzzy theory

Abstract

In practical decision-making problems, decision makers are often affected by uncertain parameters because the exact distributions of uncertain parameters are usually difficult to determine. In order to deal with this issue, the major contribution in this paper is to propose a new type of type-2 fuzzy variable called level interval type-2 fuzzy variable from the perspective of level-sets, which is a useful tool in modeling distribution uncertainty. With our level interval type-2 fuzzy variable, we give a method for constructing a parametric level interval (PLI) type-2 fuzzy variable from a nominal possibility distribution by introducing the horizontal perturbation parameters. The proposed horizontal perturbation around the nominal distribution is different from the vertical perturbation discussed in the literature. In order to facilitate the modeling in practical decision-making problems, for a level interval type-2 fuzzy variable, we define its selection variable whose distribution can be determined via its level-sets. The numerical characteristics like expected value and second order moments are important indices in practical optimization and decision-making problems. With this consideration, we establish the analytical expressions about the expected values and second order moments of the selection variables of PLI type-2 trapezoidal, normal and log-normal fuzzy variables. Furthermore, in order to derive the analytical expressions about the numerical characteristics of the selection variable for the sums of the common PLI type-2 fuzzy variables, we discuss the arithmetic about the sums of common PLI type-2 fuzzy variables. Finally, we apply the proposed optimization method to a pricing decision problem to demonstrate the efficiency of our new method. The computational results show that even a small perturbation of the nominal possibility distribution can affect the quality of solutions.