Composite fuzzy measure and its application to decision making

Abstract

A composite fuzzy measure space built up from two fuzzy measure spaces is proposed. It is applied to the automobile factory capital investment decision making problem. Firstly, in the application using a fuzzy measure on a real number, there is a problem of how to evaluate the inbetween intervals, each of which is given by a fuzzy measure. So, a composite fuzzy measure built up from two fuzzy measures defined on two fuzzy measurable spaces is proposed using composite fuzzy weights. The measurable space of this composite fuzzy measure is the direct sum of two measurable spaces. It is proved that a composite measure built up from two fuzzy measures using composite fuzzy weights will be a fuzzy measure. It is recursively extended to a composite fuzzy measure built up from plural measurable spaces. Also, the associative, composite fuzzy measure built up from three fuzzy measures is introduced. It is then applied to the automobile factory capital investment decision making problem. It is assumed that an automobile company has a sales plan of a new car. The current factory line has a capacity to manufacture 3200 new cars, additional to the current car lines. Then, by the use of this composite fuzzy measure, the differentiation of the Choquet integral becomes the important index for decision making, and it is confirmed to be a useful tool for this decision making.