Composite Fuzzy Measure and its Application to Decision-Making

Abstract

In applications using fuzzy measures (on real numbers), it becomes a problem how to evaluate in-between intervals each characterized by a fuzzy measure, especially when the Choquet integral is differentiated in real world problems. A composite fuzzy measure built from fuzzy measures defined on fuzzy measurable spaces has been proposed by Kaino and Hirota using composite fuzzy weights, where the measurable space of this composite fuzzy measure is the direct sum of measurable spaces. An associative, composite fuzzy measure built from a finite number of fuzzy measures is proposed and, in a constructive application, it is applied to the automobile plant capital investment decision-making problem. It is assumed that an automobile company plans to sell a new car. The current plant line has a capacity of 3,200 new cars in addition to current car lines. Using this composite fuzzy measure, differentiation of the Choquet integral becomes a quantitative index for decision-making, which is confirmed by this decision-making experiment.