Fuzzy Choquet integration of homogeneous possibility and probability distributions

Abstract

The fuzzy integral (FI) is an extremely flexible and powerful tool for data and information aggregation. The FI is parametrized by the fuzzy measure (FM), a normal and monotone capacity. Based on the selection of FM, the FI produces different aggregation operators. In recent years, a number of FI extensions have been put forth relative to different types of uncertain information, e.g., real-, interval- and set-valued (under various constraints). Herein, we study the applicability and behavior of different extensions of the fuzzy Choquet integral for fusing homogeneous possibility and probability distributions. This analysis is of great utility in terms of understanding what extensions and under what conditions it is possible to aggregate and maintain homogeneity within uncertain information. We show that two extensions, gFI and NDFI, can aggregate both probability and possibility distributions. While these extensions do not always maintain homogeneity, they do under certain conditions. Last, while we specifically focus on the aggregation of homogeneous uncertain information, the propositions put forth also shed light into heterogeneous information aggregation via the gFI and the NDFI.