Fuzzy integrals of crowd-sourced intervals using a measure of generalized accord

Abstract

Fuzzy integrals are non-linear combinations of a hypothesis support function and the (possibly subjective) worth of subsets of sources of information, realized by a fuzzy measure. They are used in many applications, with data fusion being the most well-known. In most applications, the fuzzy measure is built by some external knowledge about the worth of subsets of the information sources, whether by a subjective expert or objective sensor property, such as signal-to-noise ratio. In this paper, we investigate fuzzy measures for interval-valued evidence that have no intrinsic known worth; hence, the fuzzy measure cannot or should not be built in the conventional ways. Instead, the fuzzy measure is built directly from the data. We examine the previously proposed fuzzy measure of agreement, which builds the fuzzy measure by a computation of the agreement of combinations of sources (sources from which the contributed evidence has a high degree of agreement with evidence from other sources have a high worth). We also propose a new fuzzy measure of generalized accord that addresses a theoretical weakness in the agreement measure. We compare the two fuzzy measures by performing aggregation experiments with the fuzzy Choquet integral. Tests on both synthetic and real data are performed. We also compare the two measures against the aggregation results obtained by a survey of several example data sets.