Using fuzzy measures for modeling human perception of uncertainty in artificial intelligence. (January 2020) - Yager, Ronald R.
Abstract: We observe the importance of modeling human perceptions of various types of information for the construction of A. I. systems and highlight the need for modeling human perceptions of uncertainty. We introduce the concept of a fuzzy measure, μ, and discuss its use as a general structure for the representation of knowledge about an uncertain variable. We note the ability of the fuzzy measure to model various formulations of uncertain information in a unified format. We look at various properties of fuzzy, particularly the ability to fuse multiple fuzzy measures to form new measures. We introduce various operations on fuzzy measures motivated from probability theory such as the determination of expected values and variances. We emphasize the importance of the Choquet integral in these operations. We discuss two characterizing features of a fuzzy measure, its entropy and attitudinal character, and note their usefulness in helping select an appropriate measure. We finally look at the issue of answering questions about variables having information about its value modeled by a fuzzy measure. Here we must come to grips with the fact that for most measures a fundamental property of the probability measure, Prob(A) + Prob( A ¯ ) = 1, does not hold.