A Probabilistic Fuzzy Table Lookup Scheme with Negation Logic

Abstract

The well known Fuzzy Table Lookup Scheme (FTLS) is extended here by introducing negation logic within a probabilistic fuzzy logic framework. The negation logic consists of contradictory negation, medium negation, and opposite negation. As shown here, this complements well the probabilistic framework with fuzzy logic by effectively utilizing the available information while also addressing higher aspects of uncertainty. In particular, it complements information in areas where there is either insufficient observations or the observations carry high ambiguity and inaccuracy. The probabilistic fuzzy framework further allows concurrent handling of both stochastic and deterministic uncertainties in the available information. The proposed approach is implemented on two classic function types, i.e. an increasing sinusoid and a pyramid step function, with fast versus slow changes as well as with few versus many observations. Results indicate the improved performance of the proposed PFTLSwNL by up to 60% at particularly higher noise levels.