Handling Fuzzy Models in the Probabilistic Domain

Abstract

This chapter extends the fuzzy models to the probabilistic domain using the probabilistic fuzzy rules with multiple outputs. The focus has been to effectively model the uncertainty in the real world situations using the extended fuzzy models. The extended fuzzy models capture both the aspects of uncertainty, vagueness and random occurence. We also look deeper into the concepts of fuzzy logic, possibility and probability that sets the background for laying out the mathematical framework for the extended fuzzy models. The net conditional probabilistic possibility is computed that forms the key ingredient in the extension of the fuzzy models. The proposed concepts are well illustrated through two case-studies of intelligent probabilistic fuzzy systems. The study paves the way for development of computationally intelligent systems that are able to represent the real world situations more realistically.