Uncertainty models for knowledge-based systems

Abstract

This Research Monograph is a first attempt to present a general framework for the manipulation and explanation of uncertainty in the design of knowledge-based expert systems. It provides mathematical foundations and gives extension and applications of various theories of uncertainty, including Bayes' Statistics, Zadeh's Possibility Theory and Belief Functions. Also, this monograph addresses topics such as knowledge representation, inference rules, and combination of evidence. The general framework is based upon the theory of formal languages and semantic evaluations from different systems of mathematical logic. The underlying processes of reasoning lead to decision analyses in various contexts of knowledge-based system theory. A general discussion is presented on topics such as generalized set theory from a viewpoint of multi- valued logic and its connection with Category Theory. This monograph also gives a survey of the state-of-the-art of research in the areas of fuzzy sets and Zadeh's Possibility Theory.