Knowledge representation using linguistic fuzzy relations

This dissertation presents a theoretical framework for semantic representation, linguistic computation, knowledge representation, and approximate reasoning about object relations in knowledge engineering. The notions of term sets are extended; the notions of Linguistic Fuzzy Relation (LFR), Linguistic Fuzzy Similarity Relation (LSR), and Linguistic Transitive Closure (LTC) are proposed based on the theory of numerical fuzzy relation, numerical similarity relation, the extension principle, and the extended term set definitions. Theorems are given that provide conditions for the existence and uniqueness of the LTCs of an LFR under three different operations of extended max-min, extended max-product, and extended max-(DELTA); two algorithms for obtaining the LTCs are presented, and some interesting features of different LTCs are identified and illustrated by numerical examples. POOL--a semantic model for approximate reasoning--is proposed based on the theory of LFRs. A prototype system has been implemented in Franz Lisp under the UNIX Operating System (Berkley 4.2 bsd) on a SUN 2/120 workstation. Results confirm that the proposed model can provide knowledge-based systems with both representational and inferential power.