Fuzzy Semantic Models of Fuzzy Concepts in Fuzzy Systems

The fuzzy properties of language semantics are a central problem towards machine-enabled natural language processing in cognitive linguistics, fuzzy systems, and computational linguistics. A formal method for rigorously describing and manipulating fuzzy semantics is sought for bridging the gap between humans and cognitive fuzzy systems. The mathematical model of fuzzy concepts is rigorously described as a hyperstructure of fuzzy sets of attributes, objects, relations, and qualifications, which serves as the basic unit of fuzzy semantics for denoting languages entities in semantic analyses. The formal fuzzy concept is extended to complex structures where fuzzy modifiers and qualifiers are considered. An algebraic approach is developed to manipulate composite fuzzy semantic as a deductive process from a fuzzy concept to the determined semantics. The denotational mathematical structure of fuzzy semantic inference not only explains the fuzzy nature of human semantics and its comprehension, but also enables cognitive machines and fuzzy systems to mimic the human fuzzy inference mechanisms in cognitive linguistics, cognitive computing, and computational intelligence.