Qualification and Quantification of Fuzzy Linguistic Variables and Fuzzy Expressions

One of the essences of fuzzy logic is how fuzzy variables and fuzzy expressions may be transformed into precise quantities and rigorous models in fuzzy inferences. This paper presents a denotational mathematical structure and methodology for modeling fuzzy qualifications and quantifications in cognitive informatics, soft computing, and computational intelligence. Fuzzy qualifications and quantifications for both absolute and relative measures are formally elaborated on discrete and continuous fuzzy object and expressions. In addition, the qualification for characteristic attributes of fuzzy objects is modeled. Applications of fuzzy qualifications and quantifications are illustrated using a rich set of examples and real-world cases, which enable machines to mimic complex human reasoning mechanisms in cognitive informatics, soft computing, and computational intelligence.