On a Theory of Fuzzy Numbers and Fuzzy Arithmetic
نویسنده
چکیده
Fuzzy numbers in number theory are a foundation of fuzzy sets and fuzzy mathematics that extend the domain of numbers from those of real numbers to fuzzy numbers. Fuzzy arithmetic is a system of fuzzy operations on fuzzy numbers. A theory of fuzzy arithmetic is presented towards a fuzzy mathematical structure for fuzzy inference and cognitive computation. The mathematical models of fuzzy numbers and their algebraic properties enable rigorous modelling of fuzzy entities in fuzzy systems and efficient manipulation of fuzzy variables in fuzzy analysis, fuzzy inference, and fuzzy computing. The denotational mathematical structure of fuzzy arithmetic not only explains the fuzzy nature of human perceptions and language semantic representation, but also enables cognitive machines and fuzzy systems to mimic human fuzzy inference mechanisms in cognitive informatics, cognitive computing, soft computing, cognitive linguistics, measurement theory, and computational intelligence.
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