The Theory of Fuzzy Arithmetic in the Extended Domain of Fuzzy Numbers
Yingxu Wang · Journal of Advanced Mathematics and Applications · 2014
Fuzzy numbers in number theory extend the domain of numbers from those of real to fuzzy numbers, which are a foundation of fuzzy sets and fuzzy mathematics. 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.