Possible New Directions in Mathematical Foundations of Fuzzy Technology: A Contribution to the Mathematics of Fuzzy Theory

Why mathematical foundations Many successful applications of fuzzy logic and fuzzy set theory such as fuzzy control and many methods of fuzzy imag ing rst appeared as heuristics without any precise mathematical justi cation In such heuristic applica tions the choice of techniques or parameters is usu ally done empirically After a su cient amount of the corresponding empirical data becomes available this data inspires mathematical foundations for the original heuristics and empirical choices

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