Abstract
The aim of this contribution is to develop a theory of such concepts as fuzzy point, fuzzy set and fuzzy function in a similar style as is common in classical mathematical analysis. We recall some known notions and propose new ones with the purpose to show that, similarly to the classical case, a (fuzzy) set is a collection of (fuzzy) points or singletons. We show a relationship between a fuzzy function and its ordinary âskeletonâ that can be naturally associated with the original function. We show that any fuzzy function can be extended to the domain of fuzzy subsets and this extension is analogous to the Extension Principle of L. A. Zadeh.
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