An essay on the linguistic roots of fuzzy sets

This paper mainly tries to show that the membership function of a fuzzy set labeled P does show some intrinsic property related with how P is actually managed in the universe of discourse. Its final goal is to analyze an answer to the question, which intrinsic but simple property allows a function to represent a fuzzy set labeled P? The presented property exhibits that the membership function just ‘measures’ in some scale the extent up to which x is P in language, for all x in the universe of discourse. Such study is done in a form allowing to consider how to represent the ‘collective’ originated by a predicate reflecting a collective noun. As particular cases of what is presented, and when the degrees can be some kinds of numerical subsets, the Zadeh’s fuzzy sets, the interval-valued, the intuitionistic, and the type-2 fuzzy sets, appear as particular cases and to some extent are discussed. A ‘unification’ of all different kinds of fuzzy sets based on a linguistic origin is achieved.