Abstract
This paper only tries to stimulate some reflections, by showing a possible way towards rethinking fuzzy sets from their roots. A rethinking that does not change the view that fuzzy sets are mathematical entities giving extension to predicates. In such a way that, if the predicates are precise, the corresponding new entities are nothing else than classical sets. What, perhaps, is a key idea is that the use of a predicate organizes, in some way, the universe of discourse. When this organization is a preorder, the extension or L-set, appears once a degree, numerical or not, but consistent with the organization, can be defined. The ultimate goal of those above mentioned reflections, provided they would be realized in the future, is to extend the current theories of fuzzy sets to wider areas of both language and reasoning. Our objective is to reach a better knowledge of the links between language and its representations for the progress of computing with words and perceptions.
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