THE OPERATIONAL VIEWPOINT AND SOME OF ITS CONSEQUENCES: A SHORT REVIEW

This paper presents first results on fuzzy set theory (with the emphasis on probability theoretical aspects) from an operational viewpoint, a new approach that claims to be a way out of some of the difficulties and to present a consistent framework for the set-theoretical aspects of fuzzy set theory (e.g.the complementation paradoxes vanish, and fuzzy sets become a topos under this interpretation). As a preliminary conclusion of this approach we conjecture that the concept of fuzzy set has two essentially different semantical dimensions, which have not sufficiently been separated in the traditional theory, they may be considered either as an evaluation over a universe (i.e. as a connotation) or as a collection of evaluated object (i.e.as a denotation).

THE OPERATIONAL VIEWPOINT AND SOME OF ITS CONSEQUENCES: A SHORT REVIEW

This paper presents first results on fuzzy set theory (with the emphasis on probability theoretical aspects) from an operational viewpoint, a new approach that claims to be a way out of some of the difficulties and to present a consistent framework for the set-theoretical aspects of fuzzy set theory (e.g.the complementation paradoxes vanish, and fuzzy sets become a topos under this interpretation). As a preliminary conclusion of this approach we conjecture that the concept of fuzzy set has two essentially different semantical dimensions, which have not sufficiently been separated in the traditional theory, they may be considered either as an evaluation over a universe (i.e. as a connotation) or as a collection of evaluated object (i.e.as a denotation).