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Paired Structures and other opposites-based models

In this paper we present a new class of fuzzy sets, paired fuzzy sets, that tries to overcome any conflict between families of fuzzy sets that share a main characteristic: that they are generated from two basic opposite fuzzy sets. Hence, the first issue is to formalize the notion of opposition, that we will assume dependent on a specific negation, previously determined. In this way we can define a paired fuzzy set as a couple of opposite valuation fuzzy sets. Then we shall explore what kind of new valuation fuzzy sets can be generated from the semantic tension between those two poles, leading to a more complex valuation structure that still keeps the essence of being paired. In this way several neutral fuzzy sets can appear, in particular indeterminacy, ambivalence and conflict. Two consequences are then presented: on one hand, we will show how Atanassov's Intuitionistic Fuzzy Sets can be viewed as a particular paired structure when the classical fuzzy negation is considered; on the other hand, the relationship of this model with bipolarity is reconsidered from our paired view.