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Modeling Opposition with Restricted Paired Structures
Camilo Franco, J. Tinguaro Rodríguez, Javier Montero and Daniel Gómez

This paper focuses on the representation of opposite concepts as paired fuzzy concepts, under a restricted setting for general paired structures. In particular, examining the notion of bipolarity and the semantics of bivariate scales, the proposed setting allows accomplishing a faithful knowledge representation by means of appropriate aggregation functions, based on the separate evaluation of paired opposite concepts. In consequence, the specific semantics of different fuzzy models, with respect to their particular purposes as extensions of fuzzy sets, can be formally recovered and separated in the framework of paired structures, pointing out that, despite their formal equivalence, distinct models actually provide a quite different representational performance.

Keywords: Semantic opposition, semantic structure, paired structure, bipolarity, fuzzy sets, paired fuzzy sets, Atanassov’s intuitionistic fuzzy sets, intervalvalued fuzzy sets, type 2 fuzzy sets.

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