A new view on the relationships between interval valured and intuitionistic fuzzy sets

This paper proposes a novel approach to analyze the relationship between interval valued fuzzy sets (IVFS) and Atanassov’s intuitionistic fuzzy sets (AIFS), based on the recently introduced notion of paired structure. It is suggested that the different semantics of IVFS and AIFS, 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 both models actually provide a quite different representational performance.