Arithmetic operators in interval-valued fuzzy set theory (Q2372207)

The paper deals with one of the extensions of fuzzy set theory, namely with interval-valued fuzzy sets (which are equivalent to the intuitionistic fuzzy sets). The main contribution of the paper consists in the introduction of basic arithmetic operators on the interval-valued fuzzy sets and in the analysis of their properties. Also necessary and sufficient conditions for the validity of those properties are derived. Moreover, the pseudo-t-representable extensions of the Łukasiewicz t-norms and product t-norms are formulated by means of the suggested operators.