Study of Two Families of Generalized Yager's Implications for Describing the Structure of Generalized (h,e)-Implications

Abstract

[eng] In this study, we analyze the family of generalized -implications. We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized -implication in terms of two families of fuzzy implication functions. These two families can be interpreted as particular cases of the and -implications, which are two families of fuzzy implication functions that generalize the well-known f and g-generated implications proposed by Yager through a generalization of the internal factors x and, respectively. The behavior and additional properties of these two families are also studied in detail.