On residual implications derived from 2-uninorms.

Residual implications are one of the most important families of fuzzy implications, which are related to the concept of residuation in intuitionistic logic. In this paper, we focus on residual operators derived from 2-uninorms and study necessary and sufficient conditions for such operators being fuzzy implications, called R U 2 -implications. What is remarkable is that the R U 2 -implication is a generalization of residual implications generated by some popular fuzzy logic operations such as t-norms, uninorms and uni-nullnorms. Then, we obtain the block structures for R U 2 -implications, especially for ones generated by two special classes of conjunctive 2-uninorms. Moreover, the main properties of R U 2 -implications and their natural negations are discussed. Finally, we give a characterization of residual implications derived from left-continuous 2-uninorms, which preserve the residuation property. [ABSTRACT FROM AUTHOR]