S- and R-implications from uninorms continuous in \(]0,1[^2\) and their distributivity over uninorms
In the classical logic based on the Boolean truth-values scale, residual implication (R-implication for short) and S-implication (derived from the disjunction and the negation) coincide. This is no longer true in the case of fuzzy logics based on the \([0,1]\) truth-degrees scale. Uninorms, as binary operations on \([0,1]\), can be split into two disjoint classes -- conjunctive and disjunctive uninorms. Thus, based on uninorms, both R- and S-implications can be considered. In this paper, uninorms continuous on \(]0,1[^2\) are considered. General expressions for both kinds of implications in special cases are found. Moreover, several properties of such implications are studied. Special attention is paid to the distributivity of R- and S-implications over conjunctive and disjunctive uninorms.
scientific article; zbMATH DE number 5634412