On orders induced by implications

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm T. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained from the orders induced by the residual implications and the ordinal sum implications are discussed.

Keywords:

Fuzzy implications , Ordinal sum , Law of importation , Partial order , Residual implication