On the First Place Antitonicity in QL-implications

In order to obtain a demanded fuzzy implication, a number of properties have been proposed, among which the first place antitonicity, the second place monotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, Rand QL-implications all satisfy the second place monotonicity and the boundary conditions. However, not all the QL-implications satisfy the first place antitonicity as Sand Rimplications do. In this paper we study the QL-implications satisfying the first place antitonicity. First we study the relationship between the first place antitonicity and other required properties of QLimplications. And then we work on the conditions under which a QL-implication generated by different combinations of a t-conorm S, a t-norm T and a strong fuzzy negation n will satisfy the first place antitonicity, especially on the cases that both S and T are continuous. We also investigate the interrelationships between Sand R-implications on one hand and QL-implications satisfying the first place antitonicity on the other.