On the first place antitonicity in QL-implications

Yun Shi, Bart Van Gasse, Da Ruan, Etienne Kerre, Catrinel Turcanu

    Research outputpeer-review


    To obtain a demanded fuzzy implication in fuzzy systems, a number of desired properties have been proposed, among which the first place antitonicity, the second place isotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, R- and QL-implications all satisfy the second place isotonicity and the boundary conditions. However, not all the QL-implications satisfy the first place antitonicity as S- and R-implications do. In this paper we study the QL-implications satisfying the first place antitonicity. First we establish the relationship between the first place antitonicity and other required properties of QL-implications. Second we work on the conditions under which a QLimplication generated by different combinations of a t-conorm S, a t-norm T and a strong fuzzy negation N satisfy the first place antitonicity, especially in the cases that both S and T are continuous. We further investigate the interrelationships between S- and R-implications generated by left-continuous t-norms on one hand and QL-implications satisfying the first place antitonicity on the other.
    Original languageEnglish
    Pages (from-to)2988-3013
    JournalFuzzy sets and systems
    Issue number22
    StatePublished - 14 May 2008

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