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fuzzy implication; $f$-generated implication; $g$-generated implication; $h$-generated implication; $(S;N)$-implication; $S$-implication; $R$-implication
Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager_2004] has introduced two new classes of fuzzy implications called the $f$-generated and $g$-generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the $h$-generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst themselves and with the well established $(S,N)$-implications and $R$-implications. In the cases where they intersect the precise sub-families have been determined.
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