On nonstrict Archimedean triangular norms, Hamming distances, and cardinalities of fuzzy sets

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This work concerns nonstrict Archimedean triangular norms and cardinalities of fuzzy sets. Values of those t-norms are expressed in the language of Hamming distances between some fuzzy sets. We apply this optics to two important types of cardinalities, namely generalized FGCounts and generalized sigma counts. Finally, we prove that the well-known relationship between the FGCount and the sigma count of a fuzzy set is a limit property of generalized FGCounts involving Yager t-norms. © 2009 Wiley Periodicals, Inc.