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On nonstrict Archimedean triangular norms, Hamming distances, and cardinalities of fuzzy sets
Author(s) -
Wygralak Maciej
Publication year - 2009
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.20354
Subject(s) - hamming distance , mathematics , sigma , hamming code , fuzzy logic , limit (mathematics) , set (abstract data type) , combinatorics , discrete mathematics , hamming weight , fuzzy set , fuzzy number , property (philosophy) , type (biology) , algorithm , computer science , artificial intelligence , mathematical analysis , physics , ecology , philosophy , decoding methods , epistemology , quantum mechanics , biology , programming language , block code
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.