On the associative property of fuzzy Xor connectives

Authors:
Xingxing He;Yingfang Li;Keyun Qin
Affiliations:
Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, Sichuan, PR China and Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China;Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China;Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2013

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Abstract

The connective fuzzy Xor has been studied by Bedregal et al. [B.C. Bedregal, R.H.S. Reiser and G.P. Dimuro, Xor-Implications and E-Implications: Classes of fuzzy implications based on fuzzy Xor, Electronic Notes in Theoretical Computer Science 247 2009 5--18] and two methods for constructing fuzzy Xor are given. As an important property of classical Xor connective, associativity is also defined in the definition of fuzzy Xor. However, we find that some of the fuzzy Xor connectives constructed with the given methods do not satisfy associative property. This paper studies the conditions under which the fuzzy Xor constructed with the methods given in [1] satisfy associative property.