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On the Representation of Intuitionistic Fuzzy>tex<$t$>/tex<-Norms and>tex<$t$>/tex<-Conorms
Abstract
Intuitionistic fuzzy sets form an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a nonmembership degree. The only constraint on those two degrees is that their sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms and conorms is the class of continuous Archimedean nilpotent triangular norms and conorms. It has been shown that for such t-norms T there exists a permutation /spl phi/ of [0,1] such that T is the /spl phi/-transform of the Lukasiewicz t-norm. In this paper we introduce the notion of intuitionistic fuzzy t-norm and t-conorm, and investigate under which conditions a similar representation theorem can be obtained.
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Cites
Atanassov, K. T. (1986) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(86)80034-3 · Cited by 16,465
Cited by
Intuitionistic Fuzzy Aggregation Operators
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Clustering algorithm for intuitionistic fuzzy sets
Xu, Z., Chen, J., & Wu, J. (2008) · Information Sciences · doi:10.1016/j.ins.2008.06.008 · Cited by 450
Intuitionistic Fuzzy Information Aggregation Using Einstein Operations
Wang, W., & Liu, X. (2012) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2012.2189405 · Cited by 416
Liu, P. (2014) · IEEE Transactions on Fuzzy Systems · doi:10.1109/tfuzz.2013.2248736 · Cited by 403
Metadata
- Authors
- Deschrijver, G., Cornelis, C., & Kerre, E. E.
- Venue
- IEEE Transactions on Fuzzy Systems
- Published
- 2004-02
- Volume
- 12
- Issue
- 1
- Pages
- 45-61
- ISSN
- 1063-6706 (ISSN-L)
- OpenAlex
- W2131429285
- Cited by
- 562
- References
- 1
- FWCI
- 14.97
- Type
- journal article
- Language
- en
- Open access
- closed
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- Deschrijver, G., Cornelis, C., & Kerre, E. E. (2004). On the Representation of Intuitionistic Fuzzy>tex<$t$>/tex<-Norms and>tex<$t$>/tex<-Conorms. IEEE Transactions on Fuzzy Systems. https://doi.org/10.1109/tfuzz.2003.822678
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