Hyperfuzzy subalgebras of $BCK/BCI$-algebras
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초록
The notion of hyperfuzzy set was introduced by Ghosh and Samanta as a generalization of fuzzy sets and interval-valued fuzzy sets. In this article, this is applied to $BCK/BCI$-algebras. The notions of hyperfuzzy substructures/subalgebras of type $(i,j)$ for $i,j\in \{1,2,3,4\}$ are introduced, and related properties are investigated. Relations between hyperfuzzy substructure/subalgebra and its length are discussed, and the properties of hyperfuzzy subalgebras related to upper and lower level subsets are investigated.
Abstract
The notion of hyperfuzzy set was introduced by Ghosh and Samanta as a generalization of fuzzy sets and interval-valued fuzzy sets. In this article, this is applied to $BCK/BCI$-algebras. The notions of hyperfuzzy substructures/subalgebras of type $(i,j)$ for $i,j\in \{1,2,3,4\}$ are introduced, and related properties are investigated. Relations between hyperfuzzy substructure/subalgebra and its length are discussed, and the properties of hyperfuzzy subalgebras related to upper and lower level subsets are investigated.
참고문헌 (6)
- J. Ghosh, "Hyperfuzzy sets and hyperfuzzy group", Int. J. Advanced Sci Tech., 41, pp.27~37 (2012)
- Y. S. Huang, "BCI-algebra" (2006), Science Press
- Y. Imai, "On axiom systems of propositional calculi", Proc. Japan Acad., 42, pp.19~21 (1966)[DOI]
- K. Iseki, "An algebra related with a propositional calculus", Proc. Japan Acad., 42, pp.26~29 (1966)[DOI]
- J. Meng, "BCK-algebras" (1994), Kyungmoon Sa Co.
- L. A. Zadeh, "Fuzzy sets", Inform. Control, 8, pp.338~353 (1965)[DOI]