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Cubic interval-valued intuitionistic fuzzy sets and their application in BCK/BCI-algebras. (English) Zbl 1432.06015
Summary: As a new extension of a cubic set, the notion of a cubic interval-valued intuitionistic fuzzy set is introduced, and its application in BCK/BCI-algebra is considered. The notions of \(\alpha\)-internal, \(\beta\)-internal, \(\alpha\)-external and \(\beta\)-external cubic IVIF set are introduced, and the P-union, P-intersection, R-union and R-intersection of \(\alpha\)-internal and \(\alpha\)-external cubic IVIF sets are discussed. The concepts of cubic IVIF subalgebra and ideal in BCK/BCI-algebra are introduced, and related properties are investigated. Relations between cubic IVIF subalgebra and cubic IVIF ideal are considered, and characterizations of cubic IVIF subalgebra and cubic IVIF ideal are discussed.
MSC:
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
03E72 Theory of fuzzy sets, etc.
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