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Length-fuzzy subalgebras in BCK/BCI-algebras. (English) Zbl 1402.06008
Summary: As a generalization of interval-valued fuzzy sets and fuzzy sets, the concept of hyperfuzzy sets was introduced by J. Ghosh and T. K. Samanta [“Hyperfuzzy sets and hyperfuzzy group”, Int. J. Advanced Sci. Technol. 41, 27–37 (2012)]. The aim of this manuscript is to introduce the length-fuzzy set and apply it to BCK/BCI-algebras. The notion of length-fuzzy subalgebras in BCK/BCI-algebras is introduced, and related properties are investigated. Characterizations of a length-fuzzy subalgebra are discussed. Relations between length-fuzzy subalgebras and hyperfuzzy subalgebras are established.
MSC:
06F35 BCK-algebras, BCI-algebras (aspects of ordered structures)
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