Length-Fuzzy Subalgebras in BCK/BCI-Algebras

Abstract

As a generalization of interval-valued fuzzy sets and fuzzy sets, the concept of hyperfuzzy sets was introduced by Ghosh and Samanta in the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27–37]. The aim of this manuscript is to introduce the length-fuzzy set and apply it to B C K / B C I -algebras. The notion of length-fuzzy subalgebras in B C K / B C I -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.

Keywords

• hyperfuzzy set
• hyperfuzzy subalgebra
• length of hyperfuzzy set
• length-fuzzy subalgebra