Subalgebras of type (α, β) based on m-polar fuzzy points in BCK/BCI-algebras

In this article, we present the idea of quasi-coincidence of an m-polar fuzzy point with an m-polar fuzzy subset. By utilizing this new idea, we further introduce the notion of m-polar ([alpha], [beta])-fuzzy subalgebras in BCK/BCI-algebras which is a generalization of the idea of ([alpha], [beta])-bipolar fuzzy subalgebras in BCK/BCI-algebras. Some interesting results of the BCK/ BCI-algebras in terms of m-polar ([alpha], [beta])-fuzzy subalgebras are given. By using m-polar ([epsilon], [epsilon] [disjunction] q)-fuzzy subalgebras, some interesting results are obtained. Conditions for an m-polar fuzzy set to be an m-polar (q, [epsilon] [disjunction] q)-fuzzy subalgebra and an m-polar ([epsilon], [epsilon] [disjunction] q)-fuzzy subalgebra are provided. Characterizations of m-polar ([epsilon], [epsilon] [disjunction] q)-fuzzy subalgebras in BCK/BCI-algebras by using level cut subsets are explored. Keywords: BCK/BCI-algebra; m-polar fuzzy subalgebra; m-polar ([alpha], [beta])-fuzzy subalgebra; m-polar ([epsilon], [epsilon] [disjunction] q)-fuzzy subalgebra Mathematics Subject Classification: 03G25, 06F35, 08A72