Abstract
The notion of interval-valued m-polar fuzzy sets (abbreviated IVmPF) is much wider than the notion of m-polar fuzzy sets. In this paper, we apply the theory of IVmPF on BCK/BCI-algebras. We introduce the concepts of IVmPF subalgebras, IVmPF ideals and IVmPF commutative ideals and some essential properties are discussed. We characterize IVmPF subalgebras in terms of fuzzy subalgebras and subalgebras of BCK/BCI-algebras. We show that in BCK-algebra, IVmPF ideals are IVmPF subalgebras and that the converse is not valid. We provide a condition under which an IVmPF subalgebra becomes an IVmPF ideal. Further, we characterize IVmPF ideals in terms of fuzzy ideals and ideals of BCK/BCI-algebras. Moreover, we prove that in any BCK-algebra, an IVmPF commutative ideal is an IVmPF fuzzy ideal but not the converse. Also, we provide conditions under which an IVmPF ideal becomes an IVmPF commutative ideal. (C) 2021 The Authors. Published by Atlantis Press B.V.