Interval Valued m-polar Fuzzy BCK/BCI-Algebras

Authors

G. Muhiuddin^{1, *,} , D. Al-Kadi²

¹Department of Mathematics, University of Tabuk, Tabuk, 71491, Saudi Arabia

²Department of Mathematics and Statistic, College of Science, Taif University, Taif, 21944, Saudi Arabia

^*Corresponding author. Email: chishtygm@gmail.com

DOI

10.2991/ijcis.d.210223.003How to use a DOI?

Keywords

Interval-valued m-polar fuzzy sets; Interval-valued m-polar fuzzy subalgebras; Interval-valued m-polar fuzzy (commutative) ideals

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.

Copyright

© 2021 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - G. Muhiuddin
AU  - D. Al-Kadi
PY  - 2021
DA  - 2021/03/10
TI  - Interval Valued m-polar Fuzzy BCK/BCI-Algebras
JO  - International Journal of Computational Intelligence Systems
SP  - 1014
EP  - 1021
VL  - 14
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.210223.003
DO  - 10.2991/ijcis.d.210223.003
ID  - Muhiuddin2021
ER  -