### Abstract

Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as BCK/BCI-algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar (α, β)-fuzzy ideals in BCK/BCI-algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, (α, β)-fuzzy ideals, and bipolar (α, β)-fuzzy ideals in BCK/BCI-algebras. We describe the characterization of m-polar (ε, ε vq)-fuzzy ideals in BCK/BCI-algebras by level cut subsets. Moreover, we define m-polar (ε, ε vq)-fuzzy commutative ideals and explore some pertinent properties.

Original language | English |
---|---|

Article number | 44 |

Journal | Symmetry |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

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### Keywords

- BCK/BCI-algebra
- m-polar (α, β)-fuzzy ideal
- m-polar (ε, ε vq)-fuzzy commutative ideal
- m-polar (ε, ε vq)-fuzzy ideal

### ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Mathematics(all)
- Physics and Astronomy (miscellaneous)

### Cite this

*Symmetry*,

*11*(1), [44]. https://doi.org/10.3390/sym11010044

**m-Polar (α, β)-fuzzy ideals in BCK/BCI-Algebras.** / Al-Masarwah, Anas; Ahmad, Abd. Ghafur.

Research output: Contribution to journal › Article

*Symmetry*, vol. 11, no. 1, 44. https://doi.org/10.3390/sym11010044

}

TY - JOUR

T1 - m-Polar (α, β)-fuzzy ideals in BCK/BCI-Algebras

AU - Al-Masarwah, Anas

AU - Ahmad, Abd. Ghafur

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as BCK/BCI-algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar (α, β)-fuzzy ideals in BCK/BCI-algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, (α, β)-fuzzy ideals, and bipolar (α, β)-fuzzy ideals in BCK/BCI-algebras. We describe the characterization of m-polar (ε, ε vq)-fuzzy ideals in BCK/BCI-algebras by level cut subsets. Moreover, we define m-polar (ε, ε vq)-fuzzy commutative ideals and explore some pertinent properties.

AB - Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as BCK/BCI-algebras, lie algebras, groups, and symmetric groups. A symmetry of the algebraic structure, mathematically an automorphism, is a mapping of the algebraic structure onto itself that preserves the structure. This paper focuses on combining the concepts of m-polar fuzzy sets and m-polar fuzzy points to introduce a new notion called m-polar (α, β)-fuzzy ideals in BCK/BCI-algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, (α, β)-fuzzy ideals, and bipolar (α, β)-fuzzy ideals in BCK/BCI-algebras. We describe the characterization of m-polar (ε, ε vq)-fuzzy ideals in BCK/BCI-algebras by level cut subsets. Moreover, we define m-polar (ε, ε vq)-fuzzy commutative ideals and explore some pertinent properties.

KW - BCK/BCI-algebra

KW - m-polar (α, β)-fuzzy ideal

KW - m-polar (ε, ε vq)-fuzzy commutative ideal

KW - m-polar (ε, ε vq)-fuzzy ideal

UR - http://www.scopus.com/inward/record.url?scp=85061123140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061123140&partnerID=8YFLogxK

U2 - 10.3390/sym11010044

DO - 10.3390/sym11010044

M3 - Article

AN - SCOPUS:85061123140

VL - 11

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 1

M1 - 44

ER -