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Symmetry 2019, 11(1), 44; https://doi.org/10.3390/sym11010044

m-Polar ( α , β ) -Fuzzy Ideals in BCK/BCI-Algebras

School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia
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Received: 6 December 2018 / Revised: 24 December 2018 / Accepted: 29 December 2018 / Published: 3 January 2019
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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 B C K / B C I -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 B C K / B C I -algebras. The defined notion is a generalization of fuzzy ideals, bipolar fuzzy ideals, ( α , β ) -fuzzy ideals, and bipolar ( α , β ) -fuzzy ideals in B C K / B C I -algebras. We describe the characterization of m-polar ( , q ) -fuzzy ideals in B C K / B C I -algebras by level cut subsets. Moreover, we define m-polar ( , q ) -fuzzy commutative ideals and explore some pertinent properties. View Full-Text
Keywords: BCK/BCI-algebra; m-polar (α,β)-fuzzy ideal; m-polar (∈,∈∨q)-fuzzy ideal; m-polar (∈,∈∨q)-fuzzy commutative ideal BCK/BCI-algebra; m-polar (α,β)-fuzzy ideal; m-polar (∈,∈∨q)-fuzzy ideal; m-polar (∈,∈∨q)-fuzzy commutative ideal
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Al-Masarwah, A.; Ahmad, A.G. m-Polar ( α , β ) -Fuzzy Ideals in BCK/BCI-Algebras. Symmetry 2019, 11, 44.

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