Mahasin A Ahmed¹* and Esmat A Amhed²

¹College of Science, Department of Mathematics, Sudan University of Science and Technology, Khartoum, Republic of Sudan
²College of Electrical Engineering and IT Department of Electrical Engineering, Onaizah Colleges, KSA

*Corresponding Author: Mahasin A Ahmed, College of Science, Department of Mathematics, Sudan University of Science and Technology, Khartoum, Republic of Sudan.

Received: April 01, 2021; Published: August 18, 2021

Abstract

The tricky point when studying bifuzzy mathematics lies in how to carry out the ordinary concept to bifuzzy case. In other words, how to pick out the ordered pair of the rational generalization from the large ordered pairs available in. The elements of the bifuzzy sets are featured by an additional degree which is called the degree of uncertainty. This paper aims to introduce a new notion of bifuzzy commutative idealsin BCK-algebras, and various properties of these notions in the context of bifuzzy sets are established.

Keywords: BCK/BCI - Algebras; Commutativeideal; Bifuzzy Set; Bifuzzy Ideal; Bifuzzy Commutative Ideal; Cartesian Product

Bibliography

1. M Akram. “Bifuzzy ideals of K -algebras”. WSEAS Transactions on Mathematics 7.5 (2008): 313-322.
2. K Iséki and S Tanaka. “Ideal theory of BCK-algebras”. Japan Mathematics Journals 21 (1976): 351-366.
3. K Iséki and S Tanaka. “An introduction to the theory of BCK-algebras”. Japan Mathematics Journals 23 (1978): 1-26.
4. T Gerstenkornand and J Manko. “Bifuzzy probabilistic sets”. Fuzzy Sets and Systems 71 (1995): 207-214.
5. Y B Jun and J Meng. “BCK-algebra, by Kyung Moon”. SACo SeoulKorea (1994).
6. Y B Jun., et al. “Fuzzy Implicative ideals of BCK – algebras”. Fuzzy sets, and systems 89 (1997): 243-248.
7. Muhiuddin G., et al. “Implicative N - ideals of BCK - algebras based on Neutrosophic N – structures”. Discrete Mathematics, Algorithms, and Applications 11.1 (2019): 1950011.
8. G Muhiuddin and YB Jun. “Further Results of Neutrosophicsubalgebras in BCK/BCI -algebras based on Neutrosophic points”. TWMS Journal of Applied and Engineering Mathematics 2 (2020): 232-240.
9. G Takeutis Titans. “Intuitionistic fuzzy logic and Intuitionistic fuzzy set Theory”. Journal Symbolic Logic 49 (1984): 851-866.
10. G Xi. “Fuzzy BCK – algebras”. Japan Mathematics Journals 36 (1991): 935-942.
11. L A Zadeh. “Fuzzy sets”. Inform. and Control 8 (1965): 338-353.

Citation

Citation: Mahasin A Ahmed and Esmat A Amhed. “Bifuzzy Commutative Ideals in BCK-algebras". Acta Scientific Computer Sciences 3.8 (2021): 53-66.

Copyright

Copyright: © 2021 Mahasin A Ahmed and Esmat A Amhed. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.