Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Fuzzy Implicative BCK-filters in Bounded BCK-algebras

Document Type : Original Article

Author
Sadegh Khosravi Shoar
Department of Mathematics and computer science, Fasa University, Fasa, Iran
10.22034/jfsa.2024.389592.1165
Abstract
In this article, we introduce a new category of fuzzy BCK-filters, i.e., fuzzy implicative BCK-filters in bounded BCK-algebras and show that every fuzzy implicative BCK-filter is a fuzzy BCK-filter, while the opposite of this article in the case It is not established at all. We studied the properties of a fuzzy BCK-filter and introduced (x) (θ) (y µ) which is a µ fuzzy BCK-filter and we show that this is the smallest fuzzy BCK-filter containing µ. In the following, the relationship between We examine the fuzzy BCK-filters and the fuzzy BCK-algebras and show that in the torsional BCK-algebra X every fuzzy BCK-filter µ in X is a fuzzy BCK-filter if and only if X is a BCK-algebra.
Keywords
Fuzzy BCK-filter
Fuzzy Implicative BCK-filter
Involutory BCK-algebra
Bounded BCK-algebras
Subjects
[1]    C. Barbacioru , Positive implicative BCK-algebras, Mathematica Japonica, 36 (1967), 11-59.
[2]    A. Dvurec~ enskij, S. Pulmannova, New trends in quantum structures, Springer Science 2000.
[3]    Y. Huang, BCI-algebras, Science Press, 2006.
[4]    Y. Huang, On involutory BCK-algebras, Soochow Journal of Mathematics, 32(1), (2006), 51-57.
[5]    I. H. Hwang, H. S. Kim, J. Neggers, Some implicativities for groupoids and BCK-algebras, Mathe- matics, 2019, 7(10), 973.
[6]    Y. Imai, K. Iseki, On axiom systems of propositional calculi XIV, Proceedings of the Japan Academy, Series A, 42 (1966), 19-22.
 
[7]    Y. B. Jun, S. M. Hong and J. Meng, Fuzzy BCK-filters, Scientiae Mathematicae Japonicae, 47(1) (1998), 45--49.
[8]    S. Khosravi Shoar, R. A. Borzooei, R. Moradian, A. Radfar, PC-lattices, a class of bounded BCK- algebras, Bulletin of the Section of Logic, 47/1 (2018), 33--44.
[9]    S. Khosravi Shoar, Ei, involutory and EQI-ideal in bounded BCK-algebras, Afrika Matematika, 27 (2016) 313-324.
[10]    B. L. Meng, Some reuslts of BCK-filters, Information Sciences, 130 (2000) 185-194.
[11]    J. Meng, BCK-filters, Mathematica Japonica, 44 (1996), 119-129.
[12]    J. Meng, On ideals in BCK-algebras, Mathematica Japonica, 40, 143-154 (1994).
[13]    J. Meng, Y. B. Jun, BCK-algebra, Kyung Moosa, Seoul, Korea, 1994.
[14]    S. Tanaka, A new class of algebras, Mathematics Seminar Notes 3 (1975), 37-43.
[15]    L.A. Zadeh, Fuzzy sets, Information Control, 8 (1965) 338-353.
Fuzzy Systems and its Applications
Volume 7, Issue 1 - Serial Number 14
Open Access Statement
June 2024
Pages 229-246

  • Receive Date 12 March 2023
  • Revise Date 06 September 2024
  • Accept Date 08 October 2024