On uni-soft p-semisimple ideals and uni-soft strong ideals in BCI-algebras

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Mathematical and Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Mathematics Education, Chinju National University of Education, Jinju, Korea

3 UniveDepartment of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabiarsity of Tabuk

Abstract

In this paper, the notions of uni-soft p-semisimple ideals and uni-soft strong ideals in BCI-algebras are introduced and related properties are investigated. Some conditions for a uni-soft ideal to be a uni-soft p-semisimple ideal are given. Also, a necessary and sufficient condition for a uni-soft ideal to be a uni-soft strong ideal is given. Finally, the relationships between uni-soft p-semisimple ideals and uni-soft strong ideals are investigated.
 

Keywords

References

[1] H. Ataks, N. Cagman, Soft set and soft groups, Information Sciences, 177 (2007), 27{35.
[2] K. Atanassov, Fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.
[3] K. Atanassov, Operators over interval valued intuitionstic fuzzy sets, Fuzzy Sets and System,
64 (1994), 159{174.
[4] H. Bordbar, R.A. Borzooei, Y.B. Jun, Uni-commutative ideals and uni-soft ideals in BCI-
algebras, 14(2) (2018), 235{247.
[5] D. Chen, E.C.C. Tsang, D.S. Yeung, X. Wang, The parametrization reduction of soft sets and
its applications, Computers and Mathematics with Applications, 49(5-6) (2005), 757{763.
[6] F. Feng, Y.B. Jun, X. Zhao, Soft semirings, Computational and Applied Mathematics, 56
(2008), 2621{2628.
[7] W.L. Gau, D.J. Buehrer, Vague sets, IEEE Trains System Man Cybernet, 32(2) (1993), 610{
614.
[8] Y. Imai, K. Iseki, On axiom systems of propositional calculi, XIV. Proc. Japan Academy, 42
(1966), 19{22.
[9] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Academy, 42 (1966),
26{29.
[10] K. Iseki, On BCI-algebras, Mathematics Seminar Notes, 8 (1980), 125{130.
[11] K. Iseki, S. Tanaka, Ideal theory of BCK-algebras, Mathematica Japonica, 21 (1976), 351{366.
[12] Y.B. Jun, Union soft sets with applications in BCK/BCI-algebras, Bulletin of the Korean
Mathematical Society, 56 (2013), 1937{1956.
[13] Y.B. Jun, C.H. Park, Application of soft sets in ideal theory of BCK/BCI-algebras, Infor-
mation Sciences, 178 (2008), 2466{2475.
[14] P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Computers and Mathematics with Applica-
tions, 45 (2003), 555{562.
[15] P.K. Maji, A.R. Roy, R. Biswas, An application of soft set in a decision making problem,
Computers and Mathematics with Applications, 44 (2002), 1077{1083.
[16] J. Meng, Y.B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul, 1994.
[17] D.A. Molodtsov, Soft set theory -  rst results, Computers and Mathematics with Applications,
37 (1999), 19{31.
[18] Z. Pawlak, Rough sets, International Journal of Information and Computer Sciences, 11 (1982),
341{356.
[19] H. Yisheng, BCI-algebra, Science Press, China, 2006.
[20] L.A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
[21] H.J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic, Boston, MA,
1996.
Journal of Algebraic Hyperstructures and Logical Algebras
Volume 2, Issue 3
August 2021
Pages 99-108

Files

Share

How to cite

Statistics