Positive Implicative Soju Ideals in BCK-Algebras

Authors

  • Xiao Long Xin School of Mathematics, Northwest University, Xi'an, China
  • Rajab Ali Borzooei Department of Mathematics, Shahid Beheshti University, Teheran, Iran
  • Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju, Korea

DOI:

https://doi.org/10.18778/0138-0680.48.1.01

Keywords:

soju subalgebra, soju ideal, positive implicative soju ideal

Abstract

The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.

References

U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Computers & Mathematics with Applications 59 (2010), pp. 3458–3463.
Google Scholar

M. Agarwal, K.K. Biswasa and M. Hanmandlu, Generalized intuitionistic fuzzy soft sets with applications in decision-making, Applied Soft Computing 13 (2013), pp. 3552–3566.
Google Scholar

H. Aktas and N. Çağman, Soft sets and soft groups, Information Sciences 177 (2007), pp. 2726–2735.
Google Scholar

K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), no. 1, pp. 87–96.
Google Scholar

K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994), no. 2, pp. 137–142.
Google Scholar

Z. Bashir, J. Wątróbski, T. Rashid, W. Salabun and J. Ali, Intuitionistic-fuzzy goals in Zero-Sum multi criteria matrix games, Symmetry 2017, 9, p. 158.
Google Scholar

S. K. De, R. Biswas and A. R. Roy, An application of intuitionistic fuzzy sets in medical diagnosis, Fuzzy Sets and Systems 117 (2001), pp. 209–213.
Google Scholar

F. Feng, Y. B. Jun and X. Zho, Soft semirings, Computers & Mathematics with Applications 56 (2008), pp. 2621–2628.
Google Scholar

Y. Huang, BCI-algebra, Science Press, Beijing, 2006.
Google Scholar

K. Iséki, On BCI-algebras, Mathematics Seminar Notes 8 (1980), pp. 125–130.
Google Scholar

K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Mathematica Japonica 23 (1978), pp. 1–26.
Google Scholar

Y. Jiang, Y. Tang and Q. Chen, An adjustable approach to intuitionistic fuzzy soft sets based decision making, Applied Mathematical Modelling 35 (2011), pp. 824–836.
Google Scholar

Y. B. Jun, Soft BCK / BCI-algebras, Computers & Mathematics with Applications 56 (2008), pp. 1408–1413.
Google Scholar

Y. B. Jun, Intuitionistic fuzzy finite switchboard state machines, Journal of Applied Mathematics and Computing 20 (2006), no. 1-2, pp. 315–325.
Google Scholar

Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideals of BCK-algebras, International Journal of Mathematics and Mathematical Sciences 24 (2000), no. 12, pp. 839–849.
Google Scholar

Y. B. Jun, K. J. Lee and J. Zhan, Soft p-ideals of soft BCI-algebras, Computers & Mathematics with Applications 58 (2009), pp. 2060–2068.
Google Scholar

Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK / BCI-algebras, Information Sciences 178 (2008), pp. 2466–2475.
Google Scholar

Y. B. Jun, S. Z. Song and E. H. Roh, Soju structures with applications in BCK / BCI-algebras, Afrika Matematika (submitted).
Google Scholar

P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Computers & Mathematics with Applications 44 (2002), pp. 1077–1083.
Google Scholar

J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa Co. Seoul, Korea 1994.
Google Scholar

D. Molodtsov, Soft set theory—First results, Computers & Mathematics with Applications 37 (1999), pp. 19–31.
Google Scholar

A. K. Srivastava and S. P. Tiwari, , Soft Computing 14 (2010), pp. 571–578.
Google Scholar

M. Touqeer and N. Çağman, On some properties of p-ideals based on intuitionistic fuzzy sets, Cogent Mathematics (2016), 3: 1210001.
Google Scholar

Z. Zhang, A rough set approach to intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling 36 (2012), pp. 4605–4633.
Google Scholar

Downloads

Published

2019-03-30

How to Cite

Xin, X. L., Borzooei, R. A., & Jun, Y. B. (2019). Positive Implicative Soju Ideals in BCK-Algebras. Bulletin of the Section of Logic, 48(1), 1–18. https://doi.org/10.18778/0138-0680.48.1.01

Issue

Section

Research Article

Most read articles by the same author(s)

1 2 > >>