Fuzzy Soft Positive Implicative Hyper BCK-Ideals

Authors

  • Tolesa Dekeba Bekele Department of Mathematics, College of Natural and Computational Science, Dire Dawa University, Dire Dawa

DOI:

https://doi.org/10.26713/jims.v13i2.1651

Keywords:

06F35, 03G25, 06D72

Abstract

In this paper, the author contributed the concepts of fuzzy soft positive implicative hyper BCK-ideal of types (≪,⊆,⊆), (≪,≪,⊆) and (⊆,≪,⊆) are introduced some related properties are considered. Relations between double-framed soft hyper BCK-ideal and double-framed soft strong hyper BCK-ideal are discussed. Additionally, the author demonstrate that the level set of fuzzy soft positive implicative hyper BCK-ideal of types (≪,⊆,⊆), (≪,≪,⊆) and (⊆,≪,⊆) are positive implicative hyper BCK ideal of types (≪,⊆,⊆), (≪,≪,⊆) and (⊆,≪,⊆), respectively. The conditions for a fuzzy soft set to be a fuzzy soft positive implicative hyper BCK-ideal of types (≪,⊆,⊆), (≪,≪,⊆) and (⊆,≪,⊆), are initiated respectively, and the circumstances for a fuzzy soft set to be a fuzzy soft weak hyper BCK-ideal are also considered.

Downloads

References

A. Aygünoglu and H. Aygün, Introduction to fuzzy soft groups, Computers & Mathematics with Applications 58(6) (2009), 1279 – 1286, DOI: 10.1016/j.camwa.2009.07.047.

J. Y. Bae, X. X. Long, M. M. Zahedi and R. E. Hwan, Strong hyper BCK-ideals of hyper BCK-algebras, Mathematica Japonicae 51(3) (2000), 493 – 498, https://ci.nii.ac.jp/naid/10010623326/en/.

H. Bordbar, S. Khademan, R. A. Borzooei, M. M. Zahedi and Y. B. Jun, Double-framed soft set theory applied to hyper BCK-algebras, New Mathematics and Natural Computation 17(1) (2021), 215 – 228, DOI: 10.1142/S1793005721500113.

H. Bordbar, S. Z. Song, M. R. Bordbar and Y. B. Jun, Fuzzy soft set theory with applications in hyper BCK-algebras, Journal of Intelligent & Fuzzy Systems 38(2) (2020), 1789 – 1797, DOI: 10.3233/JIFS-190103.

R. A. Borzooei and M. Bakhshi, On positive implicative hyper BCK-ideals, Scientiae Mathematicae Japonicae 59(3) (2004), 505 – 516, https://ci.nii.ac.jp/naid/10013664130/en/.

N. í‡a˘gman, F. í‡ıtak and S. Engino˘glu, Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy System 1(1) (2010), 21 – 35.

N. Cagman and S. Enginoglu, Fuzzy soft matrix theory and its application in decision making, Iranian Journal of Fuzzy Systems 9(1) (2012), 109 – 119, DOI: 10.22111/ijfs.2012.229.

P. Corsini and V. Leoreanu, Applications of Hyper structure Theory. Advances in Mathematics, Kluwer Academic Publishers, Dordrecht (2003).

F. Fatimah and J. C. R. Alcantud, The multi-fuzzy N-soft set and its applications to decision-making, Neural Computing and Applications 33 (2021), 11437 – 11446, DOI: 10.1007/s00521-020-05647-3.

S. Khademan, M. M. Zahedi, R. A. Borzooei and Y. B. Jun, Fuzzy soft positive implicative hyper BCK-ideals of several types, Miskolc Mathematical Notes 22(1) (2021), 299 – 315, DOI: 10.18514/MMN.2021.2855.

S. Khademan, M. M. Zahedi, Y. B. Jun and R.A. Borzooei, Fuzzy soft positive implicative hyper BCK-ideals in hyper BCK-algebras, Journal of Intelligent & Fuzzy Systems 36(3) (2019), 2605 – 2613, DOI: 10.3233/JIFS-181755.

S. Khademan, M. M. Zahedi, R. A. Borzooei and Y. B. Jun, Neutrosophic hyper BCK-ideals, Infinite Study 27 (2019), 201 – 217.

Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences 178(11) (2008), 2466 – 2475, DOI: 10.1016/j.ins.2008.01.017.

Y. B. Jun and W. H. Shim, Fuzzy structures of PI ((ll ,subseteqq,subseteqq)) BCK-ideals in hyper BCK-algebras, International Journal of Mathematics and Mathematical Sciences 2003 (2003), Article ID 471490, DOI: 10.1155/S0161171203110277.

V. Leoreanu-Fotea and B. Davvaz, Join n-spaces and lattices, Journal of Multiple-Valued Logic & Soft Computing 15 (2009), 421 – 432.

V. Leoreanu-Fotea and B. Davvaz, n-Hypergroups and binary relations, European Journal of Combinatorics 29(5) (2008), 1207 – 1218, DOI: 10.1016/j.ejc.2007.06.025.

F. Marty, Sur uni generalization de la notion de group, 8th Congress Math. Scandienaves, Stockholm (1934), 45 – 49.

R. K. Maji, A. R. Roy and R. Biswas, Fuzzy soft sets, Journal of Fuzzy Mathematics 9(3) (2001), 589 – 602.

D. Molodtsov, Soft set theory ” first results, Computers & Mathematics with Applications 37(4-5) (1999), 19 – 31, DOI: 10.1016/S0898-1221(99)00056-5.

G. Muhiuddin and D. Al-Kadi, Bipolar fuzzy implicative ideals of BCK-algebras, Journal of Mathematics 2021 (2021), Article ID 6623907, DOI: 10.1155/2021/6623907.

Y. J. Seo, H. S. Kim, Y. B. Jun and S. S. Ahn, Multipolar intuitionistic fuzzy hyper BCK-ideals in hyper BCK-algebras, Mathematics 8(8) (2020), 1373, DOI: 10.3390/math8081373.

B. J. Young and L. X. Xiao, Positive implicative hyper BCK-algebras, Scientiae Mathematicae Japonicae 55(1) (2002), 97 – 106, https://ci.nii.ac.jp/naid/10010238729/en/.

Downloads

Published

2021-08-10
CITATION

How to Cite

Bekele, T. D. (2021). Fuzzy Soft Positive Implicative Hyper BCK-Ideals. Journal of Informatics and Mathematical Sciences, 13(2), 105–117. https://doi.org/10.26713/jims.v13i2.1651

Issue

Vol. 13 No. 2 (2021)

Section

Research Article

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.