Fuzzy Soft Positive Implicative Hyper BCK-Ideals
DOI:
https://doi.org/10.26713/jims.v13i2.1651Keywords:
06F35, 03G25, 06D72Abstract
In this paper, the author contributed the concepts of fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\) 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 \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\) are positive implicative hyper BCK ideal of types \((\ll ,\subseteq ,\subseteq)\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\), respectively. The conditions for a fuzzy soft set to be a fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\), 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/.
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