(ᾶ, α)-crossing cubic QS-ideal of QS-algebra
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As an extension of bipolar-valued fuzzy sets, the notion of (ᾶ, α)-crossing cubic QS-ideals of a QS-algebra is introduced, and several related properties are investigated. Characterizations of (ᾶ, α)-crossing cubic QS-ideal in QS-algebras are established. The relations between (ᾶ, α)-crossing cubic subalgebras and (ᾶ, α)-crossing cubic QS-ideals of a QS-algebras are studied. Moreover, the homomorphic image (pre-image) of (ᾶ, α)-crossing cubic QS-ideal of a QS-algebra under a homomorprhism of QS-algebras is discussed.
Abstract
As an extension of bipolar-valued fuzzy sets, the notion of (ᾶ, α)-crossing cubic QS-ideals of a QS-algebra is introduced, and several related properties are investigated. Characterizations of (ᾶ, α)-crossing cubic QS-ideal in QS-algebras are established. The relations between (ᾶ, α)-crossing cubic subalgebras and (ᾶ, α)-crossing cubic QS-ideals of a QS-algebras are studied. Moreover, the homomorphic image (pre-image) of (ᾶ, α)-crossing cubic QS-ideal of a QS-algebra under a homomorprhism of QS-algebras is discussed.
참고문헌 (20)
- K. Iseki, "Ideal theory of BCK-algebras", Mathematica Japonica, 21(4), pp.351~366 (1976)
- K. Iseki, "An introduction to the theory of BCK-algebras", Mathematica Japonica, 23(1), pp.1~26 (1978)
- K. Iseki, "On BCI-algebras", Mathematics Seminar Notes, 8(1), pp.125~130 (1980)
- J. Neggers, "On Q-algebras", IJMMS, 27, pp.749~757 (2001)
- S. S. Ahn, "On QS-algebras", J. Chungcheong Math. Soc, 12, pp.33~41 (1999)
- M. Kondo, "On the class of QS-algebras", IJMMS, 49, pp.2630~2631 (2004)
- A. T. Hameed, "Fuzzy QS-ideals of QS-algebra", International Journal of Algebra, 11(1), pp.43~52 (2017)
- A. B. Saeid, "Fuzzy QS-algebras with interval-valued membership functions", Bull Malays Math. Sci. Soc, 29(1), pp.169~177 (2006)
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
- O. G. Xi, "Fuzzy BCK-algebras", Math. Japon, 36(5), pp.935~942 (1991)
- Y. B. Jun, "Cubic sets", Annal. Fuzzy Math. Inform, 4(1), pp.83~98 (2012)
- Y. B. Jun, "Cubic subalgebras and ideals of BCK=BCI-algebras", Far East Journal of Mathematical Sciences, 44(2), pp.239~250 (2010)
- Y. B. Jun, "Cubic structures applied to ideals of BCI-algebras", Computers & Mathematics with Applications, 62(9), pp.3334~3342 (2011)
- W-R. Zhang, "Bipolar fuzzy sets", Proc. of IEEE, pp.835~840 (1998)
- K. M. Lee, "Bipolar-valued fuzzy sets and their operations", Proc. Int. Conf. on IntelligentTechnologies, pp.307~312 (2000)
- 전영배, "N-IDEALS OF BCK", BCI-ALGERBAS, 2009, pp.22(3), 417~437[DOI]
- Y. B. Jun, "N-structures applied to closed ideals in BCH-algebras", Int. J. Math. Math. Sci, 2010 (2010)
- YOUNG BAE JUN, "Crossing cubic structures as an extension of bipolar fuzzy sets", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 22(1), pp.1~15 (2021), 기초자연과학연구소[DOI]
- Y. B. Jun, "Crossing cubic ideals of BCK=BCI-algebras", Journal of Algebraic Hyperstructures and Logical Algebras, 2(1), pp.17~31 (2021)
- "The concept of a linguistic variable and its application to approximate reasoning-I", Inform. Sci, 8, pp.199~249 (1975)