Some Orders in Groupoids and Its Applications to Fuzzy Groupoids
الموضوعات : Transactions on Fuzzy Sets and Systems
Akbar Rezaei
1
,
Choonkil Park
2
,
Hee Sik Kim
3
1 - Department of Mathematics, Payame Noor University, Tehran, Iran.
2 - Department of Mathematics, Hanyang University, Seoul, Korea.
3 - Department of Mathematics, Hanyang University, Seoul, Korea.
الکلمات المفتاحية: Below, Above, Transitive, Fuzzy, Contractive, Contained, ($\alpha-, \beta-, \gamma_{\alpha}-, \gamma_{\beta}-$)Order-Preserving (reversing).,
ملخص المقالة :
In this paper, we continue the investigation started in [1]. We obtain new results derived from novel concepts developed in analogy with others already established, e.g., the fact that leftoids (X, ∗) for φ are super-transitive if and only if φ(φ(x)) = φ(x) for all x ∈ X. In addition we apply fuzzy subsets in this context and we derive a number of results as consequences.
[1] Ahn SS, Kim YH, Neggers J. Fuzzy upper bounds in groupoids. The Scientific World Journal. 2014; 2014(1): 697012. DOI: https://doi.org/10.1155/2014/697012
[2] Huang Y. BCI-Algebra. Science Press: Beijing; 2006.
[3] Meng J, Jun YB. BCK-Algebras. Kyung Moon Sa: Seoul; 1994.
[4] Kim YH, Kim HS, Neggers J. Selective groupoids and frameworks induced by fuzzy setsets. Iranian Journal of Fuzzy Systems. 2017; 14(3): 151-160. DOI: https://doi.org/10.22111/IJFS.2017.3261
[5] Kim HS, Neggers J. Fuzzy pogroupoids. Information Sciences. 2005; 175(1-2): 108-119. DOI: https://doi.org/10.1016/j.ins.2004.10.003
[6] Neggers J. Partially ordered sets and groupoids. Kyungpook Mathematical Journal. 1976; 16(1): 7-20. https://koreascience.kr/article/JAKO197625748111702.pdf
[7] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[8] Rosenfeld A. Fuzzy groups. Journal of Mathematical Analysis and Applications. 1971; 35(3): 512-517. DOI:
https://doi.org/10.1016/0022-247X(71)90199-5
[9] Mordeson JN, Malik DS. Fuzzy Commutative Algebra. Singapore: World Scientific; 1998.
[10] Ahsan J, Mordeson JN, Shabir M. Fuzzy Semirings with Applications to Automata Theory. New York: Springer; 2012.
[11] Han JS, Kim HS, Neggers J. On linear fuzzifications of groupoids with special emphasis on BCK-algebras. Journal of Intelligent & Fuzzy Systems. 2013; 24(1): 105-110. DOI: https://doi.org/10.3233/IFS-2012-0534
[12] Liu YL, Kim HS, Neggers J. Hyperfuzzy subsets and subgroupoids. Journal of Intelligent & Fuzzy Systems. 2017; 33(3): 1553-1562. DOI: https://doi.org/10.3233/JIFS-17104
[13] Kim HS, Neggers J. The semigroups of binary systems and some perspectives. Bulletin of Korean Mathematical Society. 2008; 45(4): 651-661. DOI: https://doi.org/10.4134/BKMS.2008.45.4.651
[14] Shin SJ, Kim HS, Neggers J. On abelian and related fuzzy subsets of groupoids. The Scientific World Journal. 2013; 2013(1): 476057. DOI: https://doi.org/10.1155/2013/476057
[15] Allen PJ, Kim HS, Neggers J. Several types of groupoids induced by two-variable functions. Springer Plus. 2016; 5: 1715-1725. DOI: https://doi.org/10.1186/s40064-016-3411-y
[16] Allen PJ, Kim HS, Neggers J. Companion d-algebras. Mathematica Slovaca. 2007; 57(2): 93-106. DOI:hppts://doi.org/10.2478/s12175-007-0001-z
[17] Kim HS, Neggers J, Ahn SS. On pre-commutative algebras. Mathematics. 2019; 7(4): Paper 336-342. DOI: https://doi.org/10.3390/math7040336
[18] Hwang IH, Kim HS, Neggers J. Some implicativities for groupoids and BCK-algebras. Mathematics. 2019; 7(10): 973-980. DOI: https://doi.org/10.3390/math7100973
[19] Clark J, Holton DA. A First Look at Graph Theory. Singapore: World Scientic; 1991.
[20] Kim HS, Neggers J, So KS. Order related concepts for arbitrary groupoids. Bulletin of Korean Mathematical Society. 2017; 54(4): 1373-1386. DOI: https://doi.org/10.4134/BKMS.b160593
