N-Hyper Sets
Abstract
:1. Introduction
2. Preliminaries
3. (Extended) -Hyper Sets
- an -substructure of with type 1 (briefly, -substructure of ) if it satisfies:
- an -substructure of with type 2 (briefly, -substructure of ) if it satisfies:
- an -substructure of with type 3 (briefly, -substructure of ) if it satisfies:
- an -substructure of with type 4 (briefly, -substructure of ) if it satisfies:
4. Conclusions
Author Contributions
Acknowledgments
Conflicts of Interest
References
- Zadeh, L.A. Fuzzy sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef]
- Jun, Y.B.; Lee, K.J.; Song, S.Z. -ideals of BCK/BCI-algebras. J. Chungcheong Math. Soc. 2009, 22, 417–437. [Google Scholar]
- Ceven, Y. -ideals of rings. Int. J. Algebra 2012, 6, 1227–1232. [Google Scholar]
- Jun, Y.B.; Öztürk, M.A.; Roh, E.H. -structures applied to closed ideals in BCH-algebras. Int. J. Math. Math. Sci. 2010, 943565. [Google Scholar] [CrossRef]
- Khan, A.; Jun, Y.B.; Shabir, M. -fuzzy quasi-ideals in ordered semigroups. Quasigroups Relat. Syst. 2009, 17, 237–252. [Google Scholar]
- Khan, A.; Jun, Y.B.; Shabir, M. -fuzzy ideals in ordered semigroups. Int. J. Math. Math. Sci. 2009, 814861. [Google Scholar] [CrossRef]
- Khan, A.; Jun, Y.B.; Shabir, M. -fuzzy filters in ordered semigroups. Fuzzy Syst. Math. 2010, 24, 1–5. [Google Scholar]
- Khan, A.; Jun, Y.B.; Shabir, M. -fuzzy bi-ideals in ordered semigroups. J. Fuzzy Math. 2011, 19, 747–762. [Google Scholar]
- Jun, Y.B.; Alshehri, N.O.; Lee, K.J. Soft set theory and -structures applied to BCH-algebras. J. Comput. Anal. Appl. 2014, 16, 869–886. [Google Scholar]
- Jun, Y.B.; Lee, K.J.; Kang, M.S. Ideal theory in BCK/BCI-algebras based on soft sets and -structures. Discret. Dyn. Nat. Soc. 2012, 910450. [Google Scholar] [CrossRef]
- Jun, Y.B.; Song, S.Z.; Lee, K.J. The combination of soft sets and -structures with applications. J. Appl. Math. 2013, 420312. [Google Scholar] [CrossRef]
- Bucolo, M.; Fortuna, L.; la Rosa, M. Complex dynamics through fuzzy chains. IEEE Trans. Fuzzy Syst. 2004, 12, 289–295. [Google Scholar] [CrossRef]
X | a | b | c | d |
---|---|---|---|---|
X | a | b | c | d |
---|---|---|---|---|
0 | ||||
X | a | b | c | d |
---|---|---|---|---|
X | a | b | c | d |
---|---|---|---|---|
X | a | b | c | d |
---|---|---|---|---|
0 | ||||
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Jun, Y.B.; Song, S.-Z.; Kim, S.J. N-Hyper Sets. Mathematics 2018, 6, 87. https://doi.org/10.3390/math6060087
Jun YB, Song S-Z, Kim SJ. N-Hyper Sets. Mathematics. 2018; 6(6):87. https://doi.org/10.3390/math6060087
Chicago/Turabian StyleJun, Young Bae, Seok-Zun Song, and Seon Jeong Kim. 2018. "N-Hyper Sets" Mathematics 6, no. 6: 87. https://doi.org/10.3390/math6060087