headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
Vol. 68, Issue 1
» 2018
» 2017
» 2016
» 2015
» 2014
» 2013
» 2012
» 2011
» 2010
» 2009
» 2008
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

On generalized fuzzy sets in ordered LA-semihypergroups; pp. 43–54

(Full article in PDF format) https://doi.org/10.3176/proc.2019.1.06


Authors

Muhammad Gulistan, Naveed Yaqoob, Seifedine Kadry, Muhammad Azhar

Abstract

Using the notion of generalized fuzzy sets, we introduce the notions of generalized fuzzy hyperideals, generalized fuzzy bi-hyperideals, and generalized fuzzy normal bi-hyperideals in an ordered nonassociative and non-commutative algebraic structure, namely an ordered LA-semihypergroup, and we characterize these hyperideals. We provide some results related to the images and preimages of generalized fuzzy hyperideals in ordered LA-semihypergroups.

Keywords

ordered LA-semihypergroups, generalized fuzzy sets, generalized fuzzy hyperideals.

References

1. Marty , F. Sur une generalization de la notion de groupe. In 8iem Congres Mathématiciens Scandinaves. Stockholm. , 1934 , 45–49.

2. Corsini , P. and Leoreanu , V. Applications of Hyperstructure Theory. Kluwer Academic Publications , 2003.
https://doi.org/10.1007/978-1-4757-3714-1

3. Davvaz , D. and Fotea , V. L. Hyperring Theory and Applications. International Academic Press , USA , 2007.

4. Bonansinga , P. and Corsini , P. On semihypergroup and hypergroup homomorphisms. Boll. Un. Mat. Ital. , 1982 , 6 , 717–727.

5. Corsini , P. and Cristea , I. Fuzzy sets and non complete 1-hypergroups. An. Sti. U. Ovid. Co-Mat. , 2005 , 13 , 27–54.

6. Davvaz , B. Some results on congruences on semihypergroups. Bull. Malays. Math. Sci. Soc. , 2000 , 23 , 53–58.

7. Hasankhani , A. Ideals in a semihypergroup and Green’s relations. Ratio Math. , 1999 , 13 , 29–36.

8. Hila , K. and Dine , J. On hyperideals in left almost semihypergroups. ISRN Algebra , 2011 , Article ID 953124 , 8 pages.

9. Yaqoob , N. , Corsini , P. , and Yousafzai , F. On intra-regular left almost semihypergroups with pure left identity. J. Math. , 2013 , Article ID 510790 , 10 pages.

10. Yousafzai , F. and Corsini , P. Some characterization problems in LA-semihypergroups. J. Algebra , Numb. Th. Adv. Appl. , 2013 , 10 , 41–55.

11. Heidari , D. and Davvaz , B. On ordered hyperstructures. U.P.B. Sci. Bull. Series A , 2011 , 73 , 85–96.

12. Yaqoob , N. and Gulistan , M. Partially ordered left almost semihypergroups. J. Egyptian Math. Soc. , 2015 , 23 , 231–235.
https://doi.org/10.1016/j.joems.2014.05.012

13. Zadeh , L. A. Fuzzy sets. Inform. Control , 1965 , 8 , 338–353.
https://doi.org/10.1016/S0019-9958(65)90241-X

14. Murali , V. Fuzzy points of equivalent fuzzy subsets. Inform. Sci. , 2004 , 158 , 277–288.
https://doi.org/10.1016/j.ins.2003.07.008

15. Pu , P. M. and Liu , Y. M. Fuzzy topology I , neighborhood structure of a fuzzy point and Moore-Smith convergence. J. Math. Anal. Appl. , 1980 , 76 , 571–599.
https://doi.org/10.1016/0022-247X(80)90048-7

16. Bhakat , S. K. and Das , P. (2;2 _q)-fuzzy subgroups. Fuzzy Sets Syst. , 1996 , 80 , 359–368.
https://doi.org/10.1016/0165-0114(95)00157-3

17. Pibaljommee , B. , Wannatong , K. , and Davvaz , B. An investigation on fuzzy hyperideals of ordered semihypergroups. Quasigroups Relat. Syst. , 2015 , 23 , 297–308.

18. Tang , J. , Khan , A. , and Luo , Y. F. Characterizations of semisimple ordered semihypergroups in terms of fuzzy hyperideals. J. Intell. Fuzzy Syst. , 2016 , 30 , 1735–1753.
https://doi.org/10.3233/IFS-151884

19. Azhar , M. , Gulistan , M. , Yaqoob , N. , and Kadry , S. On fuzzy ordered LA-semihypergroups. Int. J. Anal. Appl. , 2018 , 16 , 276–289.

20. Azhar , M. , Yaqoob , N. , Gulistan , M. , and Khalaf , M. On (2;2 _qk)-fuzzy hyperideals in ordered LA-semihypergroups. Disc. Dyn. Nat. Soc. , 2018 , Article ID 9494072 , 13 pages.

21. Shabir , M. and Mahmood , T. Semihypergroups characterized by (2g ;2g _qd )-fuzzy hyperideals. J. Intell. Fuzzy Syst. , 2015 , 28 , 2667–2678.
https://doi.org/10.3233/IFS-151544

22. Shabir , M. , Jun , Y. B. , and Nawaz , Y. Semigroups characterized by (2g ;2g _qk)-fuzzy ideals. Comput. Math. Appl. , 2010 , 60 , 1473–1493.
https://doi.org/10.1016/j.camwa.2010.06.030

23. Rehman , N. and Shabir , M. Some characterizations of ternary semigroups by the properties of their (2g ;2g _qd )-fuzzy ideals. J. Intell. Fuzzy Syst. , 2014 , 26 , 2107–2117.

 
Back

Current Issue: Vol. 68, Issue 1, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December