Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

LATTICE ORDERED FUZZY SOFT GROUPS

  • Received : 2018.01.31
  • Accepted : 2018.02.28
  • Published : 2018.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

In several fields the soft set theory has a very vast range uses and applications. A soft group is a proper family of subgroups and a fuzzy soft group is a proper family of fuzzy subgroups. Here in this paper the concept of lattice ordered fuzzy soft groups is introduced. Also its some properties are studied and discussed. In addition, the defintion of lattice order fuzzy soft right (left) cosets and lattice order soft product of fuzzy soft subgroups and some related results are discussed to clear these ideas.

Keywords

References

  1. B. Ahmad and A. Kharal, on fuzzy soft sets, Adv. Fuzzy Syst. 2009 (2009), Article ID 586507.
  2. H. Aktas and N. Cagman, Soft sets and soft group, Inform. Sci. 177 (2007) 2726-2735. https://doi.org/10.1016/j.ins.2006.12.008
  3. M. I. Ali, A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing. 11 (2011) 3329-3332. https://doi.org/10.1016/j.asoc.2011.01.003
  4. M. I. Ali, F. Feng, X. Y. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers & Mathematics with Applications. 57 (2009) 1547-1553. https://doi.org/10.1016/j.camwa.2008.11.009
  5. M. I. Ali, T. Mahmood, M. M. Rehman and M. F. Aslam, on lattice ordered soft sets, Applied Soft Computing, 36 (2015) 499-505. https://doi.org/10.1016/j.asoc.2015.05.052
  6. M. I. Ali, M. Shabir and M. Naz, Algebraic structures of soft sets associated with new operations, Computers & Mathematics with Applications. 61 (9) (2011) 2647-2654. https://doi.org/10.1016/j.camwa.2011.03.011
  7. M. Aslam and S. M. Qureshi, Some contributions to soft groups, Annals of Fuzzy Mathematics and Informatics 4 (1) (2012) 177-195.
  8. M. F. Aslam, Study of fuzzy soft sets with some order on set of parameters, MS Thesis, International Islamic University Islamabad, 2014.
  9. A. Aygunoglu and H. Aygun, Introduction to fuzzy soft groups, Computers & Mathematics with Applications. 58 (2009) 1279-1286. https://doi.org/10.1016/j.camwa.2009.07.047
  10. G. Birkhoff, Lattice Theory, American Mathematical Society, (1967).
  11. N. Cagman, F. Citak and S. Enginoglu, Fuzzy soft set theory and its applications, Iran. J. Fuzzy Syst. 8. 3 (2011) 137-147.
  12. D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parameterization reduction of soft sets and its applications, Computers & Mathematics with Applications. 49 (2005) 757-763. https://doi.org/10.1016/j.camwa.2004.10.036
  13. F. Karaaslam and N. Cagman, Fuzzy Soft Lattice Theory, ARPN Journal of science and Technology, 3 (2013) 2225-7217.
  14. F. Feng, Y. B. Jun and X. Z. Zhao, Soft semirings, Computers & Mathematics and Applications. 56 (2008) 2621-2628. https://doi.org/10.1016/j.camwa.2008.05.011
  15. F. Feng, C. Li, B. Davvaz and M. I. Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft computing 14 (2010) 899-911. https://doi.org/10.1007/s00500-009-0465-6
  16. J. B. Fraleigh, A first course in abstract algebra, Addison-wesley Publishing Company, (1982).
  17. Y. B. Jun, Soft BCK/BCI-algebras, Computers & Mathematics with Applications. 56 (2008) 1408-1413. https://doi.org/10.1016/j.camwa.2008.02.035
  18. Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-Algebras, Inf. Sci. 178 (2008) 2466-2475.
  19. M. Khan, B. Davvaz, N. Yaqoob, M. Gulistan and M. M. Khalaf, On-intuitionistic (fuzzy ideals, fuzzy soft ideals) of subtraction algebras, Songk-lanakarin J. of Science and Technology, 37 (4) (2015) 465-475.
  20. Fu Li, Soft Lattices, Global journal. 10 (2010) 56-58.
  21. Fu Li, Notes on soft operations, APRN journal. 6 (2011) 2222-2233.
  22. P. K. Maji, R. Biswas and R. Roy, Soft set theory, Computers & Mathematics with Applications. 45 (2003) 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
  23. P. K. Maji and A. R. Roy, A fuzzy soft set theoretic approach to decision making problem, Computers & Mathematics with Applications. 203 (2007) 412-418.
  24. P. K. Maji, A. R. Roy and R. Biswas, A fuzzy soft sets, journal of fuzzy mathematics. 3 (2001) 589-602.
  25. P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Computers & Mathematics with Applications. 44 (2002) 1077-1083. https://doi.org/10.1016/S0898-1221(02)00216-X
  26. W. K. Min, Similarity in soft set theory, Applied Math. Letters, 25 (2012) 310-314. https://doi.org/10.1016/j.aml.2011.09.006
  27. D. Molodtsov, Soft set theory- first results, Computers & Mathematics with Applications. 37 (1999) 19-31.
  28. J. N. Mordeson, K. R. Bhntani and A. Rosenfeld, Fuzzy Group Theory, Spinger, (2005).
  29. D. Pei and D. Miao, From soft sets to information systems, granular computing, IEEEInt. Conf. 2 (2005) 617-621.
  30. A. Rosenfeld, Fuzzy groups, J. Math. Anal. 35 (1971) 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
  31. J. Vimala, Fuzzy Lattice ordered Group, International Journal of scientic and Engineering Research. 5 (9) (2014).
  32. N. Yaqoob, M. Akram and M. Aslam, Intuitionistic fuzzy soft groups induced by (t,s)-norm, Indian J. of Science and Technology, 6 (4) (2013) 4282-4289.
  33. X. H. Yuan, C. Zhang and Y. H. Ren, Generalized fuzzy groups and many-valued Implications, Fuzzy Sets and Systems. 138 (2003) 205-211. https://doi.org/10.1016/S0165-0114(02)00443-8
  34. L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X