Some Algebraic Properties of Generalized Fuzzy Rough Approximations Derived by Fuzzy Set-Valued Homomorphism of LA-G-Semigroups

Öz

In this paper we define the concept of fuzzy set valued homomorphism of LA- G-semigroups and mention some features of them. We also investigate the approximations of a generalized fuzzy approximation space constructed on LA-G-semigroups and derived by fuzzy set valued homomorphisms of LA-G-semigroups. Especially, we focus on some algebraic properties of fuzzy subsets in terms of protection of some properties under these approximations.

Anahtar Kelimeler

• Fuzzy set valued homomorphism,Generalized fuzzy approximation space,Fuzzy LA-G-semigroups,Generalized fuzzy approximation space

Bulanık Küme Değerli LA-G-Yarıgrup Homomorfileri ile Türetilmiş Genelleştirilmiş Bulanık Kaba Yaklaşımların Bazı Cebirsel Özellikleri

Öz

Bu çalışmada bulanık küme değerli LA-Gamma-yarıgrup homomorfisi kavramını tanımlayacağız ve onların bazı özelliklerine değineceğiz. Ayrıca LA-Gamma-yarıgruplar üzerine inşa edilmiş ve bulanık küme değerli LA-Gamma-yarıgrup homomorfisi ile üretilmiş genelleştirilmiş bulanık yaklaşım uzayının yaklaşımlarını araştıracağız. Özellikle, bu yaklaşımlar altında bazı özelliklerin korunması açısından bulanık alt kümelerin bazı cebirsel özelliklerine odaklanacağız.

Anahtar Kelimeler

• Bulanık Küme değerli homomorfi,Bulanık LA-G-semigoup,Genelleştirilmiş bulanık yaklaşım uzayı

Kaynakça

1. 1] Ali, M.I., Davvaz, B. and Shabir, M. 2013. Some properties of generalized rough sets, Information Sciences, 224 (2013), 170-179.
2. [2] Ali, M.I., Shabir, M. and Tanveer, S. 2012. Roughness in hemirings, Neural Comput and Applic 21 (2012),171-180.
3. [3] Baczynski, M. and Jayaram, B. 2008. Fuzzy implications Studies in Fuzziness and Soft Computing, Vol.231, Springer Berlin Heidelberg.
4. [4] Biswas, R. and Nanda, S.1994. Rough groups and rough subgroups, Bulletin of the Polish Academy of Sciences mathematics 42 (1994), 251-254.
5. [5] Davvaz, B. 2008. A short note on algebraic T-rough sets, Information Sciences 178 (2008), 3247-3252.
6. [6] Dubois, D. and Prade, H. 1990. Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems 17, (1990), 191-209.
7. [7] Ekiz, C., Ali, M.I. and Yamak, S. 2017 TL-fuzzy set valued homomorphisms and generalized (I;T)-Lfuzzy rough sets on groups, Filomat 31:13 (2017), 4153-4166.
8. [8] Ekiz, C., Çelik, Y. and Yamak, S. 2013 Generalized TL-fuzzy rough rings via T L-fuzzy relational morphisms, Journal of Inequalities and Applications 2013.1 (2013), 279.

9. [9] Ekiz, C., Çelik, Y. and Yamak, S. 2014 Generalized (I;T)-L-fuzzy rough sets based on TL-fuzzy relational morphisms on semigroups, Annals of Fuzzy Mathematics and Informatics 8, (2014), 571-592.
10. [10] Fodor, J.C. and Roubens, M. 1994 Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Dordrecht.
11. [11] Hooshmandasl, M.R., Karimi, A., Almbardar, M. and Davvaz, B. 2013. Axiomatic systems for rough set-valued homomorphisms of associative rings, International Journal of Approximate Reasoning 54 (2), (2013), 297-306.
12. [12] Ignjatovi´c, J., ´ Ciri´c, M. and Bogdanovi´c, S. 2009. Fuzzy homomorphisms of algebras, Fuzzy Sets and Systems 160, (2009), 2345-2365.
13. [13] Jun, Y.B. and Lee, C.Y. 1981. Fuzzy G-rings, Pusan Kyongnam Math. J., 84, (1981), 264-269.
14. [14] Kazıım, M.A. and Naseeruddin, M. 1972. On almost semigroups, The Alig. Bull. Math. 2, (1972),1-7.
15. [15] Khan, M., and Khan, N. A. 2009. 2009arXiv0904.0077K
16. [16] Khan, M., Smarandache, F. and Anis, S. 2015. Theory of Abel Grassmann’s Groupoids, Educational Publisher, Columbus.
17. [17] Kim, J.P. and Bae, D.R. 1997. Fuzzy congruences in groups, Fuzzy Sets and Systems 85, (1997), 115-120.
18. [18] Klement, E.P., Mesiar R. and Pap, E. 2000. Triangular Norms, Kluwer Academic Publishers, Dordrecht
19. [19] Kuroki, N. 1997. Rough ideals in semigroups, Information Sciences 100, (1997), 139-163.
20. [20] Li, F. and Yin, Y. 2012. The u-lower and T-upper fuzzy rough approximation operators on a semigroup, Information Sciences 195, (2012), 241-255.
21. [21] Li, F., Yin, Y. and Lu, L. 2007. (I;T )-fuzzy rough approximation operators and T L-fuzzy rough ideals on a ring, Information Sciences 177, (2007), 4711- 4726.
22. [22] Pawlak, Z. 1982. Rough sets, Int. J. Comput. Information Sciences 11, (1982), 341-356.
23. [23] Radzikowska, A.M. and Kerre, E.E. 2002. A comparative study of rough sets, Fuzzy Sets and Systems 126, (2002), 137-155.
24. [24] Sen, M. K. 1981 On G-semigroups. ss 1-8. Sen, M. K., ed. 1981. Proceeding of International Symposium on Algebra and Its Applications, Decker Publication, New York, 30s.
25. [25] Shah, T. and Rehman, I. 2010. On G-ideals and G- bi-ideals in G-AG-groupoids, International Journal of Algebra 4 (2010), no.6,267-276.
26. [26] Shah, T., Rehman, I. and Khan, A. 2014. Fuzzy G- ideals in G-AG-groupoids, Hacettepe Journal of Mathematics and Statistics 43(4), (2014),625-634.
27. [27] Sen, M. K. and Saha, N. K. 1986. On G-semigroups I, Bull. Cal. Math. Soc. 78, (1986),180-186.
28. [28] Wang, Z., Yu, Y. and Dai, F. 2001. On T -congruence L-relations on groups and rings, Fuzzy Sets and Systems 119, (2001), 393-407.
29. [29] Wu, W.-Z., Leung, Y. and Mi, J.-S. 2005. On characterizations of (I;T )-fuzzy rough approximation operators, Fuzzy Sets and Systems 154, (2005), 76- 102.
30. [30] Wu, W.-Z., Leung, Y. and Shao, M.-W. 2013. Generalized fuzzy rough approximation operators determined by fuzzy implicators, International Journal of Approximate Reasoning 54, (2013), 1388-1409.
31. [31] Wu, W.-Z., Mi, J.-S. and Zhang, W.-X. 2003. Generalized fuzzy rough sets, Information Sciences 151, (2003), 263-282.
32. [32] Wu, W.-Z. and Zhang, W.-X. 2004. Constructive and axiomatic approaches of fuzzy approximation operators, Information Sciences 159, (2004), 233-254.
33. [33] Xiao, Q. 2011 T-roughness in semigroups. ss 391- 394. Xiao, Q., ed. 2011. International Conference on Computer Science and Automation Engineering, IEEE, 4s.
34. [34] Xiao, Q. and Li, Q. 2012. Generalized Lower and Upper Approximations in Quantales, Journal of Applied Mathematics 2012, (2012) Article ID 648983, 11 pages, doi:10.1155/2012/648983.
35. [35] Yamak, S., Kazancı, O. and Davvaz, B. 2011. Approximations in a module by using set-valued homomorphisms, International Journal of Computer Mathematics 88, (2011), 2901-2911.
36. [36] Yamak, S., Kazancı, O. and Davvaz, B. 2010. Generalized lower and upper approximations in a ring, Information Sciences 180, (2010), 1759-1768.
37. [37] Yao, Y.Y. 1998. Constructive and algebraic methods of the theory of rough sets, Information Sciences 109, (1998), 21-47.
38. [38] Zadeh, L.A. 1965. Fuzzy Sets, Inform. and Control 8, (1965), 338-353.