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

Yıl 2019, , 284 - 291, 25.08.2019

Canan Akın , Kübra Eyüboğlu

https://doi.org/10.19113/sdufenbed.441444

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] Ali, M.I., Davvaz, B. and Shabir, M. 2013. Some properties of generalized rough sets, Information Sciences, 224 (2013), 170-179.
• [2] Ali, M.I., Shabir, M. and Tanveer, S. 2012. Roughness in hemirings, Neural Comput and Applic 21 (2012),171-180.
• [3] Baczynski, M. and Jayaram, B. 2008. Fuzzy implications Studies in Fuzziness and Soft Computing, Vol.231, Springer Berlin Heidelberg.
• [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] Davvaz, B. 2008. A short note on algebraic T-rough sets, Information Sciences 178 (2008), 3247-3252.
• [6] Dubois, D. and Prade, H. 1990. Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems 17, (1990), 191-209.
• [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] 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] 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] Fodor, J.C. and Roubens, M. 1994 Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Dordrecht.
• [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] Ignjatovi´c, J., ´ Ciri´c, M. and Bogdanovi´c, S. 2009. Fuzzy homomorphisms of algebras, Fuzzy Sets and Systems 160, (2009), 2345-2365.
• [13] Jun, Y.B. and Lee, C.Y. 1981. Fuzzy G-rings, Pusan Kyongnam Math. J., 84, (1981), 264-269.
• [14] Kazıım, M.A. and Naseeruddin, M. 1972. On almost semigroups, The Alig. Bull. Math. 2, (1972),1-7.
• [15] Khan, M., and Khan, N. A. 2009. 2009arXiv0904.0077K
• [16] Khan, M., Smarandache, F. and Anis, S. 2015. Theory of Abel Grassmann’s Groupoids, Educational Publisher, Columbus.
• [17] Kim, J.P. and Bae, D.R. 1997. Fuzzy congruences in groups, Fuzzy Sets and Systems 85, (1997), 115-120.
• [18] Klement, E.P., Mesiar R. and Pap, E. 2000. Triangular Norms, Kluwer Academic Publishers, Dordrecht
• [19] Kuroki, N. 1997. Rough ideals in semigroups, Information Sciences 100, (1997), 139-163.
• [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] 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] Pawlak, Z. 1982. Rough sets, Int. J. Comput. Information Sciences 11, (1982), 341-356.
• [23] Radzikowska, A.M. and Kerre, E.E. 2002. A comparative study of rough sets, Fuzzy Sets and Systems 126, (2002), 137-155.
• [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] 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] 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] Sen, M. K. and Saha, N. K. 1986. On G-semigroups I, Bull. Cal. Math. Soc. 78, (1986),180-186.
• [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] 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] 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] Wu, W.-Z., Mi, J.-S. and Zhang, W.-X. 2003. Generalized fuzzy rough sets, Information Sciences 151, (2003), 263-282.
• [32] Wu, W.-Z. and Zhang, W.-X. 2004. Constructive and axiomatic approaches of fuzzy approximation operators, Information Sciences 159, (2004), 233-254.
• [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] 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] 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] Yamak, S., Kazancı, O. and Davvaz, B. 2010. Generalized lower and upper approximations in a ring, Information Sciences 180, (2010), 1759-1768.
• [37] Yao, Y.Y. 1998. Constructive and algebraic methods of the theory of rough sets, Information Sciences 109, (1998), 21-47.
• [38] Zadeh, L.A. 1965. Fuzzy Sets, Inform. and Control 8, (1965), 338-353.