NEAR APPROXIMATIONS IN VECTOR SPACES
NEAR APPROXIMATIONS IN VECTOR SPACES
Near set theory presents a fundamental basis for observation, comparison and classification of perceptual granules. Soft set theory, which is initiated by Molodtsov [1], is proposed as a general framework to model vagueness. Combine the soft sets approach with near set theory giving rise to the new concepts of soft nearness approximation space. Tasbozan et al. [2] introduce the soft sets based on a near approximation space. The relations between near sets and algebraic systems endowed with two binary operations such as rings, groups have been considered. This paper concerned a relationship between near approximation and vector spaces.
Keywords:
Lower and upper approximations, Near sets, Near soft sets, Near soft vector space, Near subsets in the vector space Soft sets.,
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- D. Molodtsov, Soft set theory first results, Comp. Math. Appl. 37 (1999) 19-31.
- H. Taşbozan, I. İcen, N. Bağırmaz, A.F. Ozcan, Soft sets and soft topology on nearness approximation spaces, Filomat. 31(13) (2017) 4117-4125.
- Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci. 11 (1982) 341{356.
- Z. Pawlak, Classification of Objects by means of Attributes, Institute for Computer Science, Polish Academy of Sciences, (1981) Report 429.
- J.F. Peters, Near sets, General theory about nearness of objects, Appl. Math. Sci. 1(53) (2007) 2029-2609.
- J.F. Peters, Near sets, Special theory about nearness of objects, Fundam. Inform. 75 (2007) 407-433.
- J.F. Peters, P. Wasilewsk, Foundations of near sets, Information Sciences. 179 (2009) 3091- 3109.
- J.F. Peters, Classification of perceptual objects by means of features, Int. J. Info. Technol. Intell. Comput. 3(2) (2008) 1-35.
- J.F. Peters, Fuzzy Sets, Near Sets, and Rough Sets for Your Computational Intelligence Toolbo, Foundations of Comput. Intel. 2 (2009) 3-25.
- J.F. Peters, R. Ramanna, Feature selection: a near set approach, (in: ECML and PKDD Workshop on Mining Complex Data, Warsaw, (2007) 1-12.
- J.F. Peters, S. Naimpally, Applications of near sets, Notices of the Amer. Math. Soc. 59(4) (2012) 536-542.
- J.F. Peters, S.K. Pal, Cantor, Fuzzy, Near, and Rough Sets in Image Analysis,CRC Pres ,Taylor and Francis Group, Boca Raton, U.S.A, (2010).
- T. Simsekler, S. Yuksel, Fuzzy soft topological spaces. Annals of Fuzzy Mathematics and Informatics, 5 (2013) 87-96.
- H. Aktas, N. Cagman, Soft sets and soft groups, Information Sciences, 177 (2007) 2726-2735.
- P.K Maji, R. Biswas, A.R. Roy, Soft set theory, Computers and Mathematics with Applications, 45 (2003) 555-562.
- F. Feng, C. Li, B. Davvaz, M.T. Ali, Soft sets combined with fuzzy sets and rough sets, Soft Comput., 14 (2010) 899-911.
- B. Davvaz, D.W. Setyawati, I. Mukhlash, Near approximations in rings. Applicable Algebra in Engineering, Communication and Computing, (2020) 1-21.
- B. Davvaz, Roughness in rings, Inform. Sci. 164 (2004) 147-163.
- C.Z. Wang, D.G. Chen, A short note on some properties of rough groups, Comput. Math. Appl. 59 (2010) 431-436.
- D. Miao, S. Han, D. Li, L. Sun, Rough Group, Rough Subgroup and Their Properties, D. Slkezak et al. (Eds.): RSFDGrC 2005, LNAI 3641, pp. 104{113, Springer-Verlag Berlin Heidelberg, (2005).
- N. Bağırmaz, A.F. Ozcan, Rough semigroups on approximation spaces, International Journal of Algebra, 9(7) (2015) 339-350.
- N. Bağırmaz, Near approximations in groups, AAECC, 30 (2019) 285-297.
- N. Kuroki, P.P. Wang, The lower and upper approximations in a fuzzy group, Information Sciences 90 (1996) 203-220.
- R. Biswas, S. Nanda, Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math. 42 (1994) 251-254.
- M. Wu, X. Xie, C. Cao, Rough subset based on congruence in a vector space, IEEE, 2008.
- M. Wu, X. Xie, Roughness in vector spaces, IEEE, 2011.
- ISSN: 2618-5660
- Başlangıç: 2018
- Yayıncı: Gökhan ÇUVALCIOĞLU