Araştırma Makalesi
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NEAR APPROXIMATIONS IN VECTOR SPACES

Yıl 2020, , 114 - 120, 31.07.2020
https://doi.org/10.33773/jum.822384

Öz

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.

Kaynakça

  • 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.
Yıl 2020, , 114 - 120, 31.07.2020
https://doi.org/10.33773/jum.822384

Öz

Kaynakça

  • 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.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Hatice Taşbozan

Yayımlanma Tarihi 31 Temmuz 2020
Gönderilme Tarihi 6 Kasım 2020
Kabul Tarihi 11 Şubat 2021
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Taşbozan, H. (2020). NEAR APPROXIMATIONS IN VECTOR SPACES. Journal of Universal Mathematics, 3(2), 114-120. https://doi.org/10.33773/jum.822384
AMA Taşbozan H. NEAR APPROXIMATIONS IN VECTOR SPACES. JUM. Temmuz 2020;3(2):114-120. doi:10.33773/jum.822384
Chicago Taşbozan, Hatice. “NEAR APPROXIMATIONS IN VECTOR SPACES”. Journal of Universal Mathematics 3, sy. 2 (Temmuz 2020): 114-20. https://doi.org/10.33773/jum.822384.
EndNote Taşbozan H (01 Temmuz 2020) NEAR APPROXIMATIONS IN VECTOR SPACES. Journal of Universal Mathematics 3 2 114–120.
IEEE H. Taşbozan, “NEAR APPROXIMATIONS IN VECTOR SPACES”, JUM, c. 3, sy. 2, ss. 114–120, 2020, doi: 10.33773/jum.822384.
ISNAD Taşbozan, Hatice. “NEAR APPROXIMATIONS IN VECTOR SPACES”. Journal of Universal Mathematics 3/2 (Temmuz 2020), 114-120. https://doi.org/10.33773/jum.822384.
JAMA Taşbozan H. NEAR APPROXIMATIONS IN VECTOR SPACES. JUM. 2020;3:114–120.
MLA Taşbozan, Hatice. “NEAR APPROXIMATIONS IN VECTOR SPACES”. Journal of Universal Mathematics, c. 3, sy. 2, 2020, ss. 114-20, doi:10.33773/jum.822384.
Vancouver Taşbozan H. NEAR APPROXIMATIONS IN VECTOR SPACES. JUM. 2020;3(2):114-20.

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