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NEAR APPROXIMATIONS IN VECTOR SPACES

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

Abstract

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.

References

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

Abstract

References

  • 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.
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Hatice Taşbozan

Publication Date July 31, 2020
Submission Date November 6, 2020
Acceptance Date February 11, 2021
Published in Issue Year 2020

Cite

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. July 2020;3(2):114-120. doi:10.33773/jum.822384
Chicago Taşbozan, Hatice. “NEAR APPROXIMATIONS IN VECTOR SPACES”. Journal of Universal Mathematics 3, no. 2 (July 2020): 114-20. https://doi.org/10.33773/jum.822384.
EndNote Taşbozan H (July 1, 2020) NEAR APPROXIMATIONS IN VECTOR SPACES. Journal of Universal Mathematics 3 2 114–120.
IEEE H. Taşbozan, “NEAR APPROXIMATIONS IN VECTOR SPACES”, JUM, vol. 3, no. 2, pp. 114–120, 2020, doi: 10.33773/jum.822384.
ISNAD Taşbozan, Hatice. “NEAR APPROXIMATIONS IN VECTOR SPACES”. Journal of Universal Mathematics 3/2 (July 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, vol. 3, no. 2, 2020, pp. 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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