Year 2020, Volume 3 , Issue 2, Pages 114 - 120 2020-07-31

NEAR APPROXIMATIONS IN VECTOR SPACES

Hatice TAŞBOZAN [1]


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.
Lower and upper approximations, Near sets, Near soft sets, Near soft vector space, Near subsets in the vector space, Soft sets.
  • 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.
Primary Language en
Subjects Mathematics
Journal Section Research Article
Authors

Author: Hatice TAŞBOZAN (Primary Author)
Institution: MUSTAFA KEMAL UNIVERSITY
Country: Turkey


Dates

Application Date : November 6, 2020
Acceptance Date : February 11, 2021
Publication Date : July 31, 2020

Bibtex @research article { jum822384, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2020}, volume = {3}, pages = {114 - 120}, doi = {10.33773/jum.822384}, title = {NEAR APPROXIMATIONS IN VECTOR SPACES}, key = {cite}, author = {Taşbozan, Hatice} }
APA Taşbozan, H . (2020). NEAR APPROXIMATIONS IN VECTOR SPACES . Journal of Universal Mathematics , 3 (2) , 114-120 . DOI: 10.33773/jum.822384
MLA Taşbozan, H . "NEAR APPROXIMATIONS IN VECTOR SPACES" . Journal of Universal Mathematics 3 (2020 ): 114-120 <https://dergipark.org.tr/en/pub/jum/issue/60304/822384>
Chicago Taşbozan, H . "NEAR APPROXIMATIONS IN VECTOR SPACES". Journal of Universal Mathematics 3 (2020 ): 114-120
RIS TY - JOUR T1 - NEAR APPROXIMATIONS IN VECTOR SPACES AU - Hatice Taşbozan Y1 - 2020 PY - 2020 N1 - doi: 10.33773/jum.822384 DO - 10.33773/jum.822384 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 114 EP - 120 VL - 3 IS - 2 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.822384 UR - https://doi.org/10.33773/jum.822384 Y2 - 2021 ER -
EndNote %0 Journal of Universal Mathematics NEAR APPROXIMATIONS IN VECTOR SPACES %A Hatice Taşbozan %T NEAR APPROXIMATIONS IN VECTOR SPACES %D 2020 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 3 %N 2 %R doi: 10.33773/jum.822384 %U 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
AMA Taşbozan H . NEAR APPROXIMATIONS IN VECTOR SPACES. JUM. 2020; 3(2): 114-120.
Vancouver Taşbozan H . NEAR APPROXIMATIONS IN VECTOR SPACES. Journal of Universal Mathematics. 2020; 3(2): 114-120.
IEEE H. Taşbozan , "NEAR APPROXIMATIONS IN VECTOR SPACES", Journal of Universal Mathematics, vol. 3, no. 2, pp. 114-120, Jul. 2020, doi:10.33773/jum.822384