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Soft congruence relation over lattice

Year 2017, Volume: 46 Issue: 6, 1035 - 1042, 01.12.2017

Susanta Bera Sankar Kumar Roy , Faruk Karaaslan , Naim Çağman

Abstract

In this paper, we first describe soft congruence relation over a lattice. We then define the concepts of complete soft congruence relation. Besides
this, the concepts of upper and lower approximations of a subset in a lattice are depicted based on this soft congruence relation. We then give their related properties with examples to investigate their characterizations.

Keywords

Rough sets Soft sets Lattices Soft congruence relations

References

  • Ali, M.I., Feng, F., Liu, X., Min, W. K. and Shabir, M. On some new operations in soft set theory, Computers and Mathematics with Applications 57, 1547-1553, 1999.
  • Babitha, K.V. and Sunil, J.J. Soft set relations and functions, Computers and Mathematics with Applications 60, 1840-1849, 2010.
  • Babitha, K.V. and Sunil, J. J. Transitive closures and ordering on soft sets, Computers and Mathematics with Applications 62, 2235-2239, 2011.
  • Bera, S. and Roy, S.K. Rough modular lattice, Journal of Uncertain Systems 7, 289-293, 2013.
  • Bozena, K. Soft set approach to the subjective assessment of sound quality, in: IEEE Conferences 669-674, 1998.
  • Chen, D., Tsang, E.C.C., Yeung, D.S. and Wang, X. The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications 49, 757-763, 2005.
  • Çagman, N., and Enginoglu, S. Soft set theory and uni-int decision making, European Journal of Operational Research 207, 848 - 855, 2010.
  • Estaji, A.A., Hooshmandasl, M.R. and Davvaz,B. Rough set theory applied to lattice theory, Information Sciences 200, 108-122, 2012.
  • Feng, F., Ali, M. I. and Shabir, M. Soft relations applied to semi groups, Filomat 27(7), 1183-1196, 2013.
  • Iwinski, T.B. Algebraic approach to rough sets, Bulletin of the Polish Academy of Sciences, Mathematics 35, 673- 683, 1987.
  • Järvinen, J. Lattice theory for rough sets, Lecture Notes in Computer Science 4374, 400-498, 2007.
  • Jang, Y., Tang, Y., Chen, Q., Wang, J., and Tang, S. Extending soft sets with description logics, Computers and Mathematics with Applications 59, 2087-2096, 2010.
  • Liao, Z., Wu, L. and Hu, M. Rough lattice, IEEE International Conference on Granular Computing 716-719, 2010.
  • Molodtsov, D. Soft set theory- first results, Computers and Mathematics with Applications 37, 19-31, 1999.
  • Maji, P.K., Biswas, R. and Roy, A.R. Soft set theory, Computers and Mathematics with Applications 45, 555-562, 2003.
  • Milind, M.M., Sengupta, S. and Ray, A.K. Texture classification using a novel soft set theory based classification algorithm, Springer, Berlin, Heidelberg 246-254, 2006.
  • Park, J.H., Kim, O.H. and Kwun, Y.C. Some properties of soft set relations, Computers and Mathematics with Applications 63, 1079-1088, 2012.
  • Pawlak, Z. Rough Sets, International Journal of Computer and Information Sciences 11(5), 341-356, 1982.
  • Pawlak, Z. Rough sets theoretical aspects of reasoning about data, Academic Publisher 1991.
  • Roy, S.K. and Bera, S. Soft rough lattice, Kragujevac Journal of Mathematics 39, 13-20, 2015.
  • Roy, S.K. and Bera, S. Approximation of rough soft set and its application to lattice, Fuzzy Information and Engineering 7, 379-387, 2015.
  • Roy, S.K. and Bera, S. Soft rough approach to lattice-ideal, The Journal of Fuzzy Mathematics 24, 49-55, 2016.
  • Roy, S.K. and Bera, S. Distributive lattice: a rough set approach, Malaya Journal of Matematik 2, 273-276, 2014.
  • Rana, D. and Roy, S.K. Concept lattice: a rough set approach, Malaya Journal of Matematik 3(1), 14-22, 2015.
  • Rana, D. and Roy, S.K. Rough lattice over Boolean algebra, Journal of New Theory 2, 63-68, 2015.
  • Rana, D. and Roy, S.K. Homomorphism in rough lattice, Journal of New Theory 5, 19-25, 2015.
  • Rana, D. and Roy, S.K. Lattice of rough intervals, Journal of New Results in Science 2, 39-46, 2013.
  • Xiao, Q.M., and Zhang, Z.L. Rough prime ideals and rough fuzzy prime ideals in semigroups, Information Sciences 176, 725-733, 2006.
  • Rana, D and Roy, S.K. Rough set approach on lattice, Journal of Uncertain Systems 5, 72-80, 2011.
  • Rasouli, S., and Davvaz, B. Roughness in MV-algebras, Information Sciences 180, 737-747, 2010.
  • Zadeh, L.A. Fuzzy sets, Information and Control 8, 338-353, 1965.

Year 2017, Volume: 46 Issue: 6, 1035 - 1042, 01.12.2017

Susanta Bera Sankar Kumar Roy , Faruk Karaaslan , Naim Çağman

Abstract

References

  • Ali, M.I., Feng, F., Liu, X., Min, W. K. and Shabir, M. On some new operations in soft set theory, Computers and Mathematics with Applications 57, 1547-1553, 1999.
  • Babitha, K.V. and Sunil, J.J. Soft set relations and functions, Computers and Mathematics with Applications 60, 1840-1849, 2010.
  • Babitha, K.V. and Sunil, J. J. Transitive closures and ordering on soft sets, Computers and Mathematics with Applications 62, 2235-2239, 2011.
  • Bera, S. and Roy, S.K. Rough modular lattice, Journal of Uncertain Systems 7, 289-293, 2013.
  • Bozena, K. Soft set approach to the subjective assessment of sound quality, in: IEEE Conferences 669-674, 1998.
  • Chen, D., Tsang, E.C.C., Yeung, D.S. and Wang, X. The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications 49, 757-763, 2005.
  • Çagman, N., and Enginoglu, S. Soft set theory and uni-int decision making, European Journal of Operational Research 207, 848 - 855, 2010.
  • Estaji, A.A., Hooshmandasl, M.R. and Davvaz,B. Rough set theory applied to lattice theory, Information Sciences 200, 108-122, 2012.
  • Feng, F., Ali, M. I. and Shabir, M. Soft relations applied to semi groups, Filomat 27(7), 1183-1196, 2013.
  • Iwinski, T.B. Algebraic approach to rough sets, Bulletin of the Polish Academy of Sciences, Mathematics 35, 673- 683, 1987.
  • Järvinen, J. Lattice theory for rough sets, Lecture Notes in Computer Science 4374, 400-498, 2007.
  • Jang, Y., Tang, Y., Chen, Q., Wang, J., and Tang, S. Extending soft sets with description logics, Computers and Mathematics with Applications 59, 2087-2096, 2010.
  • Liao, Z., Wu, L. and Hu, M. Rough lattice, IEEE International Conference on Granular Computing 716-719, 2010.
  • Molodtsov, D. Soft set theory- first results, Computers and Mathematics with Applications 37, 19-31, 1999.
  • Maji, P.K., Biswas, R. and Roy, A.R. Soft set theory, Computers and Mathematics with Applications 45, 555-562, 2003.
  • Milind, M.M., Sengupta, S. and Ray, A.K. Texture classification using a novel soft set theory based classification algorithm, Springer, Berlin, Heidelberg 246-254, 2006.
  • Park, J.H., Kim, O.H. and Kwun, Y.C. Some properties of soft set relations, Computers and Mathematics with Applications 63, 1079-1088, 2012.
  • Pawlak, Z. Rough Sets, International Journal of Computer and Information Sciences 11(5), 341-356, 1982.
  • Pawlak, Z. Rough sets theoretical aspects of reasoning about data, Academic Publisher 1991.
  • Roy, S.K. and Bera, S. Soft rough lattice, Kragujevac Journal of Mathematics 39, 13-20, 2015.
  • Roy, S.K. and Bera, S. Approximation of rough soft set and its application to lattice, Fuzzy Information and Engineering 7, 379-387, 2015.
  • Roy, S.K. and Bera, S. Soft rough approach to lattice-ideal, The Journal of Fuzzy Mathematics 24, 49-55, 2016.
  • Roy, S.K. and Bera, S. Distributive lattice: a rough set approach, Malaya Journal of Matematik 2, 273-276, 2014.
  • Rana, D. and Roy, S.K. Concept lattice: a rough set approach, Malaya Journal of Matematik 3(1), 14-22, 2015.
  • Rana, D. and Roy, S.K. Rough lattice over Boolean algebra, Journal of New Theory 2, 63-68, 2015.
  • Rana, D. and Roy, S.K. Homomorphism in rough lattice, Journal of New Theory 5, 19-25, 2015.
  • Rana, D. and Roy, S.K. Lattice of rough intervals, Journal of New Results in Science 2, 39-46, 2013.
  • Xiao, Q.M., and Zhang, Z.L. Rough prime ideals and rough fuzzy prime ideals in semigroups, Information Sciences 176, 725-733, 2006.
  • Rana, D and Roy, S.K. Rough set approach on lattice, Journal of Uncertain Systems 5, 72-80, 2011.
  • Rasouli, S., and Davvaz, B. Roughness in MV-algebras, Information Sciences 180, 737-747, 2010.
  • Zadeh, L.A. Fuzzy sets, Information and Control 8, 338-353, 1965.
There are 31 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Susanta Bera This is me

Sankar Kumar Roy

Faruk Karaaslan

Naim Çağman

Publication Date December 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 6

Cite

APA Bera, S., Roy, S. K., Karaaslan, F., Çağman, N. (2017). Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics, 46(6), 1035-1042.
AMA Bera S, Roy SK, Karaaslan F, Çağman N. Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics. December 2017;46(6):1035-1042.
Chicago Bera, Susanta, Sankar Kumar Roy, Faruk Karaaslan, and Naim Çağman. “Soft Congruence Relation over Lattice”. Hacettepe Journal of Mathematics and Statistics 46, no. 6 (December 2017): 1035-42.
EndNote Bera S, Roy SK, Karaaslan F, Çağman N (December 1, 2017) Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics 46 6 1035–1042.
IEEE S. Bera, S. K. Roy, F. Karaaslan, and N. Çağman, “Soft congruence relation over lattice”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, pp. 1035–1042, 2017.
ISNAD Bera, Susanta et al. “Soft Congruence Relation over Lattice”. Hacettepe Journal of Mathematics and Statistics 46/6 (December 2017), 1035-1042.
JAMA Bera S, Roy SK, Karaaslan F, Çağman N. Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics. 2017;46:1035–1042.
MLA Bera, Susanta et al. “Soft Congruence Relation over Lattice”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 6, 2017, pp. 1035-42.
Vancouver Bera S, Roy SK, Karaaslan F, Çağman N. Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics. 2017;46(6):1035-42.

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