Research Article
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On some properties of intuitionistic fuzzy soft boundary

Year 2020, Volume: 69 Issue: 2, 1033 - 1044, 31.12.2020
https://doi.org/10.31801/cfsuasmas.634266

Abstract

The concept of intuitionistic fuzzy soft sets in a decision making problem and the problem is solved with the help of 'similarity measurement' technique. The purpose of this paper is to initiate the concept of Intuitionistic Fuzzy(IF) soft boundary. We discuss and explore the characterizations and properties of IF soft boundary in general as well as in terms of IF soft interior and IF soft closure. Examples and counter examples are also presented to validate the discussed results.

References

  • Atanassov, K., lntuitionistic fuzzy sets, in: V. Sgurev, Ed., VII ITKR's Session, Sofia, June 1983, Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984.
  • Atanassov, K., lntuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87--96.
  • Atanassov, K. and Stoeva S., Intuitionistic fuzzy sets, Polish Symp. on Interval and Fuzzy Mathematics, Poznan, (August 1983), 23--26.
  • Chen, D., Tsang, E. C. C., Yeung, D. S., Wang, X., The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49 (2005), 757--763.
  • Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81--89.
  • Feng, F., Jun, Y. B., Liu, X., Li, L., An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234 (1) (2010), 10--20.
  • Hussain, S., A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1) (2015), 6--11.
  • Hussain, S., Ahmad, B., Some properties of soft topological spaces, Computers and Mathematics with Applications, 62(11) (2011), 4058--4067.
  • Hussain, S., Ahmad B., Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3) (2015), 559--568.
  • Hussain, S., On some soft functions, Mathematical Science Letters, 4(1)(2015), 55--61.
  • Hussain, S., On some generalized soft mappings, Hacettepe Journal of Mathematics and Statistics, 45(3) (2016), 743--754.
  • Hussain, S., Akiz, H. F., Alajlan, A. I., On algebraic properties of soft real points, Moroccan J. of Pure and Appl. Anal. (MJPAA), 4(1) (2018) 9--16.
  • Hussain, S., Akiz, H. F., Alajlan, A. I., On soft real point matrices and their operations, Fixed Point Theory and Applications, 9 (2019), 1--20.
  • Li, Z., Cui, R., On the topological structures of intuitionistic fuzzy soft sets, Annals of fuzzy Mathematics and Informatics, 5(1) (2013), 229--239.
  • Maji, P. K., Biswas, R., Roy, A. R., Fuzzy soft sets, J. Fuzzy Math., 9(3)(2001),589--602.
  • Maji, P. K., Biswas, R., Roy, A. R., Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9(3) (2001), 677--691.
  • Maji, P. K., Biswas, R., Roy, A. R., On Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 12(3) (2004), 669--683.
  • Maji, P. K., More on intuitionistic fuzzy soft sets, LNCS, 5908,(2006), 231--240.
  • Molodtsov, D., Soft set theory: first results, Computers and Mathematics with Applications, 37 (1999)19--31.
  • Roy, A. R., Maji, P. K., A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 203 (2007), 412--418.
  • Xiao, Z., Gong, K., Zou, Y., A combined forecasting approach based on fuzzy soft sets, J. Comput. Appl. Math., 228 (1) (2009), 326--333.
  • Yin, Y., Li, H., Jun, Y. B., On algebraic structure of intuitionistic fuzzy soft sets, Computers and Mathematics with Applications, 64 (2012), 2896--2911.
  • Zadeh, L. A., Fuzzy sets, Information and Control, 8(1996), 338--353.
  • Zou, Y., Xiao, Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Syst., 21(8) (2008), 941-945.
Year 2020, Volume: 69 Issue: 2, 1033 - 1044, 31.12.2020
https://doi.org/10.31801/cfsuasmas.634266

Abstract

References

  • Atanassov, K., lntuitionistic fuzzy sets, in: V. Sgurev, Ed., VII ITKR's Session, Sofia, June 1983, Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984.
  • Atanassov, K., lntuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87--96.
  • Atanassov, K. and Stoeva S., Intuitionistic fuzzy sets, Polish Symp. on Interval and Fuzzy Mathematics, Poznan, (August 1983), 23--26.
  • Chen, D., Tsang, E. C. C., Yeung, D. S., Wang, X., The parameterization reduction of soft sets and its applications, Comput. Math. Appl., 49 (2005), 757--763.
  • Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), 81--89.
  • Feng, F., Jun, Y. B., Liu, X., Li, L., An adjustable approach to fuzzy soft set based decision making, J. Comput. Appl. Math., 234 (1) (2010), 10--20.
  • Hussain, S., A note on soft connectedness, Journal of Egyptian Mathematical Society, 23(1) (2015), 6--11.
  • Hussain, S., Ahmad, B., Some properties of soft topological spaces, Computers and Mathematics with Applications, 62(11) (2011), 4058--4067.
  • Hussain, S., Ahmad B., Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44(3) (2015), 559--568.
  • Hussain, S., On some soft functions, Mathematical Science Letters, 4(1)(2015), 55--61.
  • Hussain, S., On some generalized soft mappings, Hacettepe Journal of Mathematics and Statistics, 45(3) (2016), 743--754.
  • Hussain, S., Akiz, H. F., Alajlan, A. I., On algebraic properties of soft real points, Moroccan J. of Pure and Appl. Anal. (MJPAA), 4(1) (2018) 9--16.
  • Hussain, S., Akiz, H. F., Alajlan, A. I., On soft real point matrices and their operations, Fixed Point Theory and Applications, 9 (2019), 1--20.
  • Li, Z., Cui, R., On the topological structures of intuitionistic fuzzy soft sets, Annals of fuzzy Mathematics and Informatics, 5(1) (2013), 229--239.
  • Maji, P. K., Biswas, R., Roy, A. R., Fuzzy soft sets, J. Fuzzy Math., 9(3)(2001),589--602.
  • Maji, P. K., Biswas, R., Roy, A. R., Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9(3) (2001), 677--691.
  • Maji, P. K., Biswas, R., Roy, A. R., On Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 12(3) (2004), 669--683.
  • Maji, P. K., More on intuitionistic fuzzy soft sets, LNCS, 5908,(2006), 231--240.
  • Molodtsov, D., Soft set theory: first results, Computers and Mathematics with Applications, 37 (1999)19--31.
  • Roy, A. R., Maji, P. K., A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math., 203 (2007), 412--418.
  • Xiao, Z., Gong, K., Zou, Y., A combined forecasting approach based on fuzzy soft sets, J. Comput. Appl. Math., 228 (1) (2009), 326--333.
  • Yin, Y., Li, H., Jun, Y. B., On algebraic structure of intuitionistic fuzzy soft sets, Computers and Mathematics with Applications, 64 (2012), 2896--2911.
  • Zadeh, L. A., Fuzzy sets, Information and Control, 8(1996), 338--353.
  • Zou, Y., Xiao, Z., Data analysis approaches of soft sets under incomplete information, Knowledge-Based Syst., 21(8) (2008), 941-945.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Sabir Hussain 0000-0001-9191-8172

Publication Date December 31, 2020
Submission Date October 17, 2019
Acceptance Date May 11, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Hussain, S. (2020). On some properties of intuitionistic fuzzy soft boundary. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1033-1044. https://doi.org/10.31801/cfsuasmas.634266
AMA Hussain S. On some properties of intuitionistic fuzzy soft boundary. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1033-1044. doi:10.31801/cfsuasmas.634266
Chicago Hussain, Sabir. “On Some Properties of Intuitionistic Fuzzy Soft Boundary”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1033-44. https://doi.org/10.31801/cfsuasmas.634266.
EndNote Hussain S (December 1, 2020) On some properties of intuitionistic fuzzy soft boundary. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1033–1044.
IEEE S. Hussain, “On some properties of intuitionistic fuzzy soft boundary”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1033–1044, 2020, doi: 10.31801/cfsuasmas.634266.
ISNAD Hussain, Sabir. “On Some Properties of Intuitionistic Fuzzy Soft Boundary”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1033-1044. https://doi.org/10.31801/cfsuasmas.634266.
JAMA Hussain S. On some properties of intuitionistic fuzzy soft boundary. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1033–1044.
MLA Hussain, Sabir. “On Some Properties of Intuitionistic Fuzzy Soft Boundary”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1033-44, doi:10.31801/cfsuasmas.634266.
Vancouver Hussain S. On some properties of intuitionistic fuzzy soft boundary. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1033-44.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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