Properties of Soft Intuitionistic Fuzzy Sets

S. Ruban Raj; M. Saradha

doi:https://doi.org/10.14445/22315373/IJMTT-V3I6P501

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 3 | Issue 6 | Year 2012 | Article Id. IJMTT-V3I6P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V3I6P501

Properties of Soft Intuitionistic Fuzzy Sets

S. Ruban Raj, M. Saradha

Citation :

S. Ruban Raj, M. Saradha, "Properties of Soft Intuitionistic Fuzzy Sets," International Journal of Mathematics Trends and Technology (IJMTT), vol. 3, no. 6, pp. 150-156, 2012. Crossref, https://doi.org/10.14445/22315373/IJMTT-V3I6P501

Abstract

of soft set is one of the recent topics developed for dealing The concept with the uncertainties present in most of our real life situations. The parameterization tools of soft set theory enhance the flexibility of its applications to different problems. In this work, we give definition of arbitrary fuzzy soft set, we are giving the properties with proof and examples. We further give the proof of Degree of Subset hood of fuzzy soft sets in a fuzzy soft class and verify these with examples. We also present the definitions of the subset hood of soft intuitionstic fuzzy sets along with illustrative examples.

Keywords

Soft fuzzy set; soft intuitionstic fuzzy set; intuitionstic fuzzy set; Subset hood of soft intuitionstic fuzzy set.

References

[1] H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci., 177 (2007), 2726-2735, 2007.
[2] K.T. Atanassov, Intuitionistic fuzzy set, Fuzzy Sets and Systems, 20 (1986), 87- 96.
[3] A. Fatma, On intuitionistic fuzzy relation, MSc Research Project, Faculty of Science and Technology, University Kebangsaan Malaysia, 2010.
[4] M. Irfan Ali, F. Feng, L. Xiaoyan, M. Won Keun and M. Shabir, On some new operations in soft set theory. Computers and Mathematics with Applications, 57(2009), 1547-1553.
[5] P. K. Maji, R. Biswas and A.R. Roy, Fuzzy soft set theory. The Journal of Fuzzy Mathematics, 3(2001), 589- 602.
[6] P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, An International Journal of Computers and Mathematics with Applications, 44(2002), 1077-1083.
[7] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, An International Journal of Computers and Mathematics with Applications, 45(2003), 555-562.
[8] Molodstov. D.A., “Soft Set Theory – First Result”, Computers and Mathematics with Applications, Vol. 37, pp. 19-31, 1999.
[9] Y. Xu, Y. Sun and D. Li, Intuitionistic fuzzy soft set, Science & Research Department Dalian Naval Academy Dalian China, 2010.
[10] B. Yao, L. Jin-liang and Y. Rui-xia, Fuzzy soft set and soft fuzzy set, Fourth International Conference on Natural Computation, 2008.
[11] L. A. Zadeh, Fuzzy sets, Information and Control, 8(1965), 338-353.
[12] Z. Kong, L. Gao, L. Wang and S. Li, The normal parameter reduction of soft sets and its algorithm, Comput. Math. Appl., 56 (2008), 3029-3037.
[13] Z. Kong, L. Gao, L. Wang, Comment on A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 223(2009) 540-542.
[14] S. Alkhazaleh. A. R. Salleh and N. Hassan, Possibility fuzzy soft set, Advances in Decision Sciences, vol 2011, Article ID 479756, 18 pages, doi:10.1155/2011/479756
[15] S. Alkhazaleh. A. R. Salleh and N. Hassan, Fuzzy parameterized interval-valued fuzzy soft set, Applied Mathematical Sciences, 67(2011), 3335-3346.
[16] S. Alkhazaleh. A. R. Salleh and N. Hassan, Soft multisets theory, Applied Mathematical Sciences, 72(2011),3561-3573.
[17] P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Computers and Mathematics with Application, 44 (2002), 1077-1083.
[18] H. Aktas and N. Cagman, Soft sets and soft groups, Information Science, 177 (2007), 2726-2735.