Generalized Rough Sets pp 49-65 | Cite as
Interval-Valued Intuitionistic Fuzzy Soft Topological Spaces
Chapter
First Online:
Abstract
In this chapter, the concept of interval-valued intuitionistic fuzzy soft topological space (IVIFS topological space) together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft closed sets (IVIFS closed sets) are introduced. We define neighbourhood of an IVIFS set, interior IVIFS set, interior of an IVIFS set, exterior IVIFS set, exterior of an IVIFS set, closure of a IVIFS set, IVIFS basis, and IVIFS subspace. Some examples and theorems regarding these concepts are presented.
Keywords
IVIFS topology Neighbourhood of an IVIFS set Interior IVIFS set Interior of an IVIFS set Exterior IVIFS set Exterior of an IVIFS set Closure of a IVIFS set IVIFS basis IVIFS subspaceReferences
- 1.Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M.: On some new operations in soft set theory. Comput. Math Appl. 57(9), 1547–1553 (2009)CrossRefMATHMathSciNetGoogle Scholar
- 2.Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefMATHMathSciNetGoogle Scholar
- 3.Atanassov, K., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1989)CrossRefMATHMathSciNetGoogle Scholar
- 4.Jiang, Y., Tang, Y., Chen, Q., Liu, H., Tung, J.: Interval-valued intuitionistic fuzzy soft sets and their properties. Comput. Math Appl. 60, 906–918 (2010)CrossRefMATHMathSciNetGoogle Scholar
- 5.Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math Appl. 45(555–562), 191–209 (2003)MathSciNetGoogle Scholar
- 6.Maji, P.K., Roy, A.R., Biswas, R.: Fuzzy soft sets. J. Fuzzy Math. 9(3), 589–602 (2001)MATHMathSciNetGoogle Scholar
- 7.Maji, P.K., Biswas, R., Roy, A.R.: Intuitionistic fuzzy soft sets. J. Fuzzy Math. 12(3), 677–692 (2004)MathSciNetGoogle Scholar
- 8.Molodtsov, D.: Soft set theory-first results. Comput. Math Appl. 37(4–5), 19–31 (1999)CrossRefMATHMathSciNetGoogle Scholar
- 9.Roy, S., Samanta, T.K.: A note on fuzzy soft topological. Ann. Fuzzy Math. Inform. (2011)Google Scholar
- 10.Shabir, M., Naz, M.: On soft topological spaces. Comput. Math Appl. 61, 1786–1799 (2011)CrossRefMATHMathSciNetGoogle Scholar
- 11.Simsekler, T., Yuksel, S.: Fuzzy soft topological spaces. Ann. Fuzzy Math. Inform. 3, 305–311 (2011)Google Scholar
- 12.Tanay, B., Kandemir, M.B.: Topological structure of fuzzy soft sets. Comput. Math Appl. 61, 2952–2957 (2011)CrossRefMATHMathSciNetGoogle Scholar
- 13.Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)CrossRefMATHMathSciNetGoogle Scholar
- 14.Zhaowen, L., Rongchen, C.: On the topological structure of intuitionistic fuzzy soft sets. Ann. Fuzzy Math. Inform. 5, 229–239 (2013)MATHMathSciNetGoogle Scholar
Copyright information
© Springer India 2015