On Rough Convergence of Fuzzy Numbers based on α-level sets


  • Shyamal Debnath
  • Debjani Rakshit




Rough Convergence, Fuzzy Number, Limit Point.


In this paper we have established some basic properties of rough convergence for fuzzy number sequences. Also introduce the set of rough limit points of a sequence of fuzzy number using α-level set and prove some results associated with this set.


Download data is not yet available.


Akcay F. G. and Aytar S., Rough convergence of a sequence of fuzzy number, Bull.Math. Anal. Appl. 7(4) (2015) 17-23.

Aytar S., Rough statistical convergence, Numer. Funct. Anal. Optimiz. 29(3) (2008) 291-303.

Colak R., Altin Y. and Mursaleen M., On some sets of dierence sequences of fuzzy numbers, Soft Comput. 15(4) (2010) 787-793.

Kaleva O. and Seikkala S., On fuzzy metric Spaces, Fuzzy Sets and System 12 (1984) 215-229.

Matloka M., Sequence of fuzzy numbers, Busefal 28 (1986) 28-37.

Nanda S., On Sequences of fuzzy numbers, Fuzzy Sets and System 33(1) (1989) 123-126.

Pal S. K., Chandra D. and Dutta S., Rough ideal convergence, Hacet. J. Math. Stat. 42(6) (2013) 633-640.

Phu H. X., Rough convergence in normed linear spaces, Numer. Funct. Anal. Optimiz. 22(1-2) (2001) 199-222.

Puri M. L. and Ralescu D. A., Dierential of fuzzy numbers, J. Math. Anal. Appl. 91 (1983) 552-558.

Savas E., A note on sequence of fuzzy numbers, Inform. Sci. 124 (2000) 297-300.

Tripathy B. C. and Baruah A., New type of dierence sequence spaces of fuzzy real numbers, Math. Model. Anal. 14(3) (2009) 391-397.

Tripathy B. C. and Debnath S., On generalized dierence sequence spaces of fuzzy numbers, Acta Scientiarum Tech. 35(1) (2013) 117-121.

Zadeh L. A., Fuzzy sets, Inform. Control 8(3) (1965) 338-353.



How to Cite

Debnath, S., & Rakshit, D. (2018). On Rough Convergence of Fuzzy Numbers based on α-level sets. The Journal of the Indian Mathematical Society, 85(1-2), 42–52. https://doi.org/10.18311/jims/2018/17869