Journal of Prime Research in Mathematics

# Lower interval-valued intuitionistic fuzzy separation axioms

O. R. Sayed$$^a$$, N. H. Sayed$$^b$$, Nasruddin Hassan$$^{c,*}$$

$$^a$$ Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, EGYPT.

$$^b$$ Department of Mathematics, Faculty of Science, New Valley University, EGYPT.

$$^c$$ School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Malaysia.

Correspondence should be addressed to: o_sayed@aun.edu.eg, o_r_sayed@yahoo.com

### Abstract

In this paper, some lower separation axioms in interval-valued intuitionistic fuzzy topological spaces are proposed. Furthermore, we pay some attention in determining the corresponding variations of them in intuitionistic fuzzy topological spaces. The four different types of the concepts of R◦-ness, T◦-ness and T1-ness separation axioms are developed and the corresponding R1-ness and T2-ness are defined. Also, some conclusions by establishing some results are drawn and several examples for illustration are provided.

#### Keywords:

Interval-valued intuitionistic fuzzy set, topology; fuzzy set, fuzzy topology, Lower separation axioms.