A Study on First and Second Order Bipolar Fuzzy Topological Spaces and Crisp Topological Spaces and Analyzing the Connections Between Them

Muthamizhselvi S.*¹, V. M. Vijayalakshmi²

¹Research Scholar, Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore-641043, India.

 ²Assistant Professor, Department of Science and Humanities, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore-641043, India.

Emails: muthamilselvi394@gmail.com; vmviji_sh@avinuty.ac.in

Abstract

In our previous paper we discussed about the concept of SOBPFS, SOBPFT and its mathematical modelling in medical diagnosis. In this paper, the detailed study about SOBPFT accordance with FOBPFT and crisp topological spaces are analysed and also some natural examples of SOBPFT are provided. In third section, the connections between FOBPFT and SOBPFT under five different cases are discussed. And last section tells that, from a crisp topology  on  there exists three different SOBPFT denoted by ,  and  and from a SOBPFT on  there exists three crisp topologies denoted by ,  and .  

Keywords: Fuzzy set (FS); fuzzy topology (FT); First order bipolar-fuzzy set (FOBPFS); first order bipolar-fuzzy topological spaces (FOBPFT); second order bipolar fuzzy set (SOBPFS); second order bipolar fuzzy topological spaces (SOBPFT).