Some new results of pythagorean fuzzy soft topological spaces

This paper aims to originate new notion that is pythagorean fuzzy soft topological space and investigate some important properties of pythagorean fuzzy soft topological spaces. Furthermore the notions of pythagorean fuzzy soft interior, pythagorean fuzzy soft closure, pythagorean fuzzy soft image and pre-image, pythagorean fuzzy soft continuity are presented.Publisher's Versio

Fuzzy bipolar soft topological spaces

Topological structures on soft, fuzzy soft, bipolar soft sets and etc. Were studied by several researchers. In this paper, we define topological space on fuzzy bipolar soft sets and investigate the main results. We define fuzzy bipolar soft point and then we give the definition of fuzzy bipolar soft interior and closure points. Also we search properties of fuzzy bipolar soft interior and closure of fuzzy bipolar soft set.Publisher's Versio

On bipolar soft points

The importance of point concept in all sub-branches of mathematics cannot be ignored. The point concept is needed in the establishment and continuation of some theories. Therefore, it is essential to define the point concept in bipolar soft theory. In this paper, the concept of bipolar soft points is defined and the relationship between bipolar soft points and bipolar soft sets is considered. Moreover, we investigate some bipolar soft point sets, define neighborhoods of bipolar soft points and reveal the structure of bipolar soft topological spaces such as interior, closure, boundary and bases by using neighborhoods of bipolar soft points.Publisher's Versio