Picture fuzzy topological spaces and associated continuous functions

Abstract

This paper describes a study of picture fuzzy topological spaces. We prove some basic results related to picture fuzzy sets together with the introduction of new notions such as the rank, picture fuzzy base and picture fuzzy sub-base of picture fuzzy topological spaces. With the help of these notions, we present a method to design picture fuzzy topological spaces. Furthermore, we introduce the concept of continuity to picture fuzzy topological spaces and find a necessary and sufficient condition for a picture fuzzy continuous function between two picture fuzzy topological spaces.

Keywords

• fuzzy sets
• picture fuzzy sets
• picture fuzzy topological spaces
• picture fuzzy topological bases
• picture fuzzy topological sub-bases
• continuity