On δ- Open Sets in Picture Fuzzy Topological Spaces

Abstract

Picture fuzzy sets offer a powerful mathematical tool for capturing uncertainty and imprecision that cannot be adequately handled by classical or intuitionistic fuzzy set theories. Motivated by this framework, the present work explores the concept of -open sets in the context of picture fuzzy topology. Building upon this foundation, the -interior and -closure operators are formulated and their essential characteristics are examined in detail. In addition, four new generalized categories of -open sets are put forward, specifically -preopen sets, -semiopen sets -open sets and -open sets, all of which are thoroughly analyzed under the picture fuzzy topological framework. The mutual relationships between these newly defined classes and the already established picture fuzzy open sets are explored, leading to several significant characterization results. Suitable illustrative examples are also constructed to validate and support the theoretical findings presented in this study.