In this work we introduced picture fuzzy hypersoft topological spaces (PFHSTS) as an extension of intuitionistic fuzzy hypersoft topology to address vague, incomplete, and inconsistent information. PFHSTS is a novel concept for analyzing complex systems in uncertain environments by combining the strengths of picture fuzzy sets with the parameterization features of hypersoft sets. Some basic PFHSTS concepts such as closure, interior, and exterior are defined, and their properties are examined with the help of illustrative examples. Along with the theoretical development, a group decision-making model based on the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is developed in the PFHST setting. This model is designed to handle decision problems involving imprecise and multi-dimensional information. A numerical example in the field of small firms and industries is included to demonstrate the practical implementation of the proposed method. In this study, a unified framework is proposed to extend existing fuzzy topological models by combining the concepts of picture fuzzy sets and hypersoft sets. The results show that PFHSTS deals uncertainty better and can help in making decisions in complex situations.