A Comprehensive Approach to Decision Making in Uncertain Environments Using Picture Fuzzy Hypersoft Topology

The present study proposed a new Picture Fuzzy Hypersoft Topology-based Multi-Criteria choice-Making (PFHT-MCDM) framework for solving complex decision-making problems with uncertainty, incompleteness, and multidimensional attributes. The proposed framework successfully integrates the advantages of Picture Fuzzy Sets, Hypersoft Sets and topological structures into a unified mathematical structure. The presented method combines positive, neutral and negative membership functions with multi-sub-attribute parameterisation and topological operators, which allows a more accurate representation of uncertain decision scenarios than traditional fuzzy methods. In the PFHT environment a TOPSIS based ranking algorithm has been developed and validated with an industrial investment case study. The maximum closeness coefficient (CC=0.81) was achieved in the case of Alternative A_3, and thus it was selected as the best investment option as per the results of the trial. The comparative study demonstrated that the proposed PFHT model has more representation power, better decision accuracy and higher interpretability than the classical fuzzy, intuitionistic fuzzy, image fuzzy and hypersoft methods. The practical and theoretical importance of Picture Fuzzy Hypersoft Topology for engineering and intelligent decision-support applications is pointed out. Future research can focus on the integration of PFHT with cutting-edge computational paradigms like Machine Learning, Deep Learning, Explainable Artificial Intelligence, Internet of Things and big-data analytics to develop adaptive, interpretable and intelligent decision-making systems capable of functioning under highly dynamic and uncertain environments.

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