A hybrid neutrosophic over soft plithogenic topological approach with artificial neural networks for multi-criteria decision making

Abstract

The paper introduces a new framework which uses the Neutrosophic Over Soft Plithogenic topological spaces to solve complex decision-making challenges that involve multiple criteria and uncertain conditions. The model uses neutrosophic sets and soft sets and plithogenic theory to manage truth and indeterminate and false states and attribute value contradictions. The researchers define fundamental operations which include union and intersection and complement and interior and closure and they analyze their properties to develop a reliable topological system. The proposed framework demonstrates its real-world value through a decision-making process which selects the top student. The model uses expert evaluations which experts express in neutrosophic format to generate weighted performance scores that treat positive and negative and uncertain data equally. The study introduces an Artificial Neural Network (ANN) extension to validate and improve the predictive power of the developed model. The ANN model successfully learns how neutrosophic input attributes affect the total decision scores. The system proves its accuracy through its precise prediction of results which matches actual outcomes and produces consistent ranking results. The proposed $\mathcal{N}_{\mathfrak{sp}}^{\mathfrak{o}}$--ANN framework provides a powerful and flexible tool for solving real-world decision-making problems which involve uncertainty and inconsistency and multiple criteria.