An Extended TOPSIS Technique in Cubic Vague Soft Set Relations with its Application in Renewable Energy Sources

Abstract

In this work, we address multi-criteria decision-making (MCDM) problems under high uncertainty by developing an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) within the framework of cubic vague soft set relations (CVSSR). The suggested model incorporates interval-based truth and falsity membership functions to more accurately represent dual uncertainty than current methods, which handle cubic or vague soft sets separately. In order to provide a rigorous mathematical basis for the extended TOPSIS method, the paper presents formal definitions and properties of cubic vague soft relations, equivalence relations, and functions. The model improves the accuracy of alternative ranking by redefining the calculation of positive and negative ideal solutions (PIS and NIS) under the cubic vague environment. The framework’s resilience and interpretability in actual decision-making situations are demonstrated by a real-world application in the selection of renewable energy sources. Thus, the suggested method offers a strong decision-support tool for complex systems with imprecision and vagueness as well as a theoretical breakthrough in soft set mathematics.