A novel interval valued bipolar fuzzy hypersoft topological structures for multi-attribute decision making in the renewable energy sector

Abstract

Abstract Addressing uncertainty is paramount in all decision-making scenarios to ensure robust, well-informed outcomes that can adapt to unforeseen changes and risks. For this purpose, decision-support systems are the best course of action, as they enable decision-makers to deal with decision-making errors and compile results of human intuition in group decision-making processes. When designed with the concept of topology in mind, these decision-support systems lead to better results as they allow for addressing the decision-making variables in a more detailed manner. In this study, the concept of Interval-Valued Bipolar Fuzzy Hypersoft Topology ( $$\mathbb {BFH}^{\textbf{IV}}_{\textbf{ST}}$$ ) is introduced as a novel extension of fuzzy set theory, aiming to enhance decision-making under uncertain conditions. The introduced structure integrates interval-valued bipolar fuzzy sets ( $$\mathbb {BFH}^{\textbf{IV}}_{\textbf{S}}$$ ) with hypersoft topological spaces ( $$\mathbb {BHST}$$ ), allowing for a more refined representation of imprecise and conflicting information. Fundamental properties of $$\mathbb {BFH}^{\textbf{IV}}_{\textbf{ST}}$$ such as $$\mathbb {BFH}^{\textbf{IV}}_{\textbf{S}}$$ closure, $$\mathbb {BFH}^{\textbf{IV}}_{\textbf{S}}$$ interior and $$\mathbb {BFH}^{\textbf{IV}}_{\textbf{S}}$$ exterior are explored in this paper. Also, a novel decision-making algorithm leveraging the presented structure for multi-criteria analysis and complex system modeling is designed. The algorithm is applied to select optimal renewable energy source based on their economic, environmental, and technical aspects. The effectiveness of our approach is demonstrated through comparative analyses and real-world applications, validating its superiority in handling uncertainty compared to existing fuzzy models. The versatile hybrid nature of the proposed structure allowed for efficient decision-making, showing great promise for applications involving human intuition. The findings and the method used in the analysis forms a strong foundation for future studies in topological fuzzy systems and intelligent decision-support frameworks.

Keywords

• Decision making
• Fuzzy set
• Soft set
• Topology
• Hypersoft set
• Bipolar fuzzy set