Confidence Level-Based Interval-Valued p, q, r-Spherical Fuzzy Sets with Application to Industrial Waste Management


== Abstract ==

<p>Industrialization plays a substantial role in a country&rsquo;s development and economic growth. As a developing nation, Pakistan heavily relies on its steel industry to drive economic progress. Pakistan Steel Mills Corporation (PkMC) is the largest steel producer in the country, manufacturing thousands of tonnes of steel annually. However, this high steel production has led to a significant increase in industrial solid waste. While various methods are available for managing industrial waste, the selection of the appropriate technology is a complex process due to the wide range of strategies and the multiple factors involved in the decisionmaking process. Existing research in the interval-valued p, q, r-spherical fuzzy sets (IVp, q, r-SFS) environment assumes 100% confidence-level from decision makers in evaluating scenarios, but real-world situations often differ from ideal situations. To address this limitation, this study incorporates confidence-level with IVp, q, r-SFS, to identify effective and sustainable waste management strategies for PkMC. Decision-makers can evaluate alternatives by assigning corresponding confidence values using this model to better capture uncertainty. This study develops and analyzes basic operational laws, averaging, and geometric operators, outlining their desirable properties. This study presents a step-by-step algorithm for the proposed MCDM methodology, demonstrating its reliability and efficiency through an industrial waste management example. Model results indicate energy recovery as the most suitable alternative. Comparative analysis further validates the effectiveness of the proposed model. This research offers helpful tips for improving decision-making in waste management and points out the importance of a robust methodological framework in tackling complex, uncertainty-driven challenges.OPEN ACCESS Received: 13/11/2025 Accepted: 19/12/2025 Published: 20/03/2026</p>



== Document ==
<pdf>Media:Draft_content_450145243-7508-document.pdf</pdf>