Interval-valued neutrosophic rough soft set based intelligent multi-criteria decision-making framework
Abstract
This paper introduces a new concept called Interval-Valued Neutrosophic Rough Soft Sets ( J VNRSδs ) to address vagueness, imprecision, and uncertainty in complex decision-making situations. By integrating soft, rough, and interval-valued neutrosophic set theories, the framework provides a strong approach to deal with incomplete and indeterminate data. Fundamental operations such as intersection, union, complement, and innovative aggregation union operators, designed for multi-criteria decision-making (MCDM) applications, form the theoretical basis of J N NRSs. We also introduce an innovative JVNRSSs based MCDM model ( β-model) to solve MCDM problems. The practical application of β-mode ℓ is demonstrated through a water quality assessment, where water samples are classified based on pollution scores into categories: Excellent, Safe, Moderate, Poor, and Highly Polluted, with corresponding degrees of contamination. A comparative analysis further validates the effectiveness of our proposed β-mode ℓ. Finally, our study concludes with key findings and recommendations for future research directions.
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