A Novel Generalized Interval-Valued Neutrosophic Rough Soft Set Framework for Enhanced Decision-Making: Application in Water Quality Assessment

Anjan Mukherjee ¹ ( Department of Mathematics, Tripura University Agartala, Agartala, India. )
Ajoy Kanti Das ² ( Department of Mathematics, Tripura University Agartala, Agartala, India. )
Nandini Gupta ³ ( Department of Mathematics, Bir Bikram Memorial College, Agartala, India )
Suman Patra ⁴ ( Department of Mathematics, Tripura University Agartala, Agartala, India. )
Tahir Mahmood ⁵ ( Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad, Pakistan. )
Suman Das ⁶ ( Department of Education (ITEP), NIT, Agartala, Tripura, India. )
Rakhal Das ⁷ ( Department of Mathematics, The ICFAI University Tripura, Agartala, India. )

تاريخ الإرسال : 19 الجمعة , جمادى الثانية, 1446 تاريخ التأكيد : 29 الأربعاء , رجب, 1446

الکلمات المفتاحية: Fuzzy Set, Neutrosophic Set, Soft Set, Rough Set, Generalized Neutrosophic Set, Interval-Valued Neutrosophic Set.,

ملخص المقالة :

This study introduces a novel framework, Generalized Interval-Valued Neutrosophic Rough Soft Sets (GIVNRS sets), designed to improve handling uncertainty, imprecision, and vagueness in complex decision-making scenarios. By integrating soft, rough, and generalized interval-valued neutrosophic set theories, the framework offers a robust methodology for addressing indeterminacy and incomplete data. The theoretical foundation of GIVNRS sets is built upon fundamental operations, including intersection, union, complement, and novel aggregation union operators tailored for multi-criteria decision-making (MCDM) applications. The practical applicability of the framework is demonstrated through a water quality assessment, where it successfully classifies river segments based on key water quality parameters such as pH, Dissolved Oxygen (DO), and Biochemical Oxygen Demand (BOD). The case study results show that the pollution scores for the river segments were computed, classifying the segments such as “Good,” “Moderate,” and “Poor,” with corresponding pollution levels. These findings highlight the framework’s ability to manage incomplete and inconsistent data, providing a reliable and comprehensive water quality evaluation. Compared to traditional models, the GIVNRS set approach offers enhanced flexibility, stability, and adaptability. This study not only contributes to the theoretical development of neutrosophic, soft, and rough set theories but also establishes GIVNRS sets as a powerful tool for water quality decision-making. Future research will explore further advancements in the application and computational efficiency of this framework.

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