Decision-making technique with neutrosophic Z-rough set approach for sustainable industry evaluation using sine trigonometric operators

To overcome the shortcomings of existing fuzzy decision-making models, the approximation of the neutrosophic Z-number becomes an invaluable tool in complicated circumstances including incomplete and contradictory data. To overcome the challenges of methods like multi-criteria decision-making (MCDM), trapezoidal neutrosophic numbers (TrNNs), and neutrosophic Z-numbers (NZNs), this approach integrates rough set theory, neutrosophic set theory, and Z-numbers to introduce Neutrosophic Z-Rough data. Issues like measurement reliability in TrNNs and continuity difficulties in NZNs can be addressed with the use of sophisticated aggregation techniques and Neutrosophic Z-Rough numbers (NZRNs). Using the periodicity and symmetry of the sine-trigonometric function (STF), this work investigates sine-trigonometric approaches to Neutrosophic Z-Rough numbers. New Rough Neutrosophic Z-number sine-trigonometric aggregation operators are obtained by merging the special features of the STF with the NZRNs. The method’s practical applicability within the NZRN framework is demonstrated by applying these operational notions to the MCDM approach, which supports sustainable decision-making in commercial contexts. In addition to improving the NZRN domain’s decision-making efficiency and rationality, this study guarantees a consistent and trustworthy assessment method. New approaches based on NZRNs are necessary since conventional MCDM frameworks are unable to handle the uncertainties brought forth by Industry 4.0. Results from a battery of tests—including sensitivity analyses, reliability evaluations, and comparison studies show that the suggested method is fresh, trustworthy, and excellent for gauging corporate sustainability.