An integrated outranking technique with spherical fuzzy rough numbers for the treatment of cadmium-contaminated water problem in China

The Chinese economy is one of the largest and most dynamic economies in the world. Over the past few decades, China has experienced rapid economic growth from agrarian to industrial powerhouse fueled by manufacturing, exports, and services. However, this rapid growth has also brought about challenges, including environmental issues like water contamination. The indulgence of cadmium metal in regular used water can cause serious health issues, including kidney damage and cancer. Many strategies have been implemented for treatment of water contamination. The main focus of this research is to introduce a novel methodology for treatment of cadmium contaminated water problem in China. This study seeks to demonstrate the multi-criteria group decision-making ability based on the outranking relations within the confines of a contemporary, well-organized and extremely flexible model of spherical fuzzy rough numbers. Spherical fuzzy rough numbers, amalgamation of rough numbers with traditional spherical fuzzy numbers, make the use of membership, non-membership and neutral membership degrees along with the manipulation of the subjectivity and reliance on objective uncertainties. The combination of spherical fuzzy rough numbers with an outranking multi-criteria group decision making technique, Elimination and Choice Expressing Reality, integrates spherical fuzzy logic to handle uncertainty and imprecision in multi-criteria decision-making. This approach captures degrees of uncertainty and hesitancy with spherical fuzzy numbers, improving the handling of imprecise information. The working mechanism involves generation of outranking relations among alternatives by comparing predominant and subdominant options, calculating score degrees, concordance and discordance sets, and incorporating subjective spherical fuzzy rough criteria weights. Unlike traditional methods that use crisp or conventional fuzzy numbers, this technique provides a more reliable and flexible evaluation by integrating rough set theory for better handling of imprecision and uncertainty. Finally, an outranking graph is drawn that points from the supreme option to inferior one. The legitimacy of the proposed technique is, then, testified by making its comparison with other existing techniques.