APPLICATION OF MULTI-VALUED ROUGH NEUTROSOPHIC SET AND MATRIX IN MULTI-CRITERIA DECISION-MAKING

The rough set concept is a methodology of information processing for relational databases. It is a unique uncertainty mathematics topic closely connected to fuzzy set theory. When the rough set is combined with neutrosophic set theory, an effective tool for working with indeterminacy arises. In this study, we defined a multi-valued rough neutrosophic set and a multi-valued rough neutrosophic matrix. Using separation measures, we introduced a new approach for a multi-valued neutrosophic with a rough structure. The suggested approach makes it simple to evaluate the alternatives by applying the separation formula for the multi-valued rough neutrosophic set. The flowchart for the procedure is clearly presented. Then we consider the problem of determining the condition of dengue-affected patients in a specific hospital. Using this method, we create a multi-valued, rough neutrosophic decision matrix that clearly displays the relationship between patient conditions and symptoms. We can determine which one has a serious condition by solving this problem and presenting it on the graph. The comparison of the results with the existing approaches demonstrates the reliability of the suggested method. We analyze the advantages and disadvantages of the multi-valued neutrosophic rough set and matrix to highlight the significance of the suggested structure.