Energy supplier selection by TOPSIS method based on multi-attribute decision-making by using novel idea of complex fuzzy rough information

Energy Supplier Selection is vital for sustainable energy management. Optimal supplier choices reduce environmental impact and promote resource efficiency per green principles. However, A decision model for Energy Supplier Selection is crucial in making informed choices for sustainable and efficient energy management. A complex fuzzy set (CFS) is the generalization of the fuzzy set (FS). It is a vital tool to deal with uncertain situations, especially when an object is to be described as a part of a real-life scenario. CFS represents the belongingness of anything to a real-life system with the help of two terms. Furthermore, a rough set (RS) is another tool to reduce uncertainty using approximations. The primary goal of this article is to develop a technique for selecting energy suppliers based on multiple attributes. Complex fuzzy rough sets (CFRS) are created by first making a bridge between CFS and RS. CFRS is not any new theory but is obtained by applying the idea of the roughness of CFS. Hence, CFRS is the framework that deals with uncertainty more accurately than the CFS and RS. With the development of the CFRS, we also need the operators that should deal with the information in the form of the CFRS. So, complex fuzzy rough weighted averaging (CFRWA) and complex fuzzy rough weighted geometric (CFRWG) operators are developed to deal with the information in the form of complex fuzzy rough values (CFRVs). Some basic properties of these operators are discussed and verified. Finally, the developed operators are applied to the real-life problem of multi-attribute decision-making (MADM) by using the technique for order of preference by similarity to the ideal solution (TOPSIS) method.