Hybrid multi-attribute decision making based on shadowed fuzzy numbers

Decision-making in an environment that includes different types of uncertainties represent real challenges for decision makers. Fuzzy sets and their extensions are famous forms of representing vague information. However, other different forms of uncertain data are commonly found in multiple attribute decision making (MADM) problems. This makes a serious difficulty for the decision maker to take a proper decision based on such hybrid types of uncertainties. There is a quite need for introducing an effective methodology to transform different types of uncertainties into a standard form. This paper, introduces an improved version of shadowed fuzzy numbers (SFNs) as useful transformation for different types of uncertainties. The new shadow number preserves the main characteristics of uncertainty for different types of fuzzy sets used in the problem. The new ranking method is proposed to manipulate shadowed fuzzy numbers. The features of new method are significant for decision applications.