ZE-numbers: A new extended Z-numbers and its application on multiple attribute group decision making

Abstract As the core mechanism of intelligent systems, decision-making has received widespread attention in recent years. As decision-making environments become more complex, large amounts of data are fuzzy and partially reliable. Zadeh proposed the concept of the Z-numbers, this more anthropomorphic fuzzy set representation framework describes the simultaneous existence of probability measures and probability measures of random variables, and it is regarded as a very powerful tool for modeling uncertain information. However, the representation of Z-numbers still has limitations. Therefore, we propose a new extended Z-numbers, Z E = ( ( A , B ) , E ) , E is the credibility. As the objective reliability of ( A , B ) , it restricts the original Z-numbers. At the same time, the conversion function between them is also defined. Based on this, we proposed a multi-attribute group decision-making (MAGDM) method considering the attitudes of decision-makers. Application examples show the rationality and effectiveness of the proposed methodology, and the superiority of this method is further illustrated through comparison and discussion with other methods.