A ranking model of Z-mixture-numbers based on the ideal degree and its application in multi-attribute decision making

Abstract The Z-number has a great advantage in describing uncertain information. Since Zadeh proposed Z-number, scholars have combined the Z-number with multi-attribute decision making (MADM). However, the problem of having both continuous and discrete attributes in practical MADM is rarely mentioned in the existing methods. To solve this problem, first, we propose the concept of Z-mixture-numbers and propose a new ranking model based on the idea of the ideal degree. Next, after analyzing the correlation coefficient between attributes, we propose the Z-multi-attribute decision making weighting method based on the correlation coefficient. Moreover, the Z mixture induced ordered weighted averaging (ZMIOWA) operator and the Z mixture combined weighted averaging aggregation operator (ZMCWAA) are put forward to solve the MADM problems in which continuous and discrete attributes exist simultaneously. Finally, we propose a MADM method with Z-mixture-numbers and take an example of the sharing car venture capital problem to illustrate its feasibility. It overcomes the previously unsolved problem of Z-numbers’ continuous-discrete mixed MADM.