Polar coordinate system to solve an uncertain linguistic Z-number and its application in multicriteria group decision-making

Abstract

Z-numbers have been a research hotspot because of the significant advantages in revealing the uncertainty and randomness of information. However, the computation of existing research on the linguistic Z-numbers is relatively complicated. The principal purpose of this paper is to express the linguistic Z-numbers from a new perspective and simplify the computation. Firstly, the polar coordinate system is adopted to describe the linguistic Z-numbers and form a new concept of Z-polar coordinate (ZPC). Secondly, a novel score function is defined to rank different Z-numbers. Thirdly, the Z-polar coordinate vector synthesis power weighted (ZPCVSPW) operator is proposed to integrate multiple information. To determine the weight vector of criteria in the fusion process, a new approach of calculating objective weights is suggested based on the entropy weight method (EWM) with the consideration of the uniqueness of ZPC. Finally, an example concerning multicriteria group decision-making (MCGDM) is performed to illustrate the feasibility of the proposed method. Besides, the validity of the proposed method is demonstrated by three testing criteria. The robustness analysis, complexity analysis, and comparison with other widely used methods are carried out.