Research Method Of Z-number Uncertainty Measurement Based On Spectral Analysis And Utility Function

In uncertainty research,there are many subjective and objective factors in multi-criteria group decision-making.Through the study of fuzzy theory,these factors can be well integrated,thereby im-proving the accuracy of decision-making results.This paper introduces the concept of Z-number,and study the uncertainty measurement method of Z-numbers based on spectrum analysis and utility function.At the same time,a three-stage multi-attribute group decision-making method under uncertain environment is proposed in this paper in combination with the utility function.The specific research contents are as follows:1.Spectrum analysis of Z-number is defined based on the basic idea that signal processing is often converted between time domain and frequency domain.Firstly,the membership domain parameters and frequency domain parameters are defined.According to the time domain and frequency domain ideas,the membership spectrum and frequency spectrum of Z-number are defined from the membership and frequency domains of Z-number.Secondly,combining the membership spectrum and frequency spectrum of Z-number defines the spectrum of Z-number and proves two properties that the spectrum satisfies.Finally,the calculation of a discrete Z-number spectrum is shown as an example to show the calculation Z-number spectrum process.2.Based on the structure of multidimensional Z-number(MZs),a MZs information fusion method and an uncertainty method for measuring MZs are proposed.Firstly,an information fusion method of MZs is proposed,that is,multiple Z-numbers information is fused to obtain a multi-dimensional Z-numbers.Secondly,based on the axiomatic definition of probability and the definition of MZs,a hidden probability model of MZs is established,and the multidimensional Z+-number is defined in combination with the hidden probability of MZs.Then the utility functions of discrete MZs are defined by algebra,geometry and the entropy angle,and proves the four properties that the entropy form utility function satisfies.The utility function is used to measure the uncertainty of MZs.3.Based on the utility function of MZs,a three-stage multi-criteria group decision-making method is proposed.The first stage uses the grey correlation analysis method to calculate the decision expert weights,the second stage uses the step weight evaluation ratio analysis method to calculate the criterion weights,In this stage,the selection queue method is used to sort the schemes.Finally,a multi-criteria group decision-making for a pharmaceutical factory to select green suppliers is used as an example to verify the effectiveness and feasibility of the proposed method.