Uncertainty Measurements Of Discrete Z-numbers And Their Applications

In the research of uncertainty theory,the research of fuzzy theory is very important.The formation and application of fuzzy theory have solved many complicated and abstract problems to a great extent.However,with the in-depth exploration and excavation of the research,the classical fuzzy set theory has more and more depth and breadth.At this time,researchers turned to a new fuzzy theory,Z-numbers,in the hope of solving more complex problems and making up for the shortcomings of the classical fuzzy number.Based on interval type-2 fuzzy numbers,this paper explores the application of geometric measurement,entropy measurement and language scaling functions of Z-numbers to multi-criteria decision problems.This paper is divided into three parts,the specific work is as follows:In the first part,the related concepts of interval type-2 fuzzy set,interval trapezoid type-2 fuzzy set,Z-numbers,discrete Z-numbers and hesitant uncertain language Z-numbers are mainly introduced,and the corresponding explanations are given around the specific concepts.In the second part,the geometric measurement of interval trapezoid type-2 fuzzy set and interval type-2 fuzzy set based on a truncation set are first given,and then the conjecture of Z-numbers geometric measurement is extended.This is used to measure the uncertainty of Z-numbers.Secondly,the feasibility of the geometric measurement of interval trapezoid type-2 fuzzy set,interval type-2 fuzzy set based on A truncation set and Z-numbers is illustrated by using multi-criteria decision method and practical examples.When the Z-numbers geometric measurement method is applied to the multi-criteria decision problem,different models for solv-ing the potential probability are given,and the two models have different emphases according to different needs.Finally,we make a descriptive comparison and instruction.In the process of multi-criteria.decision making,the formula of synthetic approximation index is constructed,and the scores of the solutions are sorted,which shows the effectiveness of the decision making method.The third part mainly discusses the multi-criteria group decision making problem of uncer-tain language Z-numbers,combines the entropy with the language scale function of Z-numbers,and constructs a new entropy formula.When dealing with the decision problem,the optimal model of weight is given.The basic idea is to use entropy to quantify the information of uncer-tain language Z-numbers and determine the ordering value of all the schemes in the calculation example by combining the weight,so as to realize the optimization of the decision result.