Ranking Of Z-numbers And Its Application In Multi-attribute Decision Making

Decision-making is a peculiar phenomenon of human society and one of the most fundamental attributes of the human behaviour system.Real-world decision-making often relies on human cognitive information,characterized by uncertainty and partial reliability.To model and process such uncertain information,Zadeh,the founder of Fuzzy Mathematics,proposed the concept of the Z-number in 2011.At present,the research on Z-number theory is still in its infancy.There are still problems such as complicated calculation,loss of Z-information,and deviation from the original meaning of the Z-number.This paper focuses on the critical issues in the research of Z-number theory,the ranking of Z-numbers,and the distance measure of Z-numbers.Subsequently,they are applied to the multi-attribute decision-making problem under the uncertain information environment of Z-numbers.The main work of the paper is as follows:(1)Fuzzy number ranking method based on the developed golden rule representative value.The fuzzy number is one of the main components of the Z-number,and establishing a perfect fuzzy number ranking method is the premise of the effective ranking of the Z-number.Aiming at the shortcomings of the existing fuzzy number ranking methods,such as incomplete ranking objects,complicated calculation,and neglect of interpretability,this paper constructs some golden rules about fuzzy numbers and further proposes a fuzzy number ranking method based on the developed golden rule representative value.Additionally,we compare it with other existing methods.The comparative experimental results show that the proposed method is simple to calculate and interpretable.It can not only complete the ranking of regular fuzzy numbers but also deal with some special cases,such as crisp numbers and generalized fuzzy numbers with different left heights and right heights.(2)Z-number ranking method based on the developed golden rule representative value.Z-number ranking is an important research topic in Z-number theory,and it is also an inevitable problem in decision-making based on Z-number.Aiming at the information loss problem caused by conversion methods or ignoring hidden probability distributions in existing Z-number ranking methods,this paper proposes a novel Z-number ranking method based on the developed golden rule representative value.First,the hidden probability distributions in the Z-number are estimated by tools such as genetic algorithm and maximum entropy.Then combined with the fuzzy information contained in the Z-numbers,each Z-number is decomposed into a set of fuzzy probability distributions,which can be regarded as a special set of fuzzy sets.Finally,the ranking of Z-numbers is completed using the proposed fuzzy number ranking method.The proposed Z-number ranking method can not only effectively rank Z-numbers composed of various types of fuzzy numbers but also consider the information contained in the hidden probability distribution of Z-numbers,which largely retains the original meaning of Z-numbers.(3)A novel Z-TOPSIS method based on improved distance measure of Z-numbers.The distance measure of Z-numbers is another essential issue in the decision-making process based on Z-numbers.In view of the shortcomings of the existing Z-number distance measure methods,such as incomplete consideration and information loss,this paper first proposes a weighted distance measure method,which considers the first component A,the reliability component B,and the hidden probability distribution p _X of the Z-number.And it has been proved that the proposed distance measure satisfies the three axioms of distance.Subsequently,we construct a Z-TOPSIS decision model combining the proposed Z-number ranking method.A cable supplier selection case is used to verify the effectiveness of the proposed Z-TOPSIS model.Sensitivity analysis shows the influence of different preferences of decision-makers on the decision-making process and proves the flexibility of the proposed Z-TOPSIS model.Compared with the existing Z-TOPSIS method,the proposed Z-TOPSIS method can better utilize the information contained in the Z-number and obtain more reasonable and accurate decision-making results.