| After the concept of Z-numbers has been proposed by Zadeh,the study about Z-number and its expanding concepts accept extensive attention.But Z~+-numbers,which is also pro-posed by Zadeh when he introduced Z-numbers,attract quite a little attention.Comparing Z-numbers,Z~+-numbers both contain possibility distribution and probability distribution,and Z~+-numbers present more outstanding than Z-numbers in the aspect of representing informa-tion.Moreover,the multi-attribute decision-making problems based on Z-numbers environ-ment is always a research hotspot.However,how to handle with the uncertainty of information is also the significant part in multi-attribute decision-making problems.Therefore,the hidden probability model that converting Z-numbers to Z~+-numbers and two multi-attribute decision-making methods under Z-numbers environment are discussed in this thesis.The main works are as follows:1.According to the special connection between Z-numbers and Z~+-numbers,two hid-den probability models that convert discrete Z-numbers to discrete Z~+-numbers and convert continuous Z-numbers to continuous Z~+-numbers based on linear programming and gradient descent are introduced respectively.2.In order to measure the uncertainty of information which is expressed by Z~+-numbers,several entropy formulas of discrete and continuous Z~+-numbers are designed from two dif-ferent angles,and some relative properties are proved.3.Under discrete Z~+-numbers environment,the utility function based on cut set of Z~+-numbers and attribute weights model based on comprehensive cross entropy are proposed,and corresponding adjustment of PROMETHEE method is made.Finally,combined with the decision-making problem of choosing an optimal design of electricity vehicles charge station-s(DEVCS),the feasibility of the PROMETHEE method based on discrete Z~+-numbers(PTBZ)is demonstrated.4.Under continuous gaussian Z~+-numbers(NZ~+-numbers)environment,the utility func-tion based on concentrated factor and disperse factor is defined.Moreover,the attribute weight formula based on comprehension entropy is supplemented in TOPSIS under Z~+-numbers con-text,and the preference factor and comprehension index based on positive and negative ideal solutions are introduced.At last,the problem of evaluating satisfaction degree of employees is utilized to illustrate the feasibility of the TOPSIS based on entropy and utility of NZ~+-numbers(TEUZ). |
