Normal Stochastic Multi-criteria Decision Making Methods And Application In Project Investment Decision

Because of the limitation of the human cognitive ability and the complexity of objective things, there is a lot of uncertainty in multi criteria decision making. Multi criteria decision making is a very important branch of the uncertainty multi criteria decision making, it is common in real life such as social economy, finance and project investment. Further, normal distribution is a kind of very important random distribution, and is also a very important distribution of the limit, in real life, there exist a lot of multi criteria decision making problems based on normal distribution. Therefore, it has important theoretical and practical value to study the random multi criteria decision theory and method based on normal distribution.This paper is based on a thorough study of the relevant literature, the problems of multi criteria decision making for the random variables which obey normal distribution and lognormal distribution are studied, Some new methods are proposed, and case analysis. And details are as follows:(1) According to stochastic multi-criteria decision making problems in which the criterion values take the form of normally distributed random variables and the criterion values of weighted information are known are processed by TOPSIS method. Firstly, the 2Pearson ?? distance formula between the two normal random variables is used to calculate the distance between the alternatives and the optimal scheme and the worst scheme. On this basis, the closeness of the scheme and the optimal scheme are calculated, and then get the result of the ranking of the schemes, Finally, the feasibility and validity of the method is proved by the case study.(2) Stochastic multi-criteria group decision making problems in which the criterion values take the form of normally distributed random variables and the criteria are in different priority levels are investigated. First, a new aggregation operator called normal distribution number prioritized weighted averaging(NDNPWA) operator is defined, and some desirable properties of this operator are proposed. Furthermore, based on the NDNPWA operator and the normal distribution number weighted arithmetic averaging(NDNWAA) operator, an approach is developed for solving the stochastic multi-criteria group decision making problems in which the criterion values take the form of normally distributed random variables, the criteria are in different priority levels and the decision makers are not in different priority levels. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.(3) According to stochastic multi-criteria decision making problems in which the criterion values take the form of log-normally distributed random variables and the criterion values of weighted information are known are processed by interval number and TOPSIS method. Firstly, the normal distribution of the values of the criterion is ? and ? is transformed into a normalized decision matrix. Then, the normalized decision matrix is transformed into a decision-making matrix with the logarithm normal distribution and the variance of the mathematical expectation, and the normalized decision matrix is transformed into the interval decision matrix. On this basis, using the concept and property of interval number, the scheme is sorted by TOPSIS method, and the optimal scheme is obtained.