Research On Theories And Methods For Uncertain Multiple Attribute Decision Making

Multiple attribute decision making is one of the most complex administrative processes in management, which is the procedure to find the best alternative among a set of feasible alternative, and it may involve some conflicting and incommensurable attributes. The ongoing development of society and economy has led to profound changes in the decision environments. Sometimes a single decision maker (DM) or expert may be impossible to consider all relevant aspects of a problem. In this case, the decision making problems require to be further extended to multiple attribute group decision making (MAGDM). MAGDM is among the most important activities that usually occurs in our daily life. Many existing studies use crisp values to express the decision information in MAGDM problems. However, with the increasing complexity of the decision system and the lack of knowledge or data about the problem domain, a DM may provide his/her preferences over alternatives with incomplete information, qualitative preference information or imprecision preferences. These characteristics can lead to that the values of attributes provided by decision maker maybe in the form of uncertain variables such as the interval numbers, the intuitionistic fuzzy numbers or the interval-valued intuitionistic fuzzy numbers(IVIFNs) et al. Thus, study on the uncertain multiple attribute group decision making(UMAGDM) has great significance in theory. The main contents of this work are as follows:(l)We develop a new class of aggregation operator based on utility function, which introduces the risk attitude of decision makers (DMs) in the aggregation process. First, under the general framework of utility function, we provide two new operators respectively called the generalized ordered weighted utility averaging (GOWUA) operator and the generalized ordered weighted utility proportional averaging (GOWUPA) operator and study their properties. Then, under the hyperbolic absolute risk aversion (HARA) utility function, we propose another two new operators named as the generalized ordered weighted utility averaging-hyperbolic absolute risk aversion(GOWUA-HARA)operator and the generalized ordered weighted utility proportional averaging-hyperbolic absolute risk aversion (GOWUPA-HARA) operator, respectively, and further investigate their families. To determine GOWUA-HARA operator weights and GOWUPA-HARA operator weights, we put forward their orness measures, and construct a new optimization models to determine the optimal weights, respectively. Finally, a method for MAGDM is developed based on GOWUA-HARA operator and GOWUPA-HARA operator, respectively, to do the empirical study.(2)Under the interval number uncertainty environment, we develop a new class of aggregation operator based on utility function, which introduces DMs in the aggregation process. First, under the general framework of utility function, we provide a new operator called the uncertain generalized ordered weighted utility averaging (UGOWUA) operator and study its properties. Then, under HARA utility function, we propose another a new operator named as the generalized ordered weighted HARA utility averaging (UGOWHUA) operator, and further investigate its families. To determine the UGOWHUA operator weights, we construct a new optimization model to determine the optimal weights based on the similarity measure of interval values. Furthermore, we also present a continuous generalized power ordered weighted multiple average(C-GPOWMA)operator by means of combining the continuous ordered weighted averaging(C-OWA)operator, the continuous ordered weighted harmonic(C-OWH)operator, the uncertain power ordered weighted averaging(UPOWA) operator and the generalized ordered weighted multiple averaging (GOWMA) operator, and investigate its properties and families. Finally, a method for MAGDM is developed based on UGOWHUA operator and C-GPOWMA operator, respectively, to do the empirical study.(3)We present continuous generalized interval-valued intuitionistic fuzzy ordered Shapley Einstein aggregation operators, which globally consider the importance of elements as well as reflect the interactions between them. Under C-OWA operator, Shapley function, Einstein operations on intuitionistic fuzzy sets and the generalized mean, we propose several new aggregation operators including the continuous generalized interval-valued intuitionistic fuzzy ordered Shapley Einstein averaging (C-GIIFOSEA) operator and the continuous generalized interval-valued intuitionistic fuzzy ordered Shapley Einstein hybrid averaging (C-GIIFSEHA) operator. The properties and extensions of these aggregation operators are studied. To calculate the values of Shapley function, we put forward a new cross entropy measure for IVIFNs, and construct a new optimization model based on the maximum cross entropy principle. Finally, a method for MAGDM with interval-valued intuitionistic fuzzy numbers is developed, to do the empirical study.(4)We develop a new model of the hybrid uncertain group decision. There is not the information conversion, and the alternatives are ranked directly based on original information. We utilize the projection measure of the vectors, the similarity measure of interval values and the fuzzy cross entropy of interval-valued intuitionistic fuzzy numbers instead of a distance measure, to extend the TOPSIS approach and develop a new model to deal with hybrid preference information (e.g. real numbers, interval numbers and interval-valued intuitionistic fuzzy numbers). To calculate the weighting vectors of attributes and decision makers, a model for the optimal weighting vectors of attributes based on the maximizing deviation is established, and under the similarity degree between individual decision matrices, we construct an optimal model to determine the weighting vectors of decision makers. Finally, a method for MAGDM with hybrid preference information is developed based on the extended TOPSIS, to do the empirical study.The above-mentioned contributions have further enriched the study of UMAGDM, and provide new effective theories and methods for sorting and determining the weighting vectors in UMAGDM.