Some Generalized Information Aggregation Operators And Their Applications To Multiple Attribute Decision Making

As an important branch of modern decision making, the approaches of multiple attribute decision making are widely applied to economy, management, engineering, military environment, etc. The key problem of study on multiple attribute decision making is divided into two cases. One is how to synthesize the all attributes, which means that we should construct an aggregation function (or aggregation operator) to synthesize all attributes. The other is how to determine the aggregation weights of the attributes. However, with development of modern society and economy, business scale is continually expanding; firm diversification is increasingly achieved; the decision making problems are becoming more and more complex; and the human thinking is characterized by ambiguity. These characteristics may lead to that the input arguments of attributes provided by experts maybe in the form of uncertain variables including the interval numbers, the linguistic variables and the uncertain linguistic variables, rather than the real numbers. Therefore, study on aggregation operators, aggregation weights and approaches to uncertain multiple attribute decision making has great significance in theory and application.The aim of this work is to investigate some generalized information aggregation operators and their applications to multiple attribute decision making. The main contents are as follows:(1) We present several new aggregation operators including the generalized ordered weighted logarithm averaging (GOWLA) operator, the generalized ordered weighted proportional averaging (GOWPA) operator, the generalized ordered weighted exponential proportional averaging (GOWEPA) operator, the generalized ordered weighted logarithmic proportional averaging (GOWLPA) operator and the generalized ordered weighted multiple averaging (GOWMA) operator based on a series of minimization problems with penalty functions. The properties and extensions of these aggregation operators are investigated. We also introduce methods to determine these aggregation operators weights. We develop the nonlinear objective programming model to determine the GOWLA operator weights. The generalized least squares method based on the orness measure of the GOWPA operator, the generalized least exponential squares method based on the orness measure of the GOWEPA operator are introduced to deal with the GOWPA operator weights and the GOWEPA operators weights, repectively. In order to determine the GOWLPA operator weights and the GOWMA operator weights, we investigate the generalized logarithm chi-square method and the generalized least deviation method, respectively. In the meanwhile, we give some examples to illustrate the application of the new generalized information aggregation operators to multiple attribute decision making.(2) We extend the generalized ordered weighted averaging (GOWA) operator to uncertain environment, and propose the uncertain generalized ordered weighted averaging (UGOWA) operator. We further generalize the UGOWA operator to obtain the uncertain generalized hybrid averaging operator, the quasi uncertain ordered weighted averaging operator and the uncertain generalized Choquet integral aggregation operator. Moreover, a new approach to determining the UGOWA weights is proposed based on the relative deviation measure. Then we present a new class of operators called the continuous generalized ordered weighted averaging (C-GOWA) operators, which extends the continuous ordered weighted averaging (C-OWA) operator. We investigate some properties of the C-GOWA operators, and further generalize the approaches and propose some new aggregation operators including the weighted C-GOWA operator, the ordered weighted C-GOWA operator, the combined C-GOWA operator and the combined continuous generalized Choquet integral aggregation operator, etc. We also develop a new distance measure called the continuous ordered weighted distance (COWD) measure by using the C-OWA operator in the interval distance. We study some properties and different families of the COWD measure. We further generalize the COWD measure. Finally, we give some numerical examples to illustrate the applications of these operators to group decision making with interval arguments.(3) We investigate a generalized power average (GPA) operator, which is on the basis of the power average operator and the generalized mean, and develop a generalized power ordered weighted average (GPOWA) operator based on the power ordered weighted average (POWA) operator. Some properties of these operators are discussed. Then we extend the GPA operator and the GPOWA operator to uncertain environments and present an uncertain generalized power average (UGPA) operator and the uncertain generalized power ordered weighted average (UGPOWA) operator to aggregate the input arguments taking the form of interval of numerical values. Moreover, we extend the GPA operator and the GPOWA operator to lingusitc environment and propose the linguistic generalized power average (LGPA) operator and the linguistic generalized power ordered weighted average (LGPOWA) operator. Finally, we develop some applications of these new approaches in multiple attribute group decision making problems concerning the strategic decision making and the evaluation of university faculty for tenure and promotion.(4) We present the consensus indicator induced continuous ordered weighted averaging (CI-ICOWA) operator which uses the consensus indicator of the interval additive preference relation as the order inducing variable in the induced continuous ordered weighted averaging (ICOWA) operator. Then the compatibility degree ICOWA (CD-ICOWA) operator is proposed which use the compatibility degree of two interval additive preference relations as the order inducing variable in the ICOWA operator. We also construct two models to obtain the weights of experts on the basis of these two ICOWA operators of interval additive preference relations. Based on the linguistic continuous ordered weighted averaging (LCOWA) operator, we present some concepts of the compatibility degree and compatibility index for the two interval additive linguistic preference relations. Then we study some desirable properties of the compatibility degree and the compatibility index. In order to determine the weights of experts, we construct an optimal model based on the criterion of minimizing the compatibility index in group decision making. Moreover, the concepts of compatibility degree and compatibility index for the two interval multiplicative linguistic preference relations are proposed. Then we prove some properties which are the scientific basis of using the interval multiplicative linguistic preference relations in the group decision. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we give three examples to develop the new approaches to group decision making with interval additive preference relations, interval additive linguistic preference relations, and the interval multiplicative linguistic preference relations, respectively.