Research On Some Generalized Interactive Power Average And Power Geometric Aggregation Operators And Their Applications

As an important branch of the decision-making theory, multiple attribute decision making (MADM) has drawn more and more attention for their potential in applications,especially in the areas of engineering, management, economics and politics. In recent years,the decision-making environment has become more and more complex, cumbersome and interactive, which leads to a large number of researchers being committed to constructing the methods of the MADM that can take into account the interactions among the decision information in the decision-making process. Among these, one of the most prominent works is the proposing of several kinds of interactive information aggregation operators.Considering the MADM problem where there exist some interrelationships among the decision evaluation values, this paper mainly focuses on the power average (PA) and power geometric (PG) operators, and aims to expand their theories and applications. In terms of the existing works on the PA and PG operators and their extensions 1) cannot effectively highlight the aggregation features of the PA and PG operators; 2) have few researches under the intuitionistic fuzzy or the interval-value hesitant fuzzy environment; 3) cannot handle the case where these unduly high or low arguments are regarded as the highly important elements; 4) subjectively assign the parameter in some information aggregation operators,and many others,this paper proposes some novel generalized interactive power average and power geometric aggregation operators. Based on these aggregation operators, a series of multiple attrbute decision making models and methods are constructed, and some numerical examples are provided to illustrate the feasibility and rationality of each model and method.The main works are as follows:1) Systematically review the existing works on the information aggregation operators.For convenience, the information aggregation operators are divided into two categories: the one that takes into account the interrelationships among the decision information in the decision-making process, and that ignores this interactive information. After that, several existing literatures on the information aggregation operators are reviewed with respect to each category.2) Review the theories and applications of the PA and PG operators and their extensions. The introductions, properties and aggregation features of the PA and PG operators and their extensions are detailedly introduced. After that, the main works and shortcomings of the existing research are systematically summarized, and the works which will be carried out by this paper, corresponding to the shortcomings of the existing research,are introduced.3) Establish an MAGDM method on the basis of the variable intuitionistic fuzzy power average operator. In view of the deficiency of axiomatic definitions of intuitionistic fuzzy sets among current researches, an improved axiomatic definition of intuitionistic fuzzy entropy is presented and a corresponding formula is structured. In order to effectively highlight the aggregation features of the power average operator, a variable parameter is introduced to define variable power average (VPA) operator. The related properties of VPA are proposed and verified, and an approach for determining the variable parameter is also presented. Furthermore, the VPA operator is extended to intuitionistic fuzzy environments to put forward the generalized intuitionistic fuzzy power average operator. In a framework of complex system which the performance is evaluated as intuitionistic fuzzy numbers (IFNs),with respect to a multiple attribute group decision making (MAGDM) problem, in which there are both interactions among decision information and decision-makers' weights and attributes' weights are both unknown,an interdependent MAGDM method based on an intuitionistic fuzzy entropy and the variable intuitionistic fuzzy power average operator is proposed. A practical and comparative example on the ranking of the performance for the smartphone illustrates the validity and feasibility of the proposed decision-making method.4) Establish MAGDM methods on the basis of the generalized variable interval-value hesitant fuzzy power geometric operators. With the purpose of effectively highlighting the aggregation features of the power average operator, this paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators,and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter,the influence caused by some "false" or "biased" arguments can be reduced,and the aggregation features of the power geometric operator can also be effectively highlighted. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Finally,numerical examples on the logistics supplier selection are provided to illustrate the effectiveness of the proposed techniques.5) Establish an MADM method on the basis of the extended power average operator.Classical power average (PA) operator and these operators as proposed above assume the unduly high or low arguments are the possibly "false" or "biased" inputs and assigns them with lower weights. To effectively capture the interrelationships among the aggregated arguments in various types of decision making contexts, we extend the PA operator, which we refer to as the extended PA (EPA) operator. Utilizing the EPA operator, those unduly high or low arguments are either regarded as the possibly "false" or "biased" inputs or as the highly important elements. We investigate several desirable properties of the EPA operator and analyze its primary significances in the decision-making problems. We further adopt a method of optimizing the choice of the parameter for the EPA operator. Moreover, to simultaneously take into account the interrelationships among the attributes and that among the aggregated data in the decision process, we propose an approach for the multi-attribute decision making (MADM) by utilizing the EPA operator. Finally, a practical example on the location selection and a comparison are provided to illustrate the reliability and effectiveness of the proposed approach.6) Establish an MAGDM method on the basis of the extended variable intuitionistic fuzzy power average operator. In order to further expand the theories and applications of the PA operator, the concept of generalized intuitionistic fuzzy entropy is first developed by considering the intuitive and fuzzy information with respect to an intuitionistic fuzzy set(IFS). The influence of an IFS's respective information on its generalized intuitionistic fuzzy entropy is analyzed. With the premise of determining the parameters of the generalized intuitionistic fuzzy entropy reasonably, an efficient method based on the entropy weight approach is proposed to determine the weights of decision makers and that of attributes simultaneously. After that, the concept of the extended variable power average (EVPA)operator is introduced on the basis of the VPA and EPA operators. Furthermore, the EVPA operator is extended to intuitionistic fuzzy environments to put forward the extended variable intuitionistic fuzzy power average (EVIFPA) and weighted extended variable intuitionistic fuzzy power average (WEVIFPA) operator. Finally, an MAGDM method by utilizing the WEVIFPA operator is established, and a numerical example is provided to demonstrate the validity and feasibility of the proposed method.7) Compare and analyze the similarities and differences among the PA, PG,generalized PA operators and the operators proposed in this paper. First, the similarities and differences on the definitions and aggregation mechanisms for the PA, PG, generalized PA operators and the operators proposed in this paper are compared and analyzed. After that, the applications of each operators are analyzed, respectively; and the flowchart on how to choose the proper operator according to the decision-making environment is provided.Finally, several common decision-making applications are listed.