Theories And Methods Of Heterogeneous Information Group Decision Making Problem Based On Axiomatic Design

Since the outbreak of COVID-19 in the world,people have faced a more uncertain and complex decision-making environment.For the same decision-making problem,different individuals,organizations or countries often establish a set of evaluation index system according to their own needs and make different choices.In fact,due to the different educational background,knowledge experience and decision-making habits,decision makers often use different types of decision-making information to express their views,resulting in different forms of preference structures,such as heterogeneous multi-attribute group decisionmaking or heterogeneous preference relationship group decision-making.Traditional decision-making methods are incompetent to this heterogeneous group decision-making.This heterogeneous preference information brings new challenges to group decision-making.Therefore,the study of heterogeneous preference information group decision-making method has important theoretical and practical significance.Based on the above analysis,three types of heterogeneous preference information group decision-making problems are deeply studied and explored,including heterogeneous multiattribute group decision-making problem,heterogeneous preference relationship group decision-making problem,and complex heterogeneous group decision-making problem combined with the two.The main work is detailed as follows.(1)Aiming at the problem of decision making under the background of quantitative decision information,a heterogeneous multi-attribute group decision making method based on axiomatic design concept is proposed,which can make up for the deficiency of existing information measurement(Euclidean distance,Possibility)to a certain extent.By using“information quantity” instead of the traditional “distance” formula,the differences between the alternative and the expected alternativeis are measured.The information content of common decision information such as interval number,trapezoidal fuzzy number,triangular fuzzy number,intuitive fuzzy number,linguistic term,real number and so on are defined respectively.The comparative analysis with Euclidean distance,possibility degree and closeness degree show that the information loss caused by information normalization can be avoided to some extent by using the information content in the form of probability ratio.(2)For the heterogeneous multi-attribute group decision-making problem,in which the attribute values are represented by real numbers and linguistic terms,and the weight information of attributes and experts are completely unknown,a heterogeneous multi-attribute group decision-making method based on axiomatic design is proposed.Firstly,the information content of linguistic terms is defined.Then,the deviation maximization model is constructed according to the amount of information to objectively determine the attribute weight.Afterwards,taking full account of the differences between experts,a method based on maximizing group consensus is proposed to determine the weight of experts,and the alternatives are sorted through comprehensive information content.Finally,the supplier selection and comparative analysis are conducted to illustrate the reliability of the proposed method.(3)Aiming at the heterogeneous group decision-making problem composed of interval reciprocal preference relationship and triangular fuzzy number reciprocal preference relationship,a new fuzzy best worst method(BWM)is proposed.This method allows decision makers to choose different types of preference relations according to their own experience,such as interval number,triangular fuzzy number,linguistic terms and so on.Based on the consistency of classical BWM and reciprocal preference relationship,the mathematical programming methods of interval BWM and triangular fuzzy number BWM are constructed respectively.Based on the concept of goal programming,the fuzzy programming model is cleverly transformed into an accurate mathematical programming model to obtain the optimal fuzzy weight of the alternative(or criterion).According to the characteristics of interval BWM and triangular fuzzy number BWM,a new definition of consistency ratio is given,which enriches and develops the preference relationship group decision-making method in heterogeneous environment.(4)Aiming at the complex heterogeneous information group decision-making problem in which the attribute value is in many different expressions,the attribute weight and expert weight are partially known or completely unknown,and the alternative are compared in linguistic term,a group decision-making method based on axiomatic design is proposed.Firstly,considering the differences of experts,a bi objective programming model is constructed to solve the expert weight by maximizing individual deviation and minimizing group inconsistency.Then,according to the idea of LINMAP,by maximizing consistency and minimizing inconsistency,a dual objective language fuzzy mathematical programming model is established to determine the attribute weight.The model can be cleverly transformed into a linear programming model through the scale function.Finally,the candidate schemes are sorted according to the comprehensive information.The flexibility and practicability of this method are illustrated by the selection of blockchain service providers and the comparison with other methods.