Research On Multi-Attribute Decision Making Problem Based On Probabilistic Language Information

In practical multi-attribute decision making problems,we often encounter the situation that the attributes are not independent of each other,that is,the attributes are intrinsically correlated.It is more in line with people's habits and needs to obtain expert opinions and select the best scheme through language information evaluation,among which probabilistic linguistic term sets is an excellent language expression form at present,which can not only highlight the uncertainty and hesitation of linguistic terms,but also express the different importance degree of terms themselves.This paper introduces the research background and current situation of multi-attribute decision making,probabilistic linguistic term sets(PLTS)and power aggregation operator,proposes new concept Interval-valued probabilistic linguistic term sets(IVPLTS)and its related operation,new similarity measure and four new types of operators,and constructs two kinds of multi-attribute decision making methods based on IVPLTS aggregation operator.Specific research work is as follows:(1)Based on Interval-valued probabilistic linguistic term sets(IVPLTS)and power aggregation operators,this paper constructs a multi-attribute group decision making method.The method is used to describe decision information of the correlation between attributes in the uncertain environment.Firstly,the IVPLTS and its standardization method based on the probabilistic linguistic term sets(PLTS)are defined,and a new scoring function based on interval compromise probability and the sorting method of IVPLTS are constructed.Then,the basic algorithm of IVPLTS and its properties in combination with probability knowledge are proposed.After that,based on the idea of power aggregation operators,the interval-valued probability linguistic power average(IVPLPA)and interval-valued probability linguistic power geometry(IVPLPG)operators are presented,and the ideal properties of the operators and the relationship between the IVPLPA and the IVPLPG operators are discussed.Finally,a multi-attribute group decision making method is proposed based on IVPLPA and IVPLPG operators and an example is given to illustrate the practicability and effectiveness of the proposed method.(2)Based on Interval-valued probabilistic linguistic term sets(IVPLTS)and extended power aggregation operator,this paper constructs a multi-attribute decision making method which is suitable for extreme value decision making processing with different aggregation meanings under uncertain environment.Firstly,a new similarity measure for IVPLTS is defined and its ideal properties are proved by combining relative repetition degree and probability diversity degree.Then,based on the power geometric operator,the extended power geometric operator and the Interval-valued probability linguistic extended power average(IVPLEPA)and the Interval-valued probability linguistic extended power geometry(IVPLEPG)operators are proposed,and the ideal properties,interrelations and special cases of operators are discussed.Finally,a multi-attribute decision making method based on IVPLEPA and IVPLEPG operators is proposed.The feasibility and superiority of this method are illustrated by an example and compared with other methods.Finally,the thesis summarizes the advantages and disadvantages of IVPLTS and four kinds of Interval-valued probabilistic linguistic aggregation operators,and puts forward the prospect.