Researches And Applications Of Decision-Making Methods Based On Linguistic Z-Number

Due to the complexity and uncertainty of the real world,experts often choose to use lin-guistic phrases to express preference for a certain scheme in the process of decision-making.Linguistic multi-attribute decision-making and group decision-making are important compo-nents of modern decision-making theory and decision-making system,they play an increasingly important role in the decision-making field,have important significance and function in dealing with the complexity and variability of the real world and attract extensive attention of scholars and experts at home and abroad.Taking linguistic Z-Number as the main line,this paper fo-cuses on the operators,distance formula,entropy measure and uncertain multi-attribute group decision-making problems of hesitant uncertain linguistic Z-Number(HULZN)and hesitant interval pythagorean linguistic Z-Number(HIPLZN).This paper is divided into three parts,and the specific work is as follows:The first part introduces the concept of linguistic term set and proposes two new linguistic scale functions based on the properties of linguistic scale functions.The concept of uncertain linguistic variable is introduced and several operators of uncertain linguistic variable are de-fined based on the new linguistic scale functions.In the second part,distance measure,ranking value and entropy measure of hesitant un-certain linguistic Z-Number(HULZN)are studied and a multi-attribute group decision model based on HULZN is constructed.First of all,the concept of HULZN based on uncertain lin-guistic variable is introduced,the operators of HULZN are defined based on new linguistic scale functions,which proposed in this paper.Aiming at the problem of distance algorithm in different HULZNs where the number of elements in the reliability measurement sets may be different,a new distance formula of HULZNs with decision-maker's risk attitude is pro-posed,and based on the new distance formula,the ranking value formula of HULZN is defined to measure the relative advantages and disadvantages of HULZNs.Then,three uncertainty measurement formulas of HULZN are defined named fuzziness measure,hesitation measure and interval measure.Based on the three uncertainty measure,entropy formula of HULZN is proposed to measure the uncertainty of HULZN itself.In the multi-attribute group deci-sion making problem with HULZN as the information environment,the optimal expert weight solution model is constructed based on minimize the absolute value of the difference experts'ranking matrices and the average ranking value matrix to obtain the optimal expert weight.Secondly,construct the optimal model of ranking value minus entropy maximization to obtain the optimal attribute weight,and the weighted arithmetic average(WAA)operator is used to aggregate the ranking values and attribute values of each alternative under each attribute to the comprehensive ranking value,and then the alternatives are ranked.Finally,a practical example is used to verify the feasibility and effectiveness of the proposed method,and the ranking results of the proposed method are compared with the existing results to analyze the advantages of the proposed method in this paper.In the third part,hesitant interval pythagorean linguistic Z-Number(HIPLZN)is proposed based on interval pythagorean linguistic fuzzy set(IPLFS),and a hesitant interval Pythagorean linguistic multi-attribute group decision model is proposed.Firstly,introduces the concepts and operators of intuitionistic linguistic fuzzy set(ILFS)and interval intuitionistic linguistic fuzzy set(IILFS).Based on IILFS,the concept of hesitant interval intuitionistic linguistic Z-Number(HIILZN)is proposed,and several operators of HIILZN are defined by linguistic scale functions.On the basis of HIILZN,the concept of HIPLZN is proposed,several operators of HIPLZN are defined by language scale functions,and the properties of some operators of HIPLZN are explored.Aiming at the problem of distance algorithm in different HIPLZNs where the number of elements in the reliability measurement sets may be different,a distance formula of HIPLZNs with decision-maker's risk attitude is proposed,then,HIPLZN entropy formula is proposed to measure the uncertainty of HIPLZN itself.In the multi-attribute group decision making problem with HIPLZN as the information environment,the distance similarity between expert decision matrices is divided by the entropy maximized optimal model to solve the optimal expert weight.Next,the paper constructs the optimal model of positive ideal similarity divided by entropy maximization under each attribute to obtain the attribute weight and get the ranking of alternatives.Finally,an example is given to verify the feasibility and effectiveness of the proposed method.