Research On Matching Decision-Making Methods With Probabilistic Linguistic Term Sets And Their Applications

Matching problems are widespread in real life and economic management activities.After Gale and Shapely put forward the matching problem,the matching theory has gradually attracted people’s attention and achieved rapid development,from one-to-one two-sided matching to oneto-many two-sided matching,multi-side matching and dynamic two-sided matching.The provided theory methods are applied to economic and society management areas where various resources are allocated reasonably,such as schools-students,person-post matching,suppler-demander matching,venture capitalist-entrepreneur matching,etc.The core of matching decision-making is to deal with the preference information provided by matching agents with mutual needs and to promote the judgement and choice based on effective methods.Rational and effective matching process can increase the recognition and satisfaction of the matching agents to improve the harmony of social work and life.In reality,matching agents are more inclined to express the preference using linguistic variables,which change the traditional form,i.e.,preference order.The linguistic preference information not only fits the cognitive and expression habits of agents more effectively,but also can describe their preference degrees,which has a higher applicability.With the increasing complexity of matching decision-making environment,the linguistic evaluation gradually shows the characteristics of ambiguity and uncertainty.However,the traditional way of language description usually ignores such characteristics,and there are two shortcomings: when the qualitative context is converted into a quantitative standard value,it causes serious information loss;it is difficult to completely cover the evaluation information of agents,especially,the preference degree.Thus,based on the complex and uncertain environment,how to accurately describe the preference information and keep original evaluation as soon as possible,and then convert them into quantitative indicators for programming model are particularly important.Under comprehensive consideration,this paper introduces a complex linguistic expression tool called probabilistic linguistic term set(PLTS)into matching decision-making methods and apply them to solve practice problems.The special research contents are as follows:(1)As the most basic and the most extensive research content in matching theory,two-sided matching is the main research object here.This paper reviews and analyzes the existing publications of two-sided matching field based on bibliometrics.For the keywords,this paper conducts the co-occurrences,timeline and burst detection analysis to dig out the research hotspots and their dynamic development trends in this field.Combining with science mapping analysis,according to visualization tools,we demonstrate the corresponding networks.Finally,based on the analysis results,the existing theory research and application research are classified and reviewed,and the advantages and disadvantages are summarized,which lays the foundation for the series of decision-making theory methods and their applications provided in this paper.(2)The two-sided matching decision-making method with probabilistic linguistic preference relations are studied,including mixed preference relation-based two-sided matching decisionmaking method and multi-stage two-sided matching decision-making process.The provided methods change the traditional model of pre-progressing the preference information of agents in the early stage of matching.This paper considers that agents present the preference relation by pairwise comparison.Specifically,the consistency of preference relationship needs to be checked firstly by giving the concepts of acceptable consistent and unacceptable consistent preference relationship in this paper.For the unacceptable consistent preference relationship,two kinds of modified progresses are presented,including automatic correction algorithm and correction iterative model.Next,for the former,this paper takes the expected time into consideration,computes the time satisfaction degree and makes the collaboration among agents to modify the preference satisfaction degree.Then,the whole two-sided matching decision-making procedure is given.The medical technology supply and demand matching case is used to demonstrate the provided method.For the letter,starting with symmetry characteristic of preference relationship,we define a new transformation function and a series of new information fusion method based on Choquet integral and Bonferroni mean operator.For the multi-stage matching decision-making problem,this paper gives two kinds of stage-weight calculation methods,i.e.,lognormal distribution-based increasing model and a programming model combining TOPSIS with deviation entropy.Furthermore,the complete multi-stage decision-making process is given,and then it is applied into the medical scheme selection problem for the lung cancer patient.Simulation experiment,comparison analysis and sensitive analysis are used to demonstrate and validate the provided methods further.(3)Under the probabilistic linguistic environment,the multiple attribute two-sided matching decision-making is studied.With the continuous refinement of the social division of labor,social and economic management activities have begun to become hierarchical,and different organizations have different requirements.For example,when companies recruit job candidates,they have different attributes of attention for different positions.Employees also have their own requirements for positions in the company.At this time,two-sided matching considering multiple attributes for agents is called a multi-attribute two-sided matching problem.This paper takes the completely unknown attribute weights into consideration.Then,introducing fuzzy decisionmaking trial and evaluation laboratory(FDEMATEL)balances the interaction among attribute and classifies the attributes into cause group and effect group to determine the weight values.Next,the whole decision-making procedure is as follows: 1)compare the agents’ psychological expectations of each attribute with the actual situation of the opposite agents to construct a gain and loss matrix;2)introduce prospect theory to obtain the agents’ psychological perception utility and comprehensive perception utility;in order to ensure the stability of the matching result,a probabilistic language multi-attribute boundary approximation regional comparison(PL-MABAC)is proposed.This method determines the ranking information of the agents to the opposite agents,establishes stable matching constraints,and then constructs a comprehensive programming model.Finally,the proposed method is applied to the matching problem of medical service supply and demand.Through comparative analysis,the rationality and effectiveness of the attribute determination method and matching process proposed in this paper are verified.(4)The multi-sided matching decision-making progress under the probabilistic linguistic term environment is studied.Considering the urgency and important practical significance of emergency response,this paper explores the matching process between the rescue teams and disaster points.Firstly,the problem description is presented.Then,we determine the matching degree between rescuers and rescue missions,including competency degree and time realibality degree.For the former,the peer experts are invited to evaluate the professional capability and collaboration capability of rescuers with probabilistic linguistic term sets.For the letter,the BPR function is introduced and improved to obtain the arriving time and the time reliability.By successively promoting the applicability of this function and studying the role of relevant important parameters,a more flexible and widely applicable BPR function is proposed.At the same time,this paper gives a new assumption that the current capacity of the road obeys the Gaussian distribution between the maximum and minimum values,and the rationality of this assumption is verified through sensitivity analysis and comparative analysis.Then,this paper constructs a complete multi-sided matching decision-making process,and establishes a two-stage matching programming model with the maximizing the competence and time reliability of rescuers.Finally,a numerical example is used to describe the proposed method,combined with comparative analysis,to verify the rationality and feasibility of the improvement of the BPR function applicability from multiple angles.In summary,this paper systematically studies the matching decision-making method based on probabilistic linguistic term sets from five angles: static and dynamic matching;two-sided matching,multiple attribute two-sided matching and multi-sided matching.The provided methods are used to solve medical technology and service matching,medical scheme selection,rescuers dispatch problems.The research results not only scientifically and reasonably solve the practical matching problems but also broaden the scope of application of matching decision-making theory.They are the useful supplement to the matching framework,which has important theoretical and practical significance.