Research On Two-sided Satisfaction Matching Method With Linguistic Preference Information

Two-sided matching problem refers to the problem of assigning or matching discrete resources that are inseparable from each other in two discrete sets,which has a wide range of practical background.With the continuous development of society and economy,the matching problem is becoming more and more complicated.And because of the uncertainty of the matching information and the fuzziness of human thinking,the matching agent will use the natural language to express the decision making preference in two-sided matching problem.That is the two-sided matching problem with linguistic preference information.Now,the research of the two-sided matching problem with linguistic preference information is in its initial stage of exploration.Targeted two-sided matching methods are rare and there is still lack of systematic theoretical and methodological systems.From the perspective of satisfaction,stability,fairness and psychological behavior of two-sided matching,this paper adopts the idea of gradual progression from shallow to deep to research the two-sided matching problem with linguistic preference information.The research work in this paper is divided into the following aspects.(1)Research on two-sided matching method considering the satisfaction of matching.For the two-sided matching problem with linguistic preference considering satisfaction of matching,first,according to the character of a set of linguistic evaluation scales this paper constructs matching satisfaction function and research its property.On above basis,this paper gives the definition of satisfaction matching,then aiming at maximizing the matching satisfaction degree of two-sided agent,a two-sided satisfaction matching model is established based on utility function.Second,this paper transforms linguistic preference into triangular fuzzy numbers according to fuzzy extension principle,then transforms triangular fuzzy number to the degree of matching satisfaction by defuzzification,aiming at maximizing the matching satisfaction degree of two-sided agent,a two-sided satisfaction matching model is established based on fuzzy extension principle.(2)Research on two-sided satisfaction matching method considering the stability and fairness of matching.For the two-sided matching problem with linguistic preference considering the stability and fairness of matching,first,the paper gives the definition of stable matching with linguistic preference and stable matching constraint conditions,and proves the existence of stable matching with linguistic preference.On the basis of matching satisfaction,this paper builds the two-sided satisfaction matching model considering the stability of matching.Second,this paper gives the definition of fairness matching with linguistic preference,and then builds the two-sided satisfaction matching model considering the fairness of matching on the basis of matching satisfaction.Last,taking the satisfaction,stability and fairness matching into account together,this paper builds the two-sided satisfaction matching model considering the fairness and stability of matching.(3)Research on the two-sided satisfaction matching method considering the agent's expectation information.For the two-sided matching problem with linguistic preference considering the agent's expectation information,first,for the two-sided matching problem with a single type of agent's expectation information,according to the prospect theory,this paper calculates prospect value with a single type of agent's expectation information for reference point,then aiming at maximizing the prospect value of two-sided agent,a two-sided satisfaction matching model is established considering the single type of agent's expectation information.Second,for the two-sided matching problem with multiple types of agent's expectation information,this paper confirms the reference point according to the character of multiple types of agent's expectation,then calculates prospect value according to the prospect theory,aiming at maximizing the prospect value of two-sided agent,a two-sided satisfaction matching model is established considering the multiple types of agent's expectation information.(4)Research on the two-sided satisfaction matching method considering the agent's psychological perception.For the two-sided matching problem with linguistic preference considering the agent's psychological perception,first,considering regret aversion psychological behavior,this paper calculates the perception utility of matching agent according to regret theory,then aiming at maximizing the perception utility of two-sided agent,a two-sided satisfaction matching model is established based on regret theory.Second,considering the reference dependence and loss aversion psychological behavior,this paper calculates the perception value of matching agent according to TODIM theory,then aiming at maximizing the perception value of two-sided agent,a two-sided satisfaction matching model is established based on TODIM theory.