Research on Extension Evaluation of Rural Road Maintenance Quality Based on Game Theory

The importance of rural highway maintenance is self-evident, and it is also a basic work of the highway operation department. Selecting an appropriate evaluation method can timely and accurately find the pavement diseases, and improve the timeliness of pavement repair. To improve the accuracy of pavement quality comprehensive evaluation, based on the game theory, the improved extension evaluation method was combined with subjective and objective weight determination methods in this paper, to propose a comprehensive weight determination method with a good operability. The results show that the improved extension evaluation method provides a feasible scheme for rural highway maintenance quality evaluation.


Introduction
The development of rural highways has a positive practical significance, because it can provide key support for the smooth promotion of rural revitalization strategy. The maintenance of rural highways is the top priority, which will greatly influence the normal operation and sustainable development of the local social economy. Meanwhile, a scientific and reasonable evaluation method can be adopted to timely find the highway diseases and damages [1], so that effective measures can be taken to repair the pavement diseases and the operation ability and service status of rural highways can be guaranteed, thus providing a safe, ation coefficients in the traditional specifications [3] [4] don't have dynamic changes, so that the final evaluation results cannot objectively and accurately reflect the current situation of rural highway maintenance.
In the use of rural road maintenance quality evaluation methods, Yingchang Duan et al. [5] established a high-grade road maintenance quality assessment index system, using fuzzy multi-level evaluation algorithm to establish a com-  [10], extension theory has been applied in many fields. However, the extension theory has few relevant applications in the evaluation of rural road maintenance quality. In addition, the extension method has some shortcomings in terms of integrity. Especially in the evaluation process, the weight determination has no fixed calculation model, which leads to limitations in the evaluation process.
In view of this, this paper uses the improved extension evaluation method to comprehensively evaluate the quality of rural road maintenance, and the game theory is used to combine the subjective weighting method (improved analytic hierarchy process) and the objective weighting method (simple correlation function method) to solve the problem of simple correlation function method which relies entirely on sample data to determine the index weight. The improved extension evaluation method has great advantages.

Method for Determining Extension Evaluation Weight Coefficient Based on Game Theory
The determination of the weight coefficient in the extension evaluation theory will greatly affect the results of comprehensive evaluation of multi-index road maintenance quality. The same index and data using the same calculation method to determine the weight will give different accuracy evaluation results. Choosing a scientific and reasonable method to determine the weight is the primary condition for improving the accuracy of the comprehensive evaluation results of the entire road maintenance quality. However, the existing extension evaluation theory does not have a fixed solution method for determining the index weight coefficient, generally, just the simple correlation function method is used to objectively weight each evaluation index, or only artificially subjectively determine the weights of each evaluation index, these two methods of determining weights have their advantages and disadvantages. Based on this, on the basis of objective weighting method and subjective weighting method, this paper adopts a comprehensive weighting method based on game theory to determine the weight coefficient. This method combines the subjective and objective weighting methods to obtain a balanced comprehensive weighting coefficient that can improve the accuracy of the comprehensive evaluation results of highway maintenance quality.

Method for Determining Objective Weightings
The objective weighting method is a method of determining the weight coefficient by using the objective information reflected by each evaluation index value from the actual data, and the method does not depend on the subjective judgment of the individual. In the traditional extension evaluation, the method of simple correlation function [11] is generally used to determine the objective weighting. This paper uses this method in determining the objective weighting If the category corresponding to the data of index i is larger, the index will be given a larger weight value, then take: If the category corresponding to the data of index i is larger, the index will be given a smaller weight value, then take: Then the weight of index i is:

Method for Determining Subjective Weightings
The subjective weighting method, also known as the empirical weighting meth-od, is a method of relative weight based on the experience or preference of the decision makers and comparing the importance of each index. It has nothing to do with the distribution of attribute index. Common methods include the Delphi method, the Analytic Hierarchy Process (AHP), and the superiority chart method [11] [12] [13]. Among them, the AHP method is more commonly used, which constructs the judgment matrix by establishing the hierarchical relationship of each index, and then determines the weight of each index. In this paper, the improved analytic hierarchy process is used to determine the subjective weight coefficient. This method obtains the factor weights by self-correcting and self-coordinating the judgment matrix, then obtain the eigenvector of the consistent matrix and obtain the factor weights, which reduced the eigenvalues of the matrix and its consistency test process, simplified the analytic hierarchy process.
1) Sort the importance of evaluation index By calculating the simple correlation function in Equation (1), the maximum simple correlation function value of each evaluation index and its associated quality level can be found separately. If the quality level is larger (the worse), it means that the evaluation index is more unfavorable to the final quality level, that is, more important than other indexes; if the maximum simple correlation function value of several indexes is associated with the same quality level, the more important the evaluation index of the simple correlation function is, the more important it is. According to this method, the importance of the quality assessment indexes for conservation is sorted. 3) Consistency test of judgment matrix Consistency test is performed on the judgment matrix by using the deviation consistency index CI, the random consistency index RI and the consistency ratio CR. Deviation from the consistency test index CI: To determine the largest eigenvalue of the matrix, max λ is the dimension of the matrix.
The value of the random consistency index RI varies with the dimension n of the matrix. The specific changes are shown in Table 1. In general, the smaller the CR, the better the consistency of the judgment matrix. When CR < 0.1, the consistency of the judgment matrix is within an acceptable range.

4) Correction of judgment matrix
Through the method in the literature (8), the self-coordination and self-correction of the judgment matrix were carried out to obtain a completely consistent matrix:

Method for Determining Comprehensive Weight Based on Game Theory
The method of determining the comprehensive weight based on game theory, first, we should briefly introduce the basic concepts of game theory, including participants, actions, information, strategy, payment, results and equilibrium. Among them, participants, strategy and payment are least needed to describe a game, so mainly introduce the rest several game elements, and the action and information are their "building blocks". Participants, actions, and results are collectively referred to as "rules of the game". Participant: refers to a decision-making main body in a game whose purpose is to maximize the level of payment (utility) by selecting actions (or strategies). There are L ways to empower index, and we see them as L participants. Action: ignoring the actual data and objective information. Therefore, combining the advantages of these two methods, the two kinds of empowerment are combined to obtain an integrated weighting method. However, the existing comprehensive weighting method is basically obtained by simply calculating the average of the subjective and objective weights or the weighted average, and the results are not reasonable enough. In this paper, the game theory method is used to combine the subjective and objective weighting methods to obtain the balanced comprehensive weights. The specific steps are as follows: In order to improve the accuracy of multi-index object evaluation results, L methods can be used to weight the indexes, thereby constructing a basic weight set { } In order to select the most satisfactory weight u * from all possible weights, a balance should be found between all the different weights, even if the deviation between the ideal weight and each basic weight is minimized. Linear combination coefficients k α in formula (6)