# Evaluation of Construction Asphalt Pavements Based Toposable Set Theory: A Case Study
## 1 Introduction
However, other influencing factors in the construction are often not considered comprehensively, the control of the construction process is not comprehensive enough, and there are some phenomena such as insufficient attention to the control of the overall performance of asphalt pavement. Numerous factors need to be considered when evaluating asphalt pavement construction control, and as these indicators are either quantitative or qualitative, new evaluation models need to be applied to objectively describe and address construction control issues. Around asphalt pavement, many scholars have carried out relevant research. [PERSON] et al. [16] investigated the effect of using four local industrial waste/by-product materials (marble, granite, steel slag and hydrated lime powder) as mineral fillers on asphalt mixture characteristics, and the testing results show that the asphalt mixture containing marble as a filler yields the highest stability. [PERSON] et al. [17] present the use of waste materials (marble and granite) and by-product material (steel slag) as alternative to the conventional mineral filler, and show that mixtures containing waste marble yielded the highest stability. Moreover, marble is able to improve the moisture damage resistance in terms of tensile strength ratio and loss of stability. As for the evaluation method, commonly used evaluation methods include the fuzzy comprehensive evaluation method [18], the analytic hierarchy process (AHP), and the superiority assessment method based on the toposable set theory. For example, [PERSON] et al. [19] proposed a decision framework based on fuzzy comprehensive evaluation (FCE) and analytic hierarchy process (AHP) for selecting the best mineral filler from four mineral fillers for pavement structures in selected areas. The proposed methodology combines qualitative and quantitative factors, thus increasing the credibility of the material suitability assessment. [PERSON] et al. [20] proposed a new construction quality evaluation framework, which was a combination of the building information model (BIM) and geographic information system (GIS). The framework performed the real-time and full-process quality evaluation of asphalt pavement construction. Taking the Phnom Penh-West Halluk highway construction project as a case study, the results show that the framework providesa good information environment for construction quality evaluation. [PERSON] et al. [21] proved through experiments that gap-graded mix performed better in rutting resistance than dense-graded specimens. Modification with high viscosity agents could significantly inhibit rutting propagation, offering an important improvement the construction quality of asphalt pavement. The indicator system of the fuzzy evaluation method is a static attribute. The indicator values are selected as a set of real numbers, and the measured data are interval point values of fuzziness [19; 22]. Toposable sets [23] are an extension of classical and fuzzy sets and are able to describe the degree of variability, quantitative processes and qualitative processes of things. Literature research shows that the evaluation index system of fuzzy comprehensive evaluation is a static attribute, the judgment matrix lacks elasticity, the weight determination is subjective, and the selection of index values is a real number set. Practice shows [24] that the conventional indexes of asphalt might meet the specification requirements without necessarily ensuring the asphalt is in a good state. Based on this, on the premise of meeting the requirements of the specification, this paper uses each index to classify each respective requirement. For the convenience of data analysis, each index is normalized and dimensionless [25]. Combined with expert survey data, the extension interval number judgment matrix [26] is constructed, and the extension interval values are used instead of specific point values to construct the extension judgment matrix.