Gray Relation Analysis for Optimal Selection of Bridge Reinforcement Scheme Based on Fuzzy-AHP Weights

In order to solve the problem on optimal selection of old bridge reinforcement schemes, a decision-making method of gray relation analysis based on fuzzy-AHP weights is proposed. Firstly, the fuzzy-AHP is used to develop the decision index system of old bridge reinforcement schemes and determine the weight of decision indexes. The 0.1–0.9 scale method is introduced as the index judgment criterion, and the weight judgment matrix is established. Through the consistency test, the relative weight vector of each decision index in the index layer is calculated. Secondly, according to the gray relation model of the old bridge reinforcement schemes, the decision matrix is constructed, and the gray relation coefficient matrix is calculated to obtain the gray relation coefficient corresponding to the ideal optimal scheme. Finally, the optimal scheme is determined. Through an engineering example, the reinforcement scheme of a concrete-filled steel tube arch bridge deck system is calculated and analyzed, and the best reinforcement scheme is selected. The optimal selection result is consistent with the actual reinforcement scheme available for the bridge. The decision-making method of gray relation analysis based on fuzzy-AHP weights make the evaluation system more organized and systematic and the index weight more operable and quantitative, reduce the subjective evaluation impact, and make the evaluation result more objective and reliable. Considering the fuzzy and gray information of comparison and selection, the optimal scheme with high feasibility and applicability is selected by the gray relation method.