Selection of optimal seismic intensity measures using fuzzy-probabilistic seismic demand analysis and fuzzy multi-criteria decision approach

A fuzzy decision-theoretic computational approach for selecting optimal intensity measures (IMs) under the conditions of randomness, fuzziness and uncertainty is proposed in this paper. The main objectives of this study are twofold: (a) to quantify the contribution of multiple evaluation criteria, and (b) to improve the credibility of decision-making results by selecting the appropriate multi-criteria decision making (MCDM) method. To achieve these, three components of the methodology for this approach are utilized: (1) Fuzzy-probabilistic seismic demand analysis (FPSDA) is employed to consider the aleatory and epistemic uncertainties in the seismic demand analysis. (2) Fuzzy analytical hierarchical process (FAHP) is used to determine the importance weights of multiple evaluation criteria. (3) A combination of FAHP and fuzzy technique for order preference by similarity to ideal solution (FTOPSIS) is utilized to determine the optimal IM alternatives. First, the FPSDA method in which the interval PSDA is applied to evaluate the IM performance is developed. The interval results are transformed into triangular fuzzy numbers to establish a fuzzy decision-making matrix. Subsequently, the FAHP is employed to estimate the importance of each evaluation criterion. Then, FAHP–FTOPSIS is utilized to rank the orders of the IM alternatives and select the optimal IM. An illustrative application of the proposed methodology to a five-story reinforced concrete frame structure is presented. The decision results demonstrate that by considering the maximum inter-story displacement angle (θmax), top displacement (Dt), maximum floor velocity (Vmax) and maximum floor acceleration (Amax) as engineering demand parameters (EDPs), the average spectral displacement (Sdam), Sdam, average spectral velocity (Svam), and Vamvatsikos spectral acceleration (VSa2) are the most optimal IMs, respectively. The decision-making results for multiple EDPs indicate that Svam is the optimal IM. Furthermore, the Cordova spectral acceleration (CSa) considering period prolongation has the highest closeness coefficient among the acceleration-related IMs. To verify the effectiveness of the new framework and methodology, the performance of the proposed approach is compared with that of the traditional MCDM method while ignoring fuzziness. The proposed methodology can be applied to other engineering structures and provide a reference for solving similar problems.