Developing the structural analysis considering fuzzy performance levels

The concept of performance-based engineering in the seismic design and performance evaluation of structures has gained a significant development over the past few decades. The sample performance levels in current building codes are categorized into two levels that represent incipient damage and incipient collapse. Therefore, the performance limits of buildings involve numerous uncertainties such as the lack of clarity in their definition and ambiguity in the individual judgments. The main objective of this paper is to properly address the uncertainties in the performance levels and loading conditions through the evaluation process. The limit state for each performance level is defined as fuzzy numbers to model the fuzziness inherent in their interpretation. Moreover, the fuzzy set theory is adopted to estimate the desired fuzzy structural responses, considering the uncertainty involved in loading conditions within the analysis process. In addition, a novel fuzzy decision-making approach, which includes a comparison of the developed fuzzy sets (i.e., fuzzy structural response and fuzzy performance levels), is proposed to ensure a comprehensive assessment of the building performance. Numerical examples are also given to establish the application of the proposed method. The results demonstrate that the new comparing approach can make a reliable judgment, particularly in questionable cases of decision-making that are in line with the embedded context. •A new structural performance modeling is introduced considering fuzziness in performance levels due to the cognitive source of uncertainty inherent in their interpretation.•Fuzzy structural responses are calculated on uncertain loading condition employing fuzzy set theory, α-cut approach, and an evolutionary-based optimization algorithm.•A new method of comparing two fuzzy sets (i.e. fuzzy structural response and fuzzy performance levels) is proposed to assess the performance of the structures in a reasonably accurate manner.