Safety assessment of existing structures using a filtered fuzzy relation

Most constructed systems, as well as our infrastructure system, require regular inspection and reassessment so that proper actions can be taken to maintain their current usefulness. Although the quantitative information obtained from these inspections can be analyzed systematically and consistently using probability theory, a parallel analysis is not yet developed for the qualitative information obtained. A filtered fuzzy relation algorithm which utilizes the fuzzy set theory is developed to analyze the qualitative data methodologically. The analysis yields a safety function which shows the degree of belonging for each level of safety reduction from the original design reliability. A sensitivity analysis on the membership functions associated with the input data to the resulting safety function is also performed. The results indicate that, in general, the preciseness of these membership functions has little or no influence on the safety functions. Thus the filtered fuzzy relation algorithm has practical application in assessing existing membership functions.