Fuzzy sets based interpretation of the safety factor

Abstract Safety factor is a universally utilized concept in several branches of engineering. On one hand, most engineers, as it were, neglect uncertainty, but on the other hand, the allowable stress level was introduced long time ago as a ratio of the yield stress to the so-called safety factor to provide the region for the safe utilization of the structure. Thus the uncertainty is introduced into practice by the “back door”. This observation led to a considerable literature dedicated to the probabilistic interpretation of the safety factor. The present paper deals with the novel aspect of elucidation of the concept of safety factor through the theory of fuzzy sets, apparently for the first time in the literature. The aim of the paper is to present the safety factor that is uniformly employed by engineers, but in the new light. The safety factor in the fuzzy setting is introduced. The ideas are illustrated on two strength of material problems; simple examples are chosen so as to allow for clearer illustration of ideas.