Four alternative definitions of the fuzzy safety factor

The concept of safety factor is nearly universally applied in structural engineering. There are presently several approaches for probabilistic interpretation of the safety factors in the literature. Herein we generalize the above approaches to derive four possible definitions of safety factor that are based on fuzzy sets: (1) the central fuzzy safety factor is defined as the ratio of the centroid abscissas of the membership functions, respectively, of the capacity and the demand of the structure; (2) the characteristic value of fuzzy safety factor as the lower bound of the at cut of the fuzzy safety factor for a specified level of the membership function; (3) the mean value of fuzzy safety factor as the centroid abscissa of the fuzzy capacity-to-demand ratio; and (4) the fuzzy multiplicative safety factor is defined as the abscissa of the centroid of the capacity multiplying to the abscissa of the centroid of the inverse of the demand. Fundamental problem of the strength of materials, namely, tension of an element subjected to an axial load, is analyzed in the context of the above four fuzzy safety factors.