Development of Z number-based fuzzy inference system to predict bearing capacity of circular foundations

Abstract Precise bearing capacity prediction of circular foundations is essential in civil engineering design and construction. The bearing capacity is affected by factors such as depth, density of soil, internal angle of friction, cohesion of soil, and foundation radius. In this paper, an innovative perspective on a fuzzy inference system (FIS) was proposed to predict bearing capacity. The uncertainty of fuzzy rules is eliminated by using Z-number theory. The effective parameters, i.e., depth, density of soil, internal angle of friction, cohesion of soil, and foundation radius were considered as inputs to the proposed model. To compare regression and FIS model with Z-based FIS, statistical indices such as the coefficient of determination (R 2 ), root mean square error (RMSE), and variance account for (VAF) were employed. For training and testing Z-FIS, the R 2 was (0.977 and 0.971), the RMSE was (1.645 and 1.745), and the VAF was (98.549% and 98.138), whereas for the FIS method, the values were (0.912 and 0.904), (5.962 and 6.76), and (90.12% and 88.49%). It should be mentioned that Z theory decreased the computational time by 89.28% (174.04 s to 18.65 s). The comparison of the statistical indicators of the presented models revealed the superiority of the Z-FIS model over the FIS. Notably, sensitivity analysis revealed that the most effective parameters on bearing capacity are internal angle of friction, depth, and soil density.