This paper explores the application of soft computing techniques to detect discontinuities in physical processes, particularly in seismic analysis. The authors, Solymar Ayala Cortez, Aaron A. Velasco, and Vladik Kreinovich, from the University of Texas at El Paso, address the challenge of identifying discontinuities when exact equations are unknown. They propose using fuzzy logic to translate imprecise knowledge into a precise algorithm for detecting discontinuities. The paper begins by defining the problem, highlighting that while most physical processes are continuous, many real-world phenomena, such as phase transitions and geological faults, exhibit discontinuities. The authors emphasize the importance of detecting these discontinuities in various fields, including civil engineering, geosciences, and fracking. To address the challenge, the authors introduce the concept of "small" changes in a function, which is crucial for understanding continuity. They use fuzzy logic to describe the degree of confidence in the "small" property, assigning values between 0 and 1 to represent varying degrees of belief. This approach allows for the comparison of small changes in different quantities, leading to a simplified criterion for detecting discontinuities. The paper then applies this method to seismic analysis, using data from the 2014 Southern California study. The study involved placing over 1000 seismic sensors on a grid near the San Jacinto fault. By analyzing the amplitude of seismic signals at different sensors, the authors found that the amplitude often spikes when the sensor line crosses the fault, indicating a discontinuity. This empirical validation supports the effectiveness of the soft computing approach in detecting discontinuities. The authors conclude that their method is promising for detecting discontinuities, particularly in challenging scenarios like fracking, and hope to contribute to preventing potential ecological disasters. The paper also discusses the behavior of different seismic waves approaching the fault at various angles, providing insights into the scattering of seismic waves and the potential for more detailed fault characterization.This paper explores the application of soft computing techniques to detect discontinuities in physical processes, particularly in seismic analysis. The authors, Solymar Ayala Cortez, Aaron A. Velasco, and Vladik Kreinovich, from the University of Texas at El Paso, address the challenge of identifying discontinuities when exact equations are unknown. They propose using fuzzy logic to translate imprecise knowledge into a precise algorithm for detecting discontinuities. The paper begins by defining the problem, highlighting that while most physical processes are continuous, many real-world phenomena, such as phase transitions and geological faults, exhibit discontinuities. The authors emphasize the importance of detecting these discontinuities in various fields, including civil engineering, geosciences, and fracking. To address the challenge, the authors introduce the concept of "small" changes in a function, which is crucial for understanding continuity. They use fuzzy logic to describe the degree of confidence in the "small" property, assigning values between 0 and 1 to represent varying degrees of belief. This approach allows for the comparison of small changes in different quantities, leading to a simplified criterion for detecting discontinuities. The paper then applies this method to seismic analysis, using data from the 2014 Southern California study. The study involved placing over 1000 seismic sensors on a grid near the San Jacinto fault. By analyzing the amplitude of seismic signals at different sensors, the authors found that the amplitude often spikes when the sensor line crosses the fault, indicating a discontinuity. This empirical validation supports the effectiveness of the soft computing approach in detecting discontinuities. The authors conclude that their method is promising for detecting discontinuities, particularly in challenging scenarios like fracking, and hope to contribute to preventing potential ecological disasters. The paper also discusses the behavior of different seismic waves approaching the fault at various angles, providing insights into the scattering of seismic waves and the potential for more detailed fault characterization.