Fuzzy reasoning in the investigation of seismic behavior

In this paper, we propose a fuzzy logic-based mathematical model of a sequence of earthquakes using fuzzy reasoning tools. We formed a set of fuzzy implications in order to study them, and we computed their deviation, so that we could compare them and conclude about the most accurate one. The compositional rule of inference was considered, which is based on the generalized modus ponens scheme. The new fuzzy methodology was used for each implication. The data required for the implications were obtained from the aftershocks of an earthquake with significant effects in a specific area. The magnitude of the aftershocks and their time difference from the main incident provided the values for the new fuzzy algorithm application. Two samples were selected relative with the seismic activity, which occurred the following days. The one sample consisted of 30 values, and the other sample from all the values found in the data archives of the National Observatory of Athens. Results were shown for both samples. So a mathematical technique, which reproduces the incidents using basic information and based on only two parameters, is developed for the simulation of a seismic sequence, which follows a strong earthquake.