A Probabilistic Fuzzy Inference System for Modeling and Control of Nonlinear Process

Abstract

A new class of fuzzy inference system is introduced, a probabilistic fuzzy inference system, for the modeling and control problems, one that model and minimize the effects of uncertainties, i.e., existing randomness in many real-world systems. The fusion of two different concepts, degree of truth and probability of truth in a distinctive framework leads to this new concept. This combination is carried out both in fuzzy sets and fuzzy rules, which gives rise to probabilistic fuzzy sets and probabilistic fuzzy rules. Consuming these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed as a fuzzy probabilistic model, which improves the stochastic modeling capability. This probabilistic fuzzy inference system involves fuzzification, inference and output processing. The output processing includes order reduction and defuzzification. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. A probabilistic fuzzy inference system is applied for modeling and control of a continuous stirred tank reactor process, which exhibits dynamic nonlinearity and demonstrated its improved performance over the conventional fuzzy inference system.