Probabilistic fuzzy logic and probabilistic fuzzy systems

A concept of probabilistic fuzzy logic is introduced as a way of representing and/or modeling existing randomness in many real world systems and natural language propositions. The approach is based on combining both the concepts of probability of truth and degree of truth in a unique framework. This combination is carried out in both fuzzy sets and fuzzy rules resulting in the concepts of probabilistic fuzzy sets and probabilistic fuzzy rules, respectively. Having one of these probabilistic elements, a probabilistic fuzzy system is then introduced as a fuzzy-probabilistic model of a complex nondeterministic system. In a simple example, human skepticism about the optimal fuzzy rule base is modeled through substituting a probabilistic fuzzy rule base for a conventional one. The closed loop response of the resulting controller for tank level control is shown through simulation and is compared with a conventional fuzzy controller.