Fuzzy Boolean Nets – a nature inspired model for learning and reasoning

This paper presents Fuzzy Boolean Nets (FBN), a nature inspired Boolean neural model, in the sense that it exhibits topologic similarities with natural systems, as well as learning dynamic activity at low level and high immunity to individual errors or deletions of neurons or synaptic connections. It is shown that one can interpret reasoning in FBN as a particular case of fuzzy qualitative reasoning. It is proven that the model is a Universal Approximator since it can be interpreted as a Parzen Window probability density estimator. Also, conditions for learning a discrete set of rules without cross influence are investigated, being proven that this goal can be achieved with an appropriate net parameters relationship. Moreover, adequate parameter choices for learning continuous functions with interpolation capabilities are deduced.