A highly interpretable form of Sugeno inference systems

We present a form of fuzzy inference systems (FISs) that is highly interpretable and easy to manipulate. The form is based on a judicious choice of membership functions that have strong locality and differentiability properties and on a modification of the Sugeno and generalized Sugeno forms of the consequent polynomials so as to make them rule centered. Under these conditions, the coefficients in the consequent polynomials can be exactly interpreted as Taylor series coefficients. Besides the intuitive interpretation thus bestowed on the coefficients, we show that the new form allows easy design, manipulation, testing, training, and combination of the resulting fuzzy inference systems. The rudiments of a calculus of fuzzy inference systems are then introduced.