Degree of coverage of radial rule bases

The paper discusses how a rule base covers its input space in radial fuzzy systems. We investigate the minimal degree of firing of rules in the rule base when moving across the input space. This minimal degree is called the degree of coverage (DOC) and refers to the area of the input space where the rule base has the weakest explanatory power. Identification of the DOC corresponds to a constrained optimization problem. Whilst in general case solving this problem may be hard, in the radial fuzzy systems it may be eased by passing to convex optimization, however, at the cost of getting only a lower bound on the DOC. Moreover, we introduce an algorithm to check out different lower bounds on the DOC for the case of the specific radial rule bases.