Fuzzy Set Approximation Using Polar Co-ordinates and Linguistic Term Shifting

Fuzzy systems built on sparse rule bases apply special inference techniques. A large family of them can be described by the concept of the general methodology of the fuzzy rule interpolation (GM) [1]. Accordingly to this the conclusion is produced in two steps. First a new rule is interpolated corresponding to the position of the reference point of the observation in each antecedent dimension. Secondly the conclusion is determined by firing this rule. This paper proposes a novel set approximation method (FEAT-p) applicable in the first step of the GM for the determination of the antecedent and consequent sets of the new rule. The suggested technique introduces the concept of the polar cut and calculates the points of the shape of the sets taking into consideration all sets belonging to the actual partition. The method can handle subnormal sets, too.