Measure Inputs to Fuzzy Rules

Abstract

Our concern is with the determination of the firing level of the antecedent fuzzy set in a fuzzy systems model rule base. We first consider the case where the input information is also expressed in terms of a normal fuzzy set. We provide the requirements needed by any formulation of this operation. We next consider the case when the input information is expressed using a measure. Here we also provide the requirements for any formulation that can be used to determine the firing level of the antecedent fuzzy set when the input information is a measure. We provide some examples of these formulations. Since a probability distribution is a special case of a measure we are able to determine the firing level of fuzzy rules with probabilistic inputs. © Springer International Publishing Switzerland 2014.