Compositional Rule of Inference with a Complex Rule Using Lukasiewicz t-Norm

Abstract

Inference systems are intelligent software performed generally to help people take appropriate decisions and solve problems in specific domains. Fuzzy inference systems are a kind of these systems that are based on fuzzy knowledge. To handle the fuzziness in the inference, the compositional rule of inference is used, which has two parameters: a t-norm and an implication operator. However, most of the combinations of t-norm/implication do not give an adequate inference result that coincides with human intuitions. This was the motivation for several works to study these combinations and to identify those that are compatible, in order to guarantee a performance close to that of humans. We are interested in this paper to a more general form of rules, which is complex rules, whose premise is a conjunction of propositions. To obtain the consequence in a fuzzy inference system using the compositional rule of inference with a complex rule, we study, in this work, Lukasiewicz t-norm which was not investigated before in this context. We combine it with known implications, and we verify the satisfaction of some criteria that model human intuitions.