A short note on fuzzy relational inference systems

Martin Štěpnička, Balasubramaniam Jayaram, Yong Su
2018 Fuzzy sets and systems (Print)  
This paper is a short note contribution to the topic of fuzzy relational inference (FRI) systems and the preservation of their desirable properties. It addresses the two main fuzzy relational inferences -compositional rule of inference (CRI) introduced by Zadeh and the Bandler-Kohout subproduct (BK-Subproduct) -and their combination with two fundamental fuzzy relational models of fuzzy rule bases, namely, the Mamdani-Asilian and the implicative models. The goal of this short note article, is
more » ... eefold. Firstly, we show that one of the results provided in [37] , namely the robustness related to the combination of BK-subproduct and implicative fuzzy rule base model, was not proven correctly as it used an incorrect lemma. However, we will show that the result itself is still valid as an alternative and valid proof will be provided. Secondly, we present some of the results provided already in [23] and later on in other works in the perspective of the preservation of the desirable properties. Finally, we provide readers with a brief yet important discussion on consequences of these results in the light of the theoretical as well as practical aspects of building fuzzy inference systems.
doi:10.1016/j.fss.2017.08.006 fatcat:6gww42lisfgjlakxxidrj2sy34