A short note on fuzzy relational inference systems

This paper is a short note contribution to the topic of fuzzy relational inference systems and the preservation of their desirable properties. It addresses the two main fuzzy relational inferences – compositional rule of inference (CRI) and the Bandler–Kohout subproduct (BK-subproduct) – and their combination with two fundamental fuzzy relational models of fuzzy rule bases, namely, the Mamdani–Assilian and the implicative models. The goal of this short note article is twofold. Firstly, we show that the robustness related to the combination of BK-subproduct and implicative fuzzy rule base model was not proven correctly in [24]. However, we will show that the result itself is still valid and a valid proof will be provided. Secondly, we shortly discuss the preservation of desirable properties of fuzzy inference systems and conclude that neither the above mentioned robustness nor any other computational advantages should automatically lead to a preference of the combinations of CRI with Mamdani–Assilian models or of the BK-subproduct with the implicative models.

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