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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, isdoi:10.1016/j.fss.2017.08.006 fatcat:6gww42lisfgjlakxxidrj2sy34