Bandler-Kohout Subproduct with Yager's Classes of Fuzzy Implications

The Bandler–Kohout Subproduct (BKS) inference mechanism is one of the two established fuzzy relational inference (FRI) mechanisms, the other being Zadeh’s Compositional Rule of Inference (CRI). Both these FRIs are known to possess many desirable properties. It can be seen that many of these desirable properties are due to the rich underlying structure, viz., the residuated algebra, from which the employed operations come from. In this work we discuss the BKS relational inference system with the fuzzy implication interpreted as the Yager’s classes of implications, which do not form a residuated structure on [0, 1]. We show that many of the desirable properties, viz., interpolativity, continuity, robustness that are known for BKS with residuated implications are also available under this framework, thus expanding the choice of operations available to practitioners. Note that, to the best of the authors’ knowledge, this is the first attempt at studying the suitability of an FRI where the operations come from a non-residuated structure. Keywords—Bandler-Kohout Subproduct, Fuzzy implications, f implications, g-implications, Relational Inference, Interpolativity, Continuity and Robustness of inference.