Interpolativity of “at Least–at Most” Models of Monotone Fuzzy Rule Bases: Multiple-input Case

Among the many desirable properties of fuzzy inference systems not all of them are known to co-exist. For instance, a system based on a monotone fuzzy rule base need not be monotonic and interpolative simultaneously. Recently, Štěpnička and De Baets have investigated and shown the co-existence of the above two properties in the case of a fuzzy relational inference systems and the single-input-single-output (SISO) rule bases. An extension of these results to the multiple-input-single-output (MISO) case is not straight-forward owing to the lack of a natural ordering in higher dimensions. In this work, we study the MISO case and show that similar results are available when the monotone rule base is modeled based on at-most and at-least modifiers.