An Approach to Interval-Valued R-Implications and Automorphisms

The aim of this work is to introduce an approach for interval-valued R-implications, which satisfy some analogous properties of R-implications. We show that the best interval representation of an R-implication that is obtained from a left continuous tnorm coincides with the interval-valued R-implication obtained from the best interval representation of such t-norm, whenever this is an inclusion monotonic interval function. This provides, under this condition, a nice characterization for the best interval representation of an R-implication, which is also an interval-valued R-implication. We also introduce interval-valued automorphisms as the best interval representations of automorphisms. It is shown that interval automorphisms act on interval R-implications, generating other interval Rimplications. Keywords— Interval-valued fuzzy logic, R-implications, automorphisms, interval representations.