Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions

The aim of this paper is to introduce the dual notion of interval conjugate implications, the interval coimplications, as interval representations of corresponding conjugate fuzzy coimplications. Using the canonical representation, this paper considers both the correctness and the optimality criteria, in order to provide interpretation for fuzzy coimplications as the non-truth degree of conditional rule in expert systems and study the action of interval automorphisms on such interval fuzzy connectives. It is proved that interval automorphisms acting on N-dual interval coimplications preserve the main properties of interval implications discussed in the literature including the duality principle. Lastly, the action of interval automorphisms on interval classes of border, model and S-coimplications are considered, summarized in commutative diagrams. (C) 2013 Elsevier Inc. All rights reserved.