Interval R-Sheffer strokes and interval fuzzy Sheffer strokes endowed with admissible orders

Fuzzy Sheffer stroke is a new class of fuzzy connectives introduced by Baczynski et al., which generalizes the Sheffer stroke operation in classical logic. However, the investigation on interval extensions of fuzzy Sheffer strokes is still missing in the literature. To fill this gap, in this paper, we introduce two interval generalizations of fuzzy Sheffer strokes. Firstly, we propose the notion of interval R-Sheffer strokes based on interval directional monotonicity, studying their properties, characterization, representability and constructions. And then, we introduce the concept of interval fuzzy Sheffer strokes endowed with admissible orders. In particular, we present and compare three construction methods for interval fuzzy Sheffer strokes with respect to orders.