Interval-valued fuzzy logical connectives with respect to admissible orders

Interval-valued fuzzy logical connectives are extensions of fuzzy logical connectives to the interval-valued framework. The extensions require linear orders to define the monotonicity between intervals. As a significant linear order, the admissible order is introduced to compare any interval in interval-valued fuzzy logic. In this work, we examine several widely-used interval-valued fuzzy logical connectives with respect to admissible orders. We are concerned with interval- valued fuzzy negations, automorphisms, fuzzy implications and aggregation functions with respect to Kα,β orders and arbitrary intervals on L([0, 1]). We also make a discussion of width-preserving interval-valued fuzzy equivalence functions and dissimilarity functions with respect to arbitrary admissible orders and the intervals with the same width on L([0, 1]). Then we bring some approaches to constructing the proposed interval-valued fuzzy logical connectives with respect to admissible orders. The introduced interval-valued fuzzy logical connectives with respect to admissible orders may have a deep impact on some fields exploiting fuzzy methods dealing with intervals.