Interval-valued fuzzy logical connectives with respect to admissible orders

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 $K_{\alpha,\beta}$ orders and arbitrary intervals on $L([0, 1])$. We also make a discussion of width-preserving interval-valued fuzzy equivalence functions and fuzzy 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.