On strict lower and upper sections of weakly complete fuzzy pre-orders based on co-implication

Fono and Gwét [On strict lower and upper sections of fuzzy orderings, Fuzzy Sets and Systems 139 (2003) 583–599] introduced and studied strict lower section, strict upper section and strict order interval of a given weakly complete fuzzy pre-order R when the minimal regular fuzzy strict component of R is defined by the residual coimplicator of the Łukasiewicz t-conorm. And they gave an example of application of fuzzy strict lower sections in economics. In this paper, we generalize their framework for the minimal regular fuzzy strict component of R defined by the residual complicator of a continuous t-conorm. We show that fuzzy strict sections and fuzzy strict order intervals, defined in this general case, generate fuzzy topologies.