Filters of interval-valued residuated lattices

An important concept in the theory of residuated lattices and other algebraical structures used for formal fuzzy logic, is that of a filter. Filters can be used, amongst others, to define congruence relations. Specific kinds of filters include Boolean filters and prime filters. In this paper, we define several different filters of interval-valued residuated lattices and examine their mutual dependencies and connections. We also show that these filters are determined by their intersection with the set of exact elements, i.e., the intervals consisting of precisely one element