Further results on L-valued filters

In this paper, we explore the behavior with respect to direct and inverse images of the relations between the different generalizations of filter notion studied in [Gutiérrez García J, de Prada Vicente MA. Characteristic values of ⊤-filters. Fuzzy Sets Syst 2005;56:55-67]. Also, we give sufficient conditions for the existence of an upper bound for those generalizations of filters.