On Interval-Valued Fuzzy on Ideal Sets

Fuzzy sets, formalized by Zadeh in 1965, generalizes the classical idea of sets. The idea itself was generalized in 1975 when Zadeh introduced the interval-valued fuzzy sets. In this paper, we generalize further the above concepts by introducing interval-valued fuzzy on ideal sets, where an ideal is a nonempty collection of sets with a property describing the notion of smallness. We develop its basic concepts and properties and consider how one can create mappings of interval-valued fuzzy on ideal sets from mappings of ordinary sets. We then consider topology and continuity with respect to these sets.