Abstract
Fuzzy ideal set and fuzzy local function of fuzzy ideals with fuzzy topologies were introduced and studied by D. Sarker [10]. The purpose of this paper deals with new sort of fuzzy ideal and fuzzy local function namely fuzzy ideal and r-fuzzy open local function. Many of its characterizations, properties and connections between it and other corresponding fuzzy notions are studied. Also, we introduce r-fuzzy idealcompact, r-fuzzy ideal quasi H-closed and r-fuzzy compact modulo an fuzzy ideal in fuzzy ideal topological space in view of the definition of ˆ Sostak, and study some of their properties. Also, we investigate the behavior of r-fuzzy ideal-compact under several types of F-continuous mappings. In the last section, we define r-fuzzy I-open, r-fuzzy I-closed and F I-continuous. Also, we investigate some of their properties and the relationships between F-continuous and F I-continuous maps.
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