On fuzzy pre-I-open sets and a decomposition of fuzzy I-continuity

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and E-infinity space time theory. In this paper, we introduce and study the notion of fuzzy pre-I-open sets, which is properly placed between fuzzy openness and fuzzy pre-openness regardless the fuzzy topological ideal. Moreover, we give a decomposition of fuzzy I-continuity by proving that a function f : (X, τ, I) → (Y, σ) is fuzzy I-continuous if and only if it is fuzzy pre-I-continuous and fuzzy ∗-I-continuous.