Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openn...

Neuro-fuzzy systems-the combination of artiicial neural networks with fuzzy logic-are becoming increasingly popular. However, neuro-fuzzy systems need to be extended for applications which require context (e.g., speech, handwriting, control). Some of these applications can be modeled in the form of nite-state automata. Previously, it was proved that deterministic nite-state automata (DFAs) can ...