Abstract
The notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting. Adopting fuzzy net-theoretic approach, various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied. A category of fuzzy topological spaces is constructed. Canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by Rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity. In the process, N-compactness is characterized and fuzzy unit interval is shown to be N-compact. Also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous.
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