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The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies with fuzzy transform. It is shown here that the fuzzy transform can be viewed as fuzzy approximation operators studied in the operator-oriented view of fuzzy rough set theory and the use of fuzzy rough set results reduces efforts in proving fuzzy transform theoretic results. We present a glimpse that fuzzy topological results can also be used in similar fashion for fuzzy transform theoretical results.

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Abstract. This work is an introductory investigation, on the lines of [9] and [10], into some topological aspects of fuzzy machines (studied in [4][5][6][7][8]), wherein we introduce a topology on the state-set of a fuzzy automaton and use it, together with some standard topological results, to deduce some fuzzy automata theoretic results given in [4][5][6][7][8].