Following the introduction of fuzzy sets in 1965, a notion of fuzzy topological group was proposed by Foster in 1979: essentially he took a group and furnished it with a fuzzy topological structure. An equivalent notion of fuzzy topological group was introduced by Ma and Yu in 1984 by replacing points by fuzzy points. Recently two of the coauthors have introduced the notion of the topology induced on the set of all fuzzy singletons by the fuzzy topology. In this paper we extend the notion of fuzzy topological group by allowing the points of our strong fuzzy topological groups to be fuzzy singletons of a given group and using the induced topology. We study properties of strong fuzzy topological groups, analysing such entities as its connection with the previous notions, subgroups, images and products of strong fuzzy topological groups.
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