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A modified version of the concept of generated fuzzy subgroups by an arbitrary fuzzy set is presented in this paper. A corrected proof of a theorem due to Kumar (Fuzzy Sets and Systems 48 (1992) 267-271) is also provided. A counterexample is constructed to show that the arguments used by Kumar in his proof of the theorem are false.
This is a continuation of work in previous papers [N. Ajmal and K.V. Thomas, Fuzzy Sets and Systems 58 (1993) 217; Inform. Sci. 76 (1994) 1]. Here, we provide a common technique of constructing the join of fuzzy substructures. Consequently, it leads to the formation of various types of lattices and sublattices of fuzzy substructures of a group including those of normal and quasinormal fuzzy subgroups...
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