Abstract
We introduce here the notion of 1. (i) a fuzzy normal subgroup and 2. (ii) a fuzzy coset. We prove that for a group G, a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of G. Further, we show that the level subgroups of a fuzzy normal subgroup are all normal. We obtain several results which are analogs of some basic theorems of group theory. In particular, a fuzzy version of Lagrange's theorem is established.
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