On a generalized notion of anti-fuzzy subgroup and some characterizations

Abstract

We have presented a new notion of anti-fuzzy subgroup (AFS). For this, we have considered general t-conorm. The main contributions of this paper are fourfold: (1) we have proposed a new notion of anti-fuzzy subgroup (AFS), (2) we have also defined infimum image of a fuzzy set, (3) Furthermore, we have defined subgroup generated anti-fuzzy subgroup (SGAFS), function generated anti-fuzzy subgroup (FGAFS) and (4) we have shown that an AFS proposed earlier belong to a special class of subgroup generated anti-fuzzy subgroup (SGAFS). To justify our proposed notion we have discussed some drawbacks of the existing notion of AFS with numerical examples. Finally, we have concluded that our proposed notion is superior to the existing one.