On a Generalized Notion of Anti-fuzzy Subgroup and Some Characterizations
Sudipta Gayen1, Sripati Jha2, Manoranjan Singh3, Ranjan Kumar4
1Sudipta Gayen, Department of Mathematics, National Institute of Technology, Jamshedpur (Jharkhand), India.
2Sripati Jha, Department of Mathematics, National Institute of Technology, Jamshedpur (Jharkhand), India.
3Manoranjan Singh, Department of Mathematics, Magadh University, Bodhgaya, Gaya (Bihar), India.
4Ranjan Kumar, Department of Mathematics, National Institute of Technology, Jamshedpur (Jharkhand), India.
Manuscript received on 18 February 2019 | Revised Manuscript received on 27 February 2019 | Manuscript published on 28 February 2019 | PP: 385-390 | Volume-8 Issue-3, February 2019 | Retrieval Number: C5933028319/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Infimum Image; Subgroup Generated Anti-Fuzzy Subgroup; Function Generated Anti-Fuzzy Subgroup.
Scope of the Article: Image Processing