On Direct Product of a Fuzzy Subgroup with an Anti-fuzzy Subgroup
Sudipta Gayen1, Sripati Jha2, Manoranjan Singh3
1Sudipta Gayen, Department of Mathematics, National Institute of Technology Jamshedpur , India.
2Sripati Jha, Department of Mathematics, National Institute of Technology Jamshedpur , India.
3Manoranjan Singh, Department of Mathematics, Magadh University, Bodhgaya, Gaya, India.
Manuscript received on 09 March 2019 | Revised Manuscript received on 16 March 2019 | Manuscript published on 30 July 2019 | PP: 1105-1111 | Volume-8 Issue-2, July 2019 | Retrieval Number: B1502078219/19©BEIESP | DOI: 10.35940/ijrte.B1502.078219
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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 introduced and analysed some new refreshing concepts in the field of fuzzy abstract algebra. The main contributions of this paper are fivefold: (1) we have introduced the notion of dual-fuzzy subgroup, (2) we have defined the direct product of a fuzzy subgroup with an anti-fuzzy subgroup, (3) Furthermore, we have defined mixed level subset and mixed level subgroup, (4) we have also developed some new theories as well as propositions based on these newly defined notions and lastly (5) we have redefined these notions using general T-norm and T* conorm.
Index Terms: Fuzzy Subgroup, Anti-Fuzzy Subgroup, Dual Fuzzy Subgroup, Mixed Level Subgroup.
Scope of the Article: Fuzzy Logics