Main Article Content
Abstract
Purpose of the study: To develop (λ, μ) - anti fuzzy subgroup of a group.
Methodology: The fundamental idea of (λ, μ) - anti fuzzy subgroup to create a (λ, μ)- multi anti fuzzy subgroup.
Main Findings: (λ, μ) – multi anti fuzzy cosets of a group.
Applications of this study: The advancement of the theory of a group's multiple fuzzy subgroups.
Novelty/Originality of this study: The concept of (λ, μ) - multi anti fuzzy cosets of a group has been defined, and various associated theorems have been demonstrated using examples.
Keywords
Article Details
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References
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- Atanassov, K.T.(1994). New operation defined Over the intuitionistic fuzzy sets. Fuzzy sets and fuzzy systems, 61(2), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1 DOI: https://doi.org/10.1016/0165-0114(94)90229-1
- Balasubramanian, K.R., Revathy, R and Rajangam,.R.(2021). (ðœ†, ðœ‡)-multi fuzzy subgroups of a group. Turkish Journal of computer and Mathematical Education, 12(11), 6148 -6160.
- Basnet, D.K. & Sarma, N.K.(2010). A note on Intuitionistic Fuzzy Equivalence Relation. International Mathematical Forum, 5(67), 3301-3307.
- Biswas, R.(2006). Vague Groups. International Journal of Computational Cognition, 4(2), 20-23.
- Feng, Y. and Yao, B.(2012). On (λ, μ)-anti-fuzzy subgroups. Feng and Yao Journal of Inequalities and Applications, 2012, 78. https://doi.org/10.1186/1029-242X-2012-78 DOI: https://doi.org/10.1186/1029-242X-2012-78
- Goguen, J.A.(1967). L-fuzzy set. Journal of Mathematical analysis and Applications, 18, 145-174. https://doi.org/10.1016/0022-247X(67)90189-8 DOI: https://doi.org/10.1016/0022-247X(67)90189-8
- Mukharjee, N. P. and Bhattacharya, P.(1984). Fuzzy Normal Subgroups and Fuzzy Cosets. Information Sciences, 34(3), 225-239. https://doi.org/10.1016/0020-0255(84)90050-1 DOI: https://doi.org/10.1016/0020-0255(84)90050-1
- Muthuraj, R. and Balamurugan, S.(2013). Multi Anti Fuzzy Group and its Lower level Subgroup. Gen. Math. Notes, 17(1), 74-81.
- Muthuraj, R. and Balamurugan, S.(2014). A Study on Intuitionistic Multi Anti Fuzzy Subgroups. Applied Mathematics and Sciences: An International Journal, 1(2).
- Rosenfeld, A.(1971). Fuzzy Group. Journal Of Mathematical Analysis and Applications, 3, 12-17. DOI: https://doi.org/10.1016/0022-247X(71)90199-5
- Sabu, S. and Ramakrishnan, T.V.(2011a). Multi-Fuzzy Topology. International Journal of Applied Mathematics, 24(1), 117-129.
- Sabu, S., Ramakrishnan, T.V.(2010). Multi Fuzzy Sets. International Mathematical Forum, 50, 2471-2476.
- Sabu, S., Ramakrishnan, T.V.(2011b). Multi Fuzzy SubGroup. Int. J. Contemp. Math. Sciences, 6(8), 365-372.
- Shen, Z.(1995). The anti-fuzzy subgroup of a group. J Liaoning Normat Univ (Nat Sci), 18(2), 99–101....
- Sinoj, T.K. and Sunil, J.J.(2013). Intuitionistic Fuzzy Multi-Sets. International Journal of Engineering Sciences and Innovaive Technology, 2(6),1-24.
- Yao, B.(2005). (λ, μ)-fuzzy normal subgroups and (λ, μ)-fuzzy quotient subgroups. Journal of Fuzzy Mathematics, 13(3), 695 – 705.
- Yuan, X., Zhang, C., and Ren, Y.(2003). Generalized fuzzy groups and many-valued implications. Fuzzy Sets Syst., 138, 205–211. https://doi.org/10.1016/S0165-0114(02)00443-8 DOI: https://doi.org/10.1016/S0165-0114(02)00443-8
- Zadeh, L.A.(1965). Fuzzy set. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
References
Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and fuzzy systems, 20(1), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3 DOI: https://doi.org/10.1016/S0165-0114(86)80034-3
Atanassov, K.T.(1994). New operation defined Over the intuitionistic fuzzy sets. Fuzzy sets and fuzzy systems, 61(2), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1 DOI: https://doi.org/10.1016/0165-0114(94)90229-1
Balasubramanian, K.R., Revathy, R and Rajangam,.R.(2021). (ðœ†, ðœ‡)-multi fuzzy subgroups of a group. Turkish Journal of computer and Mathematical Education, 12(11), 6148 -6160.
Basnet, D.K. & Sarma, N.K.(2010). A note on Intuitionistic Fuzzy Equivalence Relation. International Mathematical Forum, 5(67), 3301-3307.
Biswas, R.(2006). Vague Groups. International Journal of Computational Cognition, 4(2), 20-23.
Feng, Y. and Yao, B.(2012). On (λ, μ)-anti-fuzzy subgroups. Feng and Yao Journal of Inequalities and Applications, 2012, 78. https://doi.org/10.1186/1029-242X-2012-78 DOI: https://doi.org/10.1186/1029-242X-2012-78
Goguen, J.A.(1967). L-fuzzy set. Journal of Mathematical analysis and Applications, 18, 145-174. https://doi.org/10.1016/0022-247X(67)90189-8 DOI: https://doi.org/10.1016/0022-247X(67)90189-8
Mukharjee, N. P. and Bhattacharya, P.(1984). Fuzzy Normal Subgroups and Fuzzy Cosets. Information Sciences, 34(3), 225-239. https://doi.org/10.1016/0020-0255(84)90050-1 DOI: https://doi.org/10.1016/0020-0255(84)90050-1
Muthuraj, R. and Balamurugan, S.(2013). Multi Anti Fuzzy Group and its Lower level Subgroup. Gen. Math. Notes, 17(1), 74-81.
Muthuraj, R. and Balamurugan, S.(2014). A Study on Intuitionistic Multi Anti Fuzzy Subgroups. Applied Mathematics and Sciences: An International Journal, 1(2).
Rosenfeld, A.(1971). Fuzzy Group. Journal Of Mathematical Analysis and Applications, 3, 12-17. DOI: https://doi.org/10.1016/0022-247X(71)90199-5
Sabu, S. and Ramakrishnan, T.V.(2011a). Multi-Fuzzy Topology. International Journal of Applied Mathematics, 24(1), 117-129.
Sabu, S., Ramakrishnan, T.V.(2010). Multi Fuzzy Sets. International Mathematical Forum, 50, 2471-2476.
Sabu, S., Ramakrishnan, T.V.(2011b). Multi Fuzzy SubGroup. Int. J. Contemp. Math. Sciences, 6(8), 365-372.
Shen, Z.(1995). The anti-fuzzy subgroup of a group. J Liaoning Normat Univ (Nat Sci), 18(2), 99–101....
Sinoj, T.K. and Sunil, J.J.(2013). Intuitionistic Fuzzy Multi-Sets. International Journal of Engineering Sciences and Innovaive Technology, 2(6),1-24.
Yao, B.(2005). (λ, μ)-fuzzy normal subgroups and (λ, μ)-fuzzy quotient subgroups. Journal of Fuzzy Mathematics, 13(3), 695 – 705.
Yuan, X., Zhang, C., and Ren, Y.(2003). Generalized fuzzy groups and many-valued implications. Fuzzy Sets Syst., 138, 205–211. https://doi.org/10.1016/S0165-0114(02)00443-8 DOI: https://doi.org/10.1016/S0165-0114(02)00443-8
Zadeh, L.A.(1965). Fuzzy set. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X DOI: https://doi.org/10.1016/S0019-9958(65)90241-X