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InterCriteria Analysis applied to the Turkish Health and Social Protection datasets
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Zlatko Yordanov, Veselina Bureva and Cengiz Kahraman
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56—64
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number = 5
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title =
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http://ifigenia.org/wiki/issue:nifs/29/1/65-73
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| Title of paper:
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On intuitionistic L-fuzzy socle of modules
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| Author(s):
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| P. K. Sharma
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| Post-Graduate Department of Mathematics, D.A.V. College, Jalandhar, Punjab, India
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| pksharma@davjalandhar.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 29 (2023), Number 1, pages 65–73
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| DOI:
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https://doi.org/10.7546/nifs.2023.29.1.65-73
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| Download:
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 PDF (239 Kb, File info)
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| Abstract:
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In this paper we try to study the intuitionistic 𝐿-fuzzy aspects of socle of modules over rings. We demonstrate some properties of a socle of intuitionistic 𝐿-fuzzy submodules and their relations with intuitionistic 𝐿-fuzzy essential submodules and a family of intuitionistic 𝐿-fuzzy complemented submodules of a module. Some related results are also established.
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| Keywords:
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Intuitionistic 𝐿-fuzzy submodule, Intuitionistic 𝐿-fuzzy simple submodule, Intuitionistic 𝐿-fuzzy essential submodule, Socle of an intuitionistic 𝐿-fuzzy submodule.
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| AMS Classification:
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08A72, 03F55, 16D10, 16D60.
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| References:
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- Anderson, F. W., & Fuller, K. R. (1992). Rings and Categories of Modules. 2nd edition. Springer Verlag.
- Atanassov, K. (1983). Intuitionistic fuzzy sets. VII ITKR Session, Sofia, 20–23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
- Atanassov, K., & Stoeva, S. (1984). Intuitionistic 𝐿-fuzzy sets. Cybernetics and System Research, Vol. 2. Elsevier Sci. Publ., Amsterdam, 539–540.
- Birkhoff, G. (1967). Lattice Theory. American Mathematical Society, Col. Pub., Providence.
- Deschrijver, G., & Kerre, E. E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133, 227–235.
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- Kanchan, Sharma, P. K., & Pathania, D. S. (2020). Intuitionistic 𝐿-fuzzy submodules. Advances in Fuzzy Sets and Systems, 25(2), 123–142.
- Kasch, F. (1982). Modules and Rings. Academic Press, London.
- Meena, K., & Thomas, K. V. (2011). Intuitionistic 𝐿-fuzzy subrings. International Mathematics Forum, 6(52), 2561–2572.
- Palaniappan, N., Naganathan, S., & Arjunan, K. (2009). A study on intuitionistic 𝐿-fuzzy subgroups. Applied Mathematics Sciences, 3(53), 2619–2624.
- Sharma, P. K., & Kanchan. (2018). On intuitionistic 𝐿-fuzzy prime submodules. Annals of Fuzzy Mathematics and Informatics, 16(1), 87–97.
- Sharma, P. K., & Kanchan. (2020). On intuitionistic 𝐿-fuzzy primary and 𝑃-primary submodules. Malaya Journal of Matematik, 8(4), 1417–1426.
- Sharma, P. K., Kanchan, & Pathania, D. S. (2021). Intuitionistic 𝐿-fuzzy essential and closed submodules. Notes on Intuitionistic Fuzzy Sets, 27(4), 44–54.
- Sharma, P. K., Kanchan, & Pathania, D. S. (2021). Simple and semi-simple intuitionistic 𝐿-fuzzy modules. 7th International Conference on IFS and Contemporary Mathematics, May 25–29, 2021, Turkey.
- Wang, G. J., & He, Y. Y. (2000). Intuitionistic fuzzy sets and 𝐿-fuzzy sets. Fuzzy Sets and Systems, 110, 271–274.
- Wisbauer, R. (1991). Foundations of Module and Ring Theory. Gordon and Breach, Philadelphia.
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