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The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice

Year 2024, , 23 - 32, 30.04.2024
https://doi.org/10.30931/jetas.1443272

Abstract

In this paper, we establish and describe the notions of fuzzy minimal prime filters of an Almost Distributive Lattice (ADL). We prove that a fuzzy filter is the point wise infimum of all minimal prime fuzzy filters (all fuzzy minimal prime filters) of an ADL. Mainly, we introduce the topological space on the set of all fuzzy minimal prime filters of an ADL (denoted by M(R)). For an ADL R, we prove that an open set M(R) is a base for the topology and it constitutes a base for the subspace topology on a closed set N and they are the only compact open sets.

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Thanks

I thank you all Mathematics Professors.

References

  • [1] Goguen, J.A.,"L-fuzzy sets", J. Math. Anal. Appl. 18 (1967) : 145–174.
  • [2] Liu, W.J., "Fuzzy invariant subgroups and fuzzy ideals", Fuzzy set and systems 8 (1982) : 133-139.
  • [3] Ming, H.C., "Fuzzy Topological Space", J. Math. Anal. Appl, 110 (1985) : 141-178.
  • [4] Natnael Teshale, A., "Weakly 2-absorbing filters in ADLs", Advances in Dynamical Systems and Applications 17 (2) (2022) : 483-496.
  • [5] Swamy, U.M., Santhi Sundar Raj, Ch.,A. Natnael Teshale, A., "L-fuzzy filters of almost distributive lattices", International Journal of Mathematics and Soft Computing 8 (1) (2018) : 35-43.
  • [6] Santhi Sundar Raj, Ch., Natnael Teshale, A., Swamy, U.M., "Prime and maximal fuzzy filters of ADLs", Palestine Journal of Mathematics 3 (1) (2019) : 1-10.
  • [7] Swamy, U.M., Rao, G.C., "Almost distributive lattices", J. Australian Math. Soc., (Series A) 31 (1981) : 77-91.
  • [8] Zadeh, L.A.," Fuzzy set", Inform and control 8 (1965) : 338-353.
Year 2024, , 23 - 32, 30.04.2024
https://doi.org/10.30931/jetas.1443272

Abstract

References

  • [1] Goguen, J.A.,"L-fuzzy sets", J. Math. Anal. Appl. 18 (1967) : 145–174.
  • [2] Liu, W.J., "Fuzzy invariant subgroups and fuzzy ideals", Fuzzy set and systems 8 (1982) : 133-139.
  • [3] Ming, H.C., "Fuzzy Topological Space", J. Math. Anal. Appl, 110 (1985) : 141-178.
  • [4] Natnael Teshale, A., "Weakly 2-absorbing filters in ADLs", Advances in Dynamical Systems and Applications 17 (2) (2022) : 483-496.
  • [5] Swamy, U.M., Santhi Sundar Raj, Ch.,A. Natnael Teshale, A., "L-fuzzy filters of almost distributive lattices", International Journal of Mathematics and Soft Computing 8 (1) (2018) : 35-43.
  • [6] Santhi Sundar Raj, Ch., Natnael Teshale, A., Swamy, U.M., "Prime and maximal fuzzy filters of ADLs", Palestine Journal of Mathematics 3 (1) (2019) : 1-10.
  • [7] Swamy, U.M., Rao, G.C., "Almost distributive lattices", J. Australian Math. Soc., (Series A) 31 (1981) : 77-91.
  • [8] Zadeh, L.A.," Fuzzy set", Inform and control 8 (1965) : 338-353.
There are 8 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Research Article
Authors

Natnael Amare 0000-0001-5771-0757

Early Pub Date April 29, 2024
Publication Date April 30, 2024
Submission Date February 27, 2024
Acceptance Date April 9, 2024
Published in Issue Year 2024

Cite

APA Amare, N. (2024). The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice. Journal of Engineering Technology and Applied Sciences, 9(1), 23-32. https://doi.org/10.30931/jetas.1443272
AMA Amare N. The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice. JETAS. April 2024;9(1):23-32. doi:10.30931/jetas.1443272
Chicago Amare, Natnael. “The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice”. Journal of Engineering Technology and Applied Sciences 9, no. 1 (April 2024): 23-32. https://doi.org/10.30931/jetas.1443272.
EndNote Amare N (April 1, 2024) The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice. Journal of Engineering Technology and Applied Sciences 9 1 23–32.
IEEE N. Amare, “The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice”, JETAS, vol. 9, no. 1, pp. 23–32, 2024, doi: 10.30931/jetas.1443272.
ISNAD Amare, Natnael. “The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice”. Journal of Engineering Technology and Applied Sciences 9/1 (April 2024), 23-32. https://doi.org/10.30931/jetas.1443272.
JAMA Amare N. The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice. JETAS. 2024;9:23–32.
MLA Amare, Natnael. “The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice”. Journal of Engineering Technology and Applied Sciences, vol. 9, no. 1, 2024, pp. 23-32, doi:10.30931/jetas.1443272.
Vancouver Amare N. The Space of Fuzzy Minimal Prime Filters In an Almost Distributive Lattice. JETAS. 2024;9(1):23-32.