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

Year 2024, Volume: 9 Issue: 1, 23 - 32, 30.04.2024

Natnael Amare

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.

Keywords

Almost distributive lattice (ADL), fuzzy filter, prime fuzzy filter, minimal prime fuzzy filter, fuzzy prime filter and fuzzy minimal prime filter

Supporting Institution

No support received.

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.