L - Fuzzy Almost Ideals

P.Veerammal; G.Velammal

doi:https://doi.org/10.14445/22315373/IJMTT-V50P537

International Journal of Mathematics Trends and Technology

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Volume 50 | Number 4 | Year 2017 | Article Id. IJMTT-V50P537 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P537

L - Fuzzy Almost Ideals

P.Veerammal, G.Velammal

Abstract

We consider L-Fuzzy Sets where the membership values do not necessarily form a chain. In this general setting we introduce the concept of L-Fuzzy Almost Ideals. So far L-Fuzzy Ideals have been well studied in the case where L is a distributive lattice. In this paper, we show that the natural extension of concept of L-Fuzzy Ideals to the case when L is not necessarily distributive is that of L- Fuzzy Almost Ideals.

Keywords

L-Fuzzy Sets, Fuzzy Ideals, L-Fuzzy Ideals, L-Fuzzy Almost Ideals, Non-Distributive lattice, Level set and Almost Level Set.

References

[1] J.A Goguen, L-fuzzy sets, J.Math. Anal. Appl, 1967 no.(145- 174).
[2] B.B.N.Koguep, G.Nkuimi and C.Lelevarro, On Fuzzy Prime Ideals of Lattices, AMSA Journal of Pure and Applied Mathematics, Vol.3, 2008, (1-11).
[3] Lehmke.S, Some properties of Fuzzy Ideals on a Lattice, proc. of the 6th IEEE Int. Conf. on Fuzzy Systems, Vol.2, 1997, (813-818).
[4] F.J.Lobillo, O.Cortadellas and G.Navarro, Prime Fuzzy Ideals over Non-commutative Rings, X journals de Teoria de Anillos, June15, 2012.
[5] T.K. Mukhejee and M.K.Sen, On Fuzzy Ideals of a Ring I, Fuzzy sets and Systems, Vol.21,1987, (99-104).
[6] Mohammed M. Atallah, On the L-Fuzzy Prime ideal Theorem of Distributive Lattices, The Journal of Fuzzy Mathematics, Vol.9, 2001, no.4 (825-831).
[7] Rajesh Kumar, Prime Fuzzy ideals over non-commutative rings, Fuzzy sets and systems, Vol.199, 2012, no.(108-120).
[8] Rajesh Kumar, Non- Distributivity of the lattice of Fuzzy ideals of a ring, Fuzzy Sets and Systems, Vol.97, 1998, no (393- 394).
[9] U.M. Swamy and K.L.N. Swamy, Fuzzy Prime Ideals of Rings, Journal of Mathematical Analysis and Applications, Vol.14, 1998, (94-103).
[10] Wang - Jin Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, Vol.8, 1982, (133-139).
[11] L.A. Zadeh, Fuzzy sets, Information and Control, Vol.8, 1965, (338-353).
[12] Zhang Yue, Prime L-Fuzzy Ideals and Primary L-Fuzzy Ideals. Fuzzy sets and systems, Vol.27, 1998, no.(345-350).
[13] M.M.Zahedi, A characterization of L-fuzzy prime ideals, Fuzzy Sets and Systems, Vol.44, 1991, no.(147-160).

Citation :

P.Veerammal, G.Velammal, "L - Fuzzy Almost Ideals," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 4, pp. 228-230, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P537