L-fuzzy ideals of Semilattices

Ch. Santhi Sundar Raj; B. Subrahmanyam; G. Sujatha; S. Nageswara Rao

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P520

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P520

L-fuzzy ideals of Semilattices

Ch. Santhi Sundar Raj, B. Subrahmanyam, G. Sujatha, S. Nageswara Rao

Abstract

In this paper the notion of an L-fuzzy ideal of a semilattice is introduced and proved certain important structural properties of these. 0-distributive semilattices are characterized in terms of L-fuzzy ideals and prime L-fuzzy filters. The Stones’s version separation theorem on prime filters of distributive semilattices is extended to prime L-fuzzy filters. Furthermore, the notions of prime(maximal) L-fuzzy ideals of bounded semilattices are introduced and characterized.

Keywords

0-distributive semilattice; L-fuzzy ideal; L-fuzzy filter; prime L-fuzzy filter; prime L-fuzzy ideal; frame; meet-prime element.

References

[1] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512-517.
[2] Ch.S. Sundar Raj, B. Subrahmanyam and U. M. Swamy, Fuzzy Filters of Meet-Semilattices, Int.J.Math. And Appl. 7(3)(2019) 67-76.
[3] Ch.S. Sundar Raj, B. Subrahmanyam and U. M. Swamy, Prime L-fuzzy Filters of a Semilattice, Annals of Fuzzy Mathematics and Informatics, Accepted 17 April 2020.
[4] Ch.S. Sundar Raj, T.A. Natnael and U.M. Swamy, Fuzzy Prime Ideals of ADLs, International Journal of Computing Science and Applied Mathematics 4 (2018) 32-36.
[5] D.S. Malik and Mordeson, Extensions of fuzzy subrings and fuzzy ideals, Fuzzy Sets Systems 45 (1992) 245-251.
[6] G. Gratzer, General Lattice Theory, Academic press, Newyork, 1978.
[7] G. Gratzer and E.T. Schmidt, On congrunce of lattices, Acta Math. Acad. Sci. Hungari 13 (1962) 179-185.
[8] J.C. Varlet, A generalization of the notion of pseudocomplementedness, Bull. Soc. Roy. Liege 36 (1968) 149-158.
[9] J.C. Varlet, Distributive Semilattices and Boolean lattices, Bull. Soc. Roy. Liege 41 (1972) 5-10.
[10] L.A.Zadesh, Fuzzy sets, Inform. and Control 8 (1965) 338-353.
[11] N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets Systems 5 (1981) 203-215. 15
[12] T. K. Mukherjee and M.K. Sen, On fuzzy ideals of a ring (I), Fuzzy Sets and Systems 21 (1987) 99-104.
[13] U.M. Swamy and D.V. Raju, Algebraic fuzzy systems, Fuzzy Sets and Systems 41 (1991) 187-194.
[14] U.M. Swamy and D.V. Raju, Fuzzy ideals and congruences of lattices, Fuzzy Sets and Systems 95 (1998) 249-253.
[15] U.M. Swamy and D.V. Raju, Irreducibility in algebraic fuzzy systems, Fuzzy Sets and Systems 41 (1991) 233-241.
[16] U.M. Swamy and K.L.N. Swamy, Fuzzy Prime Ideals of Rings, J. Math. Anal. Appl. 134 (1988) 94-103.
[17] W.J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems 8 (1982) 133-139.
[18] Y.S. Pawar and N.K. Thakare, 0-Distributive Semilattices, Canad. Math. Bull. 21(4) 1978.

Citation :

Ch. Santhi Sundar Raj, B. Subrahmanyam, G. Sujatha, S. Nageswara Rao, "L-fuzzy ideals of Semilattices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 160-175, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P520