On L-fuzzy ideals of multilattices

Document Type : Research Paper

Authors

Department of Mathematics and Computer Science, University of Dschang, P.O.Box 67, Dschang, Cameroon

Abstract

For a given multilattice M, the set ℑM of all ideals of M is a complete lattice and for a given complete lattice L, the set FI(M;L) of all L-fuzzy ideals ofMis also a complete lattice. The aim of this paper is to characterize L􀀀fuzzy ideals of multilattice and highlight some of their properties based on the Duality Principle. We establish that FI(M;L) is isomorphic to Hom(L∂; ℑM) where L∂ is the dual of L. Since multilattices generalize lattices, the results remain true for L-fuzzy ideals of lattices.

Keywords

References

[1] M. Benado, Les ensembles partiellement ordonns et le Thorme de raffnement de scheier, II.Thorie des multistructures, Czechoslovak Mathematical Journal, 5(80)(1955)308-344.
[2] G. Birkho , Lattice Theory, Colloquium Publications, Amer. Math. Soc., 25 (1967).
[3] I. P. Cabrera, P. Cordero, G. Gutierrez, J. Martnez, M. Ojeda-Aciego, On residuation in multilattices:  lters, congruences, and homomorphisms, Fuzzy sets and systems, 234(1) (2014)1-21.
[4] B. A. Davey, Introduction to lattices theory, Cambridge University press, (1990).
[5] B. B. Koguep Njionou, C. Nkuimi, C. Lele, On fuzzy prime ideals of lattice, SAMSA J. Pure Appl. Math., 3 (2008) 1-11.
[6] S. Lehmke, Some properties of fuzzy ideals on a lattice, Fuzzy-IEEE, 97 (1997)813-818.
[7] A. Maheswari, Member, IACSIT, M. Palanivelrajan, Introduction to Intuitionistic L-fuzzy Semi Filter (ILFSF) of Lattices, International Journal of Machine Learning and Computing, 2 (6) (2012)738-740.
[8] D. S. Malik, Fuzzy maximal, radical, and primary ideals of a ring, Inf. Sci., 53(1991)237-250.
[9] J. Martnez, G. Guetierrez, I. P. de Guzman, P. Cordero, Generalization of lattices via non-dterministic operators, Discrete Math., 295(1-3) (2005) 107-141.
[10] O. Klaucova, Characterization of multilattices by a betweeness relation, Math.Slov., 26(2) (1976) 119-129.
[11] U. M. Swamy, D. Viswanadha Raju, Fuzzy ideals and congruences of lattices,Fuzzy Sets and Systems, 95(1998)249-253.
[12] L. A. Zadeh, Fuzzy sets, Inf. Control, 8(1965)338-353.
Journal of Hyperstructures
Volume 11, Issue 1
June 2022
Pages 31-47

Files

Share

How to cite

Statistics