L-Fuzzy Filters of Almost Distributive Lattices

Natnael Teshale Amare, U.M Swamy, Ch.Santhi Sundar Raj


The notion of an Almost Distributive lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalizations of Boolean algebra and Boolean ring.  A complete lattice satisfying the infinite meet distributive law is called a frame. In this paper, we introduce the notion of $L$-fuzzy filter of a given ADL $A$ with a maximal element, where $L$ is a given frame and here we apply the general theory of algebraic fuzzy systems to the class of $L-$fuzzy filters of an ADL.

Full Text:



G. Birkhoff, Lattice Theory, Colloquium Publications, Amer. Math. Soc., 25, 1967.

J.A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145–174.

W.J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems, 8 (1982), 133-139.

T. Ramarao, C.P. Rao, D. Solomon and D. Abeje, Fuzzy Ideals and Filters of lattices, Asian

Journal of Current Engineering and Maths., 2(2013), 297–300.

A. Rosenfeld, Fuzzy groups, J. Maths. Anal. Appl., 35 (1971), 512–517.

U.M. Swamy, Ch. Santhi Sundar Raj and A. Natnael Teshale , Fuzzy Ideals of Almost Distributive

Lattices, Annals of Fuzzy Mathematics and Informatics, to appear.

U.M. Swamy and G.C. Rao, Almost Distributive Lattices, J. Australian Math. Soc., (Series A), 31 (1981), 77–91.

U.M. Swamy and D.V. Raju, Algebraic Fuzzy systems, Fuzzy sets and Systems, 41 (1991), 187–194 .

U.M. Swamy and D.V. Raju, Irriducibility in Algebraic Fuzzy systems, Fuzzy sets and Systems, 41 (1991), 233–241.

B. Venkateswarlu and R.V. Babu, Associate elements in ADLs, Asian-European Journal of

Mathematics, 7(4) (2014) 1450066 (7 pages).

L.A. Zadeh, Fuzzy set, Inform and control, 8 (1965), 338–353.


  • There are currently no refbacks.

Web Counters

IJMSC has been indexed in several world class data bases like Google Scholar, DRJI (Directory of Research Journals Indexing) ,Cite Factor, Research Bible.

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.