Some results of convex fuzzy sublattices

Abstract

In the present paper we give a procedure by which we generate a fuzzy ideal (resp. a fuzzy filter and a convex fuzzy sublattice) by a fuzzy set in a lattice. And we prove that a convex fuzzy sublattice generated by a fuzzy set is an intersection of a fuzzy ideal and a fuzzy filter generated by the same fuzzy set in a lattice. Moreover, the homomorphic image and pre-image of a fuzzy ideal (fuzzy filter and convex fuzzy sublattice) generated by a fuzzy set are studied. In particular, we prove that the set of convex fuzzy sublattices of a modular lattice can form a modular lattice. Finally, as an application of our main result, we give an interesting example in BCK-algebras.

A Novel Concept of Fuzzy Subsemigroup (Ideal)

“…In addition, Maruyama [9] studied the concept of convexity on a completely distributive lattice in 2009. As a matter of fact, there is a convex space in many other mathematical structures [10][11][12][13].…”

BCK-algebras arising from block codes

“…These algebras form an important class of logical algebras and have many applications to various domains of mathematics, such as: group theory, functional analysis, fuzzy sets theory, probability theory, topology, etc. For other details about BCK-algebras and about some new applications of them, the reader is referred to [2], [5], [6], [10], [11], [12], [13] .…”