L-Fuzzy Relations via Proximal Spaces

Abstract

Our goal in this paper is to establish a new approach that is to define proximal spaces for lattices. To make this, we used the opinion of the generalization of interval [ 0; 1] to lattices and so we introduce L-proximal spaces. In this paper, we define the L-proximity axioms that need to be satisfied by a L-relation on proximal relator spaces. Also, L-proximity of the sets is introduced on the power set of a nonempty set. We show that the spatial Simirnov proximity measure can be generalized for L-measure and it is a Lodato L-proximity relation. L-proximity relation approach can be used to solve a few issues solution of classification problems and given examples for the problems.