On two categories of many valued relations

Abstract

The purpose of these notes is to introduce the concept of a many-valued relation and to study two, in a certain sense dual, categories of such relations. Besides, we apply the concept of a manyvalued relation to the description of different approaches, both fixed-based and variable-based, to Fuzzy Topology and characterize categories related to Fuzzy Topology, in the framework of the corresponding categories of many-valued relations.