Decomposition of realizable fuzzy relations (Q1955454)

A fuzzy relation \(A\) is realizable if there exists a fuzzy relation \(B\) such that \(A=B\odot B^T\) (where \(\odot \) is the max-min composition and \(B^T\) denotes the transpose of \(B\)). The authors prove that the content of a realizable fuzzy relation is equal to the chromatic number of a simple graph generated by the realizable fuzzy relation by means of the concept of compatible partition.