Definition of Cliques Fuzzy Set and Estimation of Fuzzy Graphs Isomorphism

Graph theory has numerous applications to problems in systems analysis, operations research, economics, and transportation. However, in many cases, some aspects of a graph-theoretic problem may be uncertain. Using fuzzy graphs as the models of various systems leads to difficulties. The graph isomorphic transformations are reduced to redefinition of vertices and edges. This redefinition doesn't change properties of the graph determined by an adjacent and an incidence of its vertices and edges. In this paper, the concept of a click fuzzy set is considered. Cliques fuzzy set is an invariant concerning the isomorphism transformations of the fuzzy graphs and allows to analyse their structure. The method of definition of cliques fuzzy set is proposed and justified. This method is an extension of the Maghout method for the crisp graphs. The example of definition of cliques fuzzy set is considered. An estimation of degree isomorphism of fuzzy graphs is shown on the basis of their cliques fuzzy sets. An example of the isomorphism estimation based on cliques fuzzy sets is also considere. (C) 2015 The Authors. Published by Elsevier B.V.