This paper develops an interval-valued fuzzy [Formula: see text]-tolerance competition graphs which is the extension of basic fuzzy graphs and [Formula: see text] is any real valued function. Interval-valued fuzzy [Formula: see text]-tolerance competition graph is constructed by taking all the fuzzy sets of a fuzzy [Formula: see text]-tolerance competition graph as interval-valued fuzzy sets. Product of two IVFPTCGs and relations between them are defined. Here, some hereditary properties of products of interval-valued fuzzy [Formula: see text]-tolerance competition graphs are represented. Application of interval-valued fuzzy competition graph in image matching is given to illustrate the model.
Keywords: Competition; Interval-valued fuzzy graphs; Tolerance.