This paper develops an interval-valued fuzzy ϕ-tolerance competition graphs which is the extension of basic fuzzy graphs and ϕ is any real valued function. Interval-valued fuzzy ϕ-tolerance competition graph is constructed by taking all the fuzzy sets of a fuzzy ϕ-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 ϕ-tolerance competition graphs are represented. Application of interval-valued fuzzy competition graph in image matching is given to illustrate the model.
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