Intuitionistic fuzzy tolerance graphs with application

In this paper, intuitionistic fuzzy tolerance graphs and intuitionistic fuzzy $$\phi $$ϕ-tolerance graphs are defined and investigated several interesting properties. Here $$\phi $$ϕ is any real valued function. Particular cases of $$\phi $$ϕ, viz. min, max and sum are considered. Also, intuitionistic fuzzy unit and proper tolerance graphs are defined and investigated many interesting results. A very appropriate application of intuitionistic fuzzy tolerance graph is also presented.

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