Summary: We establish the equivalence between variational inequalities for fuzzy mappings and resolvent equations for fuzzy mappings. We use this equivalence to suggest a number of new iterative algorithms for solving variational inequalities for fuzzy mappings. We also study the convergence criteria of these iterative algorithms. The auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution. The results proved in this paper represent an improvement of previously known results.
[For Part I and Part II see Fuzzy Sets Syst. 55, No. 3, 309-312 (1993; Zbl 0785.49006) and ibid. 97, No. 1, 101-107 (1998; Zbl 0928.49012), respectively].