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This paper deals with the resolutions of fuzzy relation equations withaddition-min composition. When the fuzzy relation equations have a solution, wefirst propose an algorithm to find all minimal solutions of the fuzzy relationequations and also supply an algorithm to find all maximal solutions of thefuzzy relation equations, which will be illustrated, respectively, by numeralexamples. Then we prove that every solution of the fuzzy relation equations isbetween a minimal solution and a maximal one, so that we describe the solutionset of the fuzzy relation equations completely.

The solution set of fuzzy relation equations with addition-min composition