Minimal Solutions To Fuzzy Relation Inequalities With Addition-min Composition

In this paper,we study the fuzzy relation inequalities with addition-min compo-sition.For a fuzzy relation inequality with addition-min composition,we first show sufficient and necessary conditions that an element is a minimal solution,and that the inequality has a unique minimal solution.We then prove that every solution of the inequality has a minimal one and propose an algorithm to searching for all minimal solutions.For a system of the fuzzy rela-tion inequalities with addition-min composition,we first investigate some properties of minimal solutions.Then we obtain a sufficient and necessary condition that a solution is a minimal one,and verify that for every solution,there exists a minimal solution which is less than or equal to the solution.Finally,we give an algorithm to find a minimal solution for a given solution.