Minimal Solutions Of Fuzzy Relation Inequalities With Addition-min Composition

In this thesis,we deal with minimal solutions of fuzzy relation inequalities with addition-min composition.We first discuss the relationships between minimal solutions of single fuzzy relation inequalities with addition-min composition,and give some sufficient and necessary conditions that an element is a unique minimal solution.We then directly prove that for every solution of fuzzy relation inequalities with addition-min composition,there exists a minimal solution that is less than or equal to the solution without using Zorn's Lemma.Finally,we propose two algorithms to find a minimal solution for a given one,which will be illustrated by numeral examples.