Systems of Fuzzy Relation Equations in a Space with Fuzzy Preorder

In this paper, we consider the problem of solving sys- tems of fuzzy relation equations in a space with fuzzy preorder. Two types of these systems with different compositions are considered. New solvability criteria are proposed for systems of both types. The new criteria are weaker than all the known ones that are based on the assumption that fuzzy sets on the left-hand side of a system establish a fuzzy partition of a respective universe.

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