Keywords: monotonous fuzzy rule base, system of fuzzy relation equations, "at least" ("at most") quantifiers, fuzzy preorder, criterion of solvability Abstract In this paper, we utilize the theory of solvability of systems of fuzzy relation equations in a space with fuzzy preorder and propose a justification of solvability of systems that are modified with "at least" ("at most") quantifiers. We show that the respectively modified fuzzy sets are upper (lower) sets of a fuzzy preorder on the

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... of reals. On the basis of this, we show that the systems with the sup * composition and with the same type of modifications on both sides are solvable. Moreover, we explain why the solvability of the similarly modified systems with the inf →composition cannot be established. Last but not least we show that only opposite modifications on the left and right-hand sides of the modified system with the inf →composition guarantee its solvability.