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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 thedoi:10.2991/eusflat.2013.97 dblp:conf/eusflat/Perfilieva13 fatcat:3caiwpqtqffxjh3oeffxspggta