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The paper aims at studying the solvability of fuzzy relational equations where the input fuzzy sets may have undefined values. The appropriate operations dealing undefined values are taken from the algebras built in partial fuzzy set theory, in particular, the Bochvar operations, the Sobociński operations, the Kleene operations and the lower estimation operations are used for the investigation. We first elaborate new models using distinct operations handling undefined values and mirroring the shapes of the implicative model and Mamdani-Assilian model. Then the solvability criterions for such new systems of fuzzy relational equations are set up, and consequently, we show a way of checking whether the systems are solvable or not.

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