Upper boundary algebra, Undefined values, Partial algebra, Partial fuzzy set theory, Inference systems · Systems of fuzzy relational equations, Bandler-Kohout subproduct

Three-valued logics became a classical topic for logicians and not surprisingly, they were extended to partial fuzzy logics that allow modeling distinct types of undefined truth-values, i.e., values, that are neither true nor false, even in the graded sense. Such logics and related algebras may model reasoning with non-denoting terms, missing or unknown values, and other interesting cases. However, in order to be able to model real cases, the algebraic models need to be mirrored in applied tools such as inference systems. Therefore, the investigation of partial fuzzy relational equations that question the most natural property of such systems is a straightforward step. This step has been already made, however, satisfactory results were obtained only for the direct product inference (compositional rule of inference). Intuitively, this was due to the application of partial algebras that employ the so-called lower boundary strategy. This article introduces upper boundary algebraic strategy and shows, that equally satisfactory results may be obtained also for the Bandler-Kohout subproduct.