On computation of the compositional rule of inference under triangular norms
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
The relation between inference and interpolation in the framework of fuzzy systems
Fuzzy Sets and Systems
What are fuzzy rules and how to use them
Fuzzy Sets and Systems - Special issue dedicated to the memory of Professor Arnold Kaufmann
Fuzzy Sets and Systems
Generalized solvability behaviour for systems of fuzzy equations
Discovering the world with fuzzy logic
Fuzzy points, fuzzy relations and fuzzy functions
Discovering the world with fuzzy logic
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Compositional rule of inference as an analogical scheme
Fuzzy Sets and Systems
Correct models of fuzzy IF--THEN rules are continuous
Fuzzy Sets and Systems
System of fuzzy relation equations as a continuous model of IF-THEN rules
Information Sciences: an International Journal
Fuzzy Implications
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
IEEE Transactions on Fuzzy Systems
Checking the coherence and redundancy of fuzzy knowledge bases
IEEE Transactions on Fuzzy Systems
Fuzzy controllers with conditionally firing rules
IEEE Transactions on Fuzzy Systems
On the Law of Importation in Fuzzy Logic
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
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Fuzzy relational inference (FRI) systems form an important part of approximate reasoning schemes using fuzzy sets. The compositional rule of inference (CRI), which was introduced by Zadeh, has attracted the most attention so far. In this paper, we show that the FRI scheme that is based on the Bandler-Kohout (BK) subproduct, along with a suitable realization of the fuzzy rules, possesses all the important properties that are cited in favor of using CRI, viz., equivalent and reasonable conditions for their solvability, their interpolative properties, and the preservation of the indistinguishability that may be inherent in the input fuzzy sets. Moreover, we show that under certain conditions, the equivalence of first-infer-then-aggregate (FITA) and first-aggregate-then-infer (FATI) inference strategies can be shown for the BK subproduct, much like in the case of CRI. Finally, by addressing the computational complexity that may exist in the BK subproduct, we suggest a hierarchical inferencing scheme. Thus, this paper shows that the BK-subproduct-based FRI is as effective and efficient as the CRI itself.