Adaptive fuzzy systems and control: design and stability analysis
Adaptive fuzzy systems and control: design and stability analysis
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
The construction of possibility measures from samples on T -semi-partitions
Information Sciences—Informatics and Computer Science: An International Journal - Special issue using fuzzy algebraic structures in intelligent 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
The concept of LFLC 2000: its specificity, realization and power of applications
Computers in Industry
Normal forms in BL and ŁΠ algebras of functions
Soft Computing - A Fusion of Foundations, Methodologies and Applications
On approximate reasoning with graded rules
Fuzzy Sets and Systems
Adaptive fuzzy logic control of dynamic balance and motion for wheeled inverted pendulums
Fuzzy Sets and Systems
Fuzzy transforms: Theory and applications
Fuzzy Sets and Systems
Fuzzy transform as an additive normal form
Fuzzy Sets and Systems
IEEE Transactions on Fuzzy Systems
Continuity issues of the implicational interpretation of fuzzy rules
Fuzzy Sets and Systems
On the suitability of the Bandler-Kohout subproduct as an inference mechanism
IEEE Transactions on Fuzzy Systems
Checking the coherence and redundancy of fuzzy knowledge bases
IEEE Transactions on Fuzzy Systems
On the suitability of the Bandler-Kohout subproduct as an inference mechanism
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
Finitary solvability conditions for systems of fuzzy relation equations
Information Sciences: an International Journal
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It is well known that a fuzzy rule base can be interpreted in different ways. From a logical point of view, the conjunctive interpretation is preferred, while from a practical point of view, the disjunctive interpretation has been dominantly present. Each of these interpretations results in a specific fuzzy relation that models the fuzzy rule base. Basic interpolation requirements naturally suggest a corresponding inference mechanism: the direct image for the conjunctive interpretation and the subdirect image for the disjunctive interpretation. Interpolation then corresponds to solvability of some system of fuzzy relational equations. In this paper, we show that other types of fuzzy relations, which are closely related to Takagi-Sugeno (T-S) models, are of major interest as well. These fuzzy relations are based on addition and multiplication only, from which we get the name arithmetic fuzzy models. Under some mild requirements, these fuzzy relations turn out to be solutions of the same systems of fuzzy relational equations. The impact of these results is both theoretical and practical: There exist simple solutions to systems of fuzzy relational equations, other than the extremal solutions that have received all the attention so far, which are, moreover, easy to implement.