An introduction to fuzzy control
An introduction to fuzzy control
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Parameter conditions for monotonic Takagi-Sugeno-Kang fuzzy system
Fuzzy Sets and Systems - Fuzzy systems
Commutativity as prior knowledge in fuzzy modeling
Fuzzy Sets and Systems
Derivation of monotone decision models from noisy data
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
Fuzzy models to predict consumer ratings for biscuits based on digital image features
IEEE Transactions on Fuzzy Systems
Expert Systems with Applications: An International Journal
On the monotonicity of hierarchical sum--product fuzzy systems
Fuzzy Sets and Systems
IEEE Transactions on Fuzzy Systems
On the monotonicity of fuzzy-inference methods related to T-S inference method
IEEE Transactions on Fuzzy Systems - Special section on computing with words
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Hybrid approaches for approximate reasoning
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In the Mamdani-Assilian models considered in this study, the linguistic values of the input variables as well as the output variable are described by trapezoidal membership functions forming a fuzzy partition, the rule base is monotone and the crisp output is obtained by the Mean of Maxima (MOM) defuzzification method. It is verified for each of the three basic t-norms T"M, T"P and T"L whether a monotone input-output behaviour is obtained for any monotone rule base, or at least for any monotone smooth rule base. For models applying T"L a monotone input-output behaviour can only be guaranteed if the model has a single input variable. The monotonicity of models with two or more input variables applying T"M cannot be guaranteed for any monotone rule base, whereas when applying T"P monotonicity is only guaranteed for any monotone rule base when using a fuzzy output partition belonging to a restricted class of nine types of fuzzy partitions which contain at most five linguistic values. Finally, it is proved that a monotone input-output behaviour is always obtained for models with a monotone smooth rule base applying T"M when the linguistic output values in the consequents of the rules are defined by trapezoidal or triangular membership functions with intervals of changing membership degree of equal length-a restriction that can easily be bypassed by an auxiliary interpolation procedure-and for models with a monotone smooth rule base applying T"P for any fuzzy output partition.