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Fuzzy associative matrix
About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.
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TL;DR: An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input-output data, and an affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically.
Abstract: An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input-output data. Firstly, the fuzzy c-regression model (FCRM) clustering technique is applied to partition the product space of the given input-output data into hyper-plan-shaped clusters. Each cluster is essentially a basis of the fuzzy rule that describes the system behaviour, and the number of clusters is just the number of fuzzy rules. Particularly, a novel cluster validity criterion for FCRM is set up to choose the appropriate number of clusters (rules). Once the number of clusters is determined, the consequent parameters of each IF-THEN rule are directly obtained from the functional cluster representatives (affine linear functions). The antecedent fuzzy sets of each IF-THEN fuzzy rule are acquired by projecting the fuzzy partitions matrix U onto the axes of individual antecedent variable to obtain point-wise defined fuzzy sets and to approximate these point-wise defined fuzzy sets by normal bell-shaped membership functions. Additionally, a check and repartition algorithm is suggested to prevent the inappropriate premise structure where separate regions of data shared the same regression model. Finally, the gradient descent algorithm is included to adjust the fuzzy model precisely. An affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically. Several simulation examples are provided to demonstrate the accuracy and effectiveness of the affine T-S fuzzy modelling algorithm.
105 citations
TL;DR: It is proved that the monotonicity of interpolation functions of fuzzy control is equivalent to the monotinicity of control rules, which means that there is not any contradiction among the control rules under the condition for the control Rules being monotonic.
Abstract: Adaptive fuzzy controllers by means of variable universe are proposed based on interpolation forms of fuzzy control. First, monotonicity of control rules is defined, and it is proved that the monotonicity of interpolation functions of fuzzy control is equivalent to the monotonicity of control rules. This means that there is not any contradiction among the control rules under the condition for the control rules being monotonic. Then structure of the contraction-expansion factor is discussed. At last, three models of adaptive fuzzy control based on variable universe are given which are adaptive fuzzy control model with potential heredity, adaptive fuzzy control model with obvious heredity and adaptive fuzzy control model with successively obvious heredity.
105 citations
01 Jan 2008
TL;DR: Some operational laws of fuzzy number intuitionistic fuzzy numbers are defined, and some new arithmetic aggregation operators, such as the fuzzy number intuistic fuzzy weighted averaging (FIFWA) operators, are developed.
Abstract: A fuzzy number intuitionistic fuzzy set (FNIFS) is a generalization of intuitionistic fuzzy set. The fundamental characteristic of FNIFS is that the values of its membership function and non-membership function are trigonometric fuzzy numbers rather than exact numbers. In this paper, we define some operational laws of fuzzy number intuitionistic fuzzy numbers, and, based on these operational laws, develop some new arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator for aggregating fuzzy number intuitionistic fuzzy information. Furthermore, we give an application of the FIFHA operator to multiple attribute decision making based on fuzzy number intuitionistic fuzzy information. Finally, an illustrative example is given to verify the developed approach.
104 citations
TL;DR: A model for least-squares fitting of fuzzy-valued data is described, generalized and improved to include all fuzzy numbers represented by single maxima piecewise continuous functions with compact support.
103 citations
TL;DR: In this paper, necessary conditions for general single-input single-output fuzzy systems and a class of typical MISO fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds were investigated.
103 citations