Neural-Network-Based Fuzzy Logic Control and Decision System
IEEE Transactions on Computers - Special issue on artificial neural networks
Fuzzy Sets and Systems - Special issue on fuzzy neural control
The three semantics of fuzzy sets
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Function approximation with polynomial membership functions and alternating cluster estimation
Fuzzy Sets and Systems - Special issue on analytical and structural considerations in fuzzy modeling
Applications of b-spline approximation to geometric problems of computer-aided design.
Applications of b-spline approximation to geometric problems of computer-aided design.
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Fuzzy classifier identification using decision tree and multiobjective evolutionary algorithms
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Evolutionary learning of BMF fuzzy-neural networks using a reduced-form genetic algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Application of simulated annealing fuzzy model tuning to umbilical cord acid-base interpretation
IEEE Transactions on Fuzzy Systems
Solving fuzzy inequalities with piecewise linear membership functions
IEEE Transactions on Fuzzy Systems
Learning fuzzy rules with tabu search-an application to control
IEEE Transactions on Fuzzy Systems
Modeling proportional membership in fuzzy clustering
IEEE Transactions on Fuzzy Systems
Genetically optimized fuzzy polynomial neural networks
IEEE Transactions on Fuzzy Systems
Fuzzy interpolative reasoning via scale and move transformations
IEEE Transactions on Fuzzy Systems
MembershipMap: Data Transformation Based on Granulation and Fuzzy Membership Aggregation
IEEE Transactions on Fuzzy Systems
A Measurement-Theoretic Axiomatization of Trapezoidal Membership Functions
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Neural Networks
Operation properties and δ-equalities of complex fuzzy sets
International Journal of Approximate Reasoning
A fuzzy multi-criteria decision making model for supplier selection
Expert Systems with Applications: An International Journal
Evolutionary optimization-based tuning of low-cost fuzzy controllers for servo systems
Knowledge-Based Systems
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We present a scheme for tractable parametric representation of fuzzy set membership functions based on the use of a recursive monotonic hierarchy that yields different polynomial functions with different orders. Polynomials of the first order were found to be simple bivalent sets, while the second order polynomials represent the typical saw shape triangles. Higher order polynomials present more diverse membership shapes. The approach demonstrates an enhanced method to manage and fit the profile of membership functions through the access to the polynomials order, the number and the multiplicity of anchor points as wells as the uniformity and periodicity features used in the approach. These parameters provide an interesting means to assist in fitting a fuzzy controller according to system requirements. Besides, the polynomial fuzzy sets have tractable characteristics concerning the continuity and differentiability that depend on the order of the polynomials. Higher order polynomials can be differentiated as many times as the order of the polynomial less the multiplicity of the anchor points. An algorithmic optimization approach using the steepest descent method is introduced for fuzzy controller tuning. It was shown that the controller can be optimized to model a certain output within small number of iterations and very small error margins. The mathematics generated by the approach is consistent and can be simply generalized to standard applications. The recursive propagation was noticed for its clarity and ease of calculations. Further, the degree of association between the sets is not limited to the neighbors as in traditional applications; instead, it may extend beyond. Such approach can be useful in dynamic fuzzy sets for adaptive modeling in view of the fact that the shape parameters can be easily altered to get different profiles while keeping the math unchanged. Hypothetically, any shape of membership functions under the partition of unity constraint can be produced. The significance of the mentioned characteristics of such modeling can be observed in the field of combinatorial and continuous parameter optimization, automated tuning, optimal fuzzy control, fuzzy-neural control, membership function fitting, adaptive modeling, and many other fields that require customized as well as standard fuzzy membership functions. Experimental work of different scenarios with diverse fuzzy rules and polynomial sets has been conducted to verify and validate our results.