Exponentially Weighted l_2 Regularization Strategy in Constructing Reinforced Second-order Fuzzy Rule-based Model

07/02/2020
by   Congcong Zhang, et al.
0

In the conventional Takagi-Sugeno-Kang (TSK)-type fuzzy models, constant or linear functions are usually utilized as the consequent parts of the fuzzy rules, but they cannot effectively describe the behavior within local regions defined by the antecedent parts. In this article, a theoretical and practical design methodology is developed to address this problem. First, the information granulation (Fuzzy C-Means) method is applied to capture the structure in the data and split the input space into subspaces, as well as form the antecedent parts. Second, the quadratic polynomials (QPs) are employed as the consequent parts. Compared with constant and linear functions, QPs can describe the input-output behavior within the local regions (subspaces) by refining the relationship between input and output variables. However, although QP can improve the approximation ability of the model, it could lead to the deterioration of the prediction ability of the model (e.g., overfitting). To handle this issue, we introduce an exponential weight approach inspired by the weight function theory encountered in harmonic analysis. More specifically, we adopt the exponential functions as the targeted penalty terms, which are equipped with l2 regularization (l2) (i.e., exponential weighted l2, ewl_2) to match the proposed reinforced second-order fuzzy rule-based model (RSFRM) properly. The advantage of el 2 compared to ordinary l2 lies in separately identifying and penalizing different types of polynomial terms in the coefficient estimation, and its results not only alleviate the overfitting and prevent the deterioration of generalization ability but also effectively release the prediction potential of the model.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/02/2017

From knowledge-based to data-driven modeling of fuzzy rule-based systems: A critical reflection

This paper briefly elaborates on a development in (applied) fuzzy logic ...
research
10/28/2022

UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured Fuzzy Rules for Classification

An important constraint of Fuzzy Inference Systems (FIS) is their struct...
research
10/08/2009

Tracking object's type changes with fuzzy based fusion rule

In this paper the behavior of three combinational rules for temporal/seq...
research
01/15/2023

Max-min Learning of Approximate Weight Matrices from Fuzzy Data

In this article, we study the approximate solutions set Λ_b of an incons...
research
09/10/2015

The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms

We re-examine a practical aspect of combinatorial fuzzy problems of vari...
research
09/22/2021

Filtered integration rules for finite Hilbert transforms

A product quadrature rule, based on the filtered de la Vallée Poussin po...

Please sign up or login with your details

Forgot password? Click here to reset