When we use linear programming in possibilistic regression analysis, some coefficients tend to become crisp because of the characteristic of linear programming. On the other hand, a quadratic programming approach gives more diverse spread coefficients than a linear programming one. Therefore, to overcome the crisp characteristic of linear programming, we propose interval regression analysis based on a quadratic programming approach. Another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression. By changing the weights of the quadratic function, we can analyze the given data from different viewpoints. For data with crisp inputs and interval outputs, the possibility and necessity models can be considered. Therefore, the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed. Even though there always exist possibility estimation models, the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model. Thus, we consider polynomials as regression models since any curve can be represented by the polynomial approximation. Using polynomials, we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models. Furthermore, from the obtained possibility and necessity regression models, a trapezoidal fuzzy output can be constructed.

Interval regression analysis by quadratic programming approach

An architecture of neural networks with interval weights and its application to fuzzy regression analysis

On assessing the H value in fuzzy linear regression

This paper presents a modeling strategy of human driving behavior based on the controller switching model focusing on the driver's collision avoidance maneuver. The driving data are collected by using the three-dimensional (3-D) driving simulator based on the CAVE Automatic Virtual Environment (CAVE), which provides stereoscopic immersive virtual environment. In our modeling, the control scenario of the human driver, that is, the mapping from the driver's sensory information to the operation of the driver such as acceleration, braking, and steering, is expressed by Piecewise Polynomial (PWP) model. Since the PWP model includes both continuous behaviors given by polynomials and discrete logical conditions, it can be regarded as a class of Hybrid Dynamical System (HDS). The identification problem for the PWP model is formulated as the Mixed Integer Linear Programming (MILP) by transforming the switching conditions into binary variables. From the obtained results, it is found that the driver appropriately switches the "control law" according to the sensory information. In addition, the driving characteristics of the beginner driver and the expert driver are compared and discussed. These results enable us to capture not only the physical meaning of the driving skill but the decision-making aspect (switching conditions) in the driver's collision avoidance maneuver as well.

Modeling of driver's collision avoidance maneuver based on controller switching model

We introduce a concept of fuzzy polynomial neural networks (FPNNs), a hybrid modeling architecture combining polynomial neural networks (PNNs) and fuzzy neural networks (FNNs). The development of the FPNNs dwells on the technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The structure of the FPNN results from a synergistic usage of FNN and PNN. FNNs contribute to the formation of the premise part of the rule-based structure of the FPNN. The consequence part of the FPNN is designed using PNNs. The structure of the PNN is not fixed in advance as it usually takes place in the case of conventional neural networks, but becomes organized dynamically to meet the required approximation error. We exploit a group method of data handling (GMDH) to produce this dynamic topology of the network. The performance of the FPNN is quantified through experimentation that exploits standard data already used in fuzzy modeling. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other similar fuzzy models.

H. Tanaka

Papers

The fuzzy GMDH algorithm by possibility models and its application