The fundamental form of parts of many industrial products is boxy. For example, bodies and switch buttons of the household electric appliance are often boxy. The form of the product is constituted by those boxy parts. It is constituted by the cluster of boxy parts, even if it is apparently complicatedly seen. This research was carried out on the system for supporting the creation of the form of such product. As a beginning for constructing the system, the approach of the variable modeling used in the research on CAD was introduced. Then, fuzzy inference was applied to the system in order to consider ambiguity and nonlinearity on the design. In this study, portable telephone was taken up as a case of the boxy troduct. To begin with, the analysis on the design of portable telephone in the market was carried out using the principal component analysis. Using the result of the principal component analysis, design support system, which could acquire created form in CAD, was constructed. The simulation using the system was carried out, and it was examined from the viewpoint of the designer. As the result, it was indicated that the system might become an useful instrument for the designer. Finally, the personal viewpoint was described on how the systemcould be utilized, for designer and general consumer.

This paper discusses a Fuzzy c-Means regularized by fuzzy entropy, and proposes a new algorithm that estimates cluster numbers first and then improves clustering accuracy. In the first stage, this method estimates the cluster numbers by dividing and combining the clusters repeatedly. In the dividing process, the fuzzy entropy measures the fuzziness of the distribution of clusters, and in the combining process, new fuzzy relative entropy measures the resemblance of the shapes of clusters. In the second stage, we use Fermi-Dirac type distribution functions to represent membership functions for the clusters and adjust the shapes of Fermi-Dirac functions by applying a heuristic search method, Simulated Annealing, so as to minimize the fuzzy relative entropy. Numerical experiments show that the proposed algorithm can estimatethe cluster numbers ; the heuristic search method with the fuzzy relative entropy increases clustering accuracy for the date distributions overlapped with each other.

The goal of this paper is to design a controller for a class of nonlinear systems with delay time using fuzzy logic. The control scheme considered in this paper is the integration of two components. One is called fuzzy component, which mainly consists of so-called fuzzy approximator to approximate the unknown functions in the process. The other one is called sliding control component of the variable structure control with a sector to guarantee the global stability of the closed-loop system when a variable, involving the tracking error, travels the outside of the sector. The adaptive laws to adjust parameters in the system will be developed based on Lyapunov synthesis approach. It is shown the proposed predictive controller guarantees tracking error, between outputs of considered system and desired values, to be asymptotically in decay.

Gaussian mixture model with EM algorithm is a popular density estimation method that uses the likelihood function as a measure of fit. It can be used as a tool for clustering. The thesis of the paper is that although the iterative algorithm of Fuzzy c-Means (FCM) clustering with entropy regularization is similar to that of the Gaussian mixture model, the FCM clustering has more flexible structure since the algorithm is based on the objective fanction method. We show that just the same algorithm as the Gaussian mixture model can be derived from a modified objective function with regularization by K-L information, and in a slightly different manner such as installing an annealing parameter and addition of Gustafson and Kessel's constraints, the proposed algorithm provides more valid or useful clustering results.