This paper presents an evolutionary algorithm for graph-coloring problems. The proposed evolutionary algorithm works on artificial strings each of which represents some coloring solution. Using robust encoding and genetic operators, the algorithm exploits, and evolves better solutions. In experiments the algorithm is applied to random normal graphs instances as well as radio-coloring instances.

The simplified fuzzy rules have the advantage that the system can output real number values directly and are frequently applied to the field of control systems. In general, the precision of the fuzzy rules becomes higher as fuzzy partitions increase in number. However, when the teaching data is in both cases below, tuning of the fuzzy rules by conventional methods is not satisfactory. In the first case, where the teaching data is arranged unequally, the reasoning error by the fuzzy rules in sparse domains becomes large because the information necessary to generate the fuzzy rules is insufficient, and, in extreme cases the fuzzy rules can't be generated. Moreover, even if the fuzzy partitions increase in number, the reasoning error never comes down. On the contrary, it goes up, because the fuzzy rules not based on teaching data increase. In the second case, where the teaching data contains disturbance, the reasoning error of the fuzzy rules becomes larger. In this case, the sensitivity to the disturbance becomes higher as the fuzzy partitions increase. Of course, we cannot decrease the error by increasing the fuzzy partitions. In this paper, we propose a fuzzy reasoning model of multiple division layers using iterative transfer window to solve the above problems. This model has a multi-layer structure having both the advantages of rough fuzzy partitions and smooth fuzzy partitions. Moreover, the redundant fuzzy division layers can be decreased by an iterative transfer window. Finally, through identification experiments of two nonlinear functions having sparse domains and disturbance as teaching data, we will show the fuzzy rules generated by the proposed method have high identification precision even for those problems, and also have a low sensitivity to teaching data obtained from actual environment such as the above problems. That is to say, it was verified that the proposed method has a high generalization ability.

In this paper, we show identification methods of λ-fuzzy measure using weights of evaluation items and λ. As the definitions of fuzzy measures' weights of evaluation items are difference by weights' means, we define three standards ; singleton fuzzy measure ratio standard, inputs numbers standard and Shapley value standard. For the three standards, we consider the existence of the fuzzy measure and the properties and propose the identification methods. We consider the means of λ and propose some identification methods of a λ. Lastly, we show some new useful interaction indices which are one-to-one correspondences with λ.

This paper presents the design scheme of plane truss structures using the cellular automata. In the structural design scheme based on the cellular automata simulation, the optimization process is driven according to the local rule which is defined as the relationship between the neighboring elements. In the present scheme, the local rule is analytically derived from the mathematically defined optimization problem. The cross-sectional areas of the truss members are taken as the design variables. The design objectives are to minimize the total weight of the structure and to reduce the maximum stress below the reference stress. Besides, the special constraint condition named as "CA-constraint condition" is introduced in order to derive the local rule. The penalty function is derived from the objective functions and the constraint condition and then, stationalizing the function leads to the local rule. The present scheme is applied to the design of the plane truss structures in order to confirm the validity.

The aim of the present paper is to discuss fuzzy clustering of data with interval uncertainties. Two basic methods of standard fuzzy c-means and entropy method are considered. When handling the data with interval uncertainties, we consider two types of distances between a point and a set:nearest neighbor and farthest neighbor. Using these distances, clustering methods for data with interval uncertainties are proposed. Exact optimization algorithms for cluster centers based on the two distances are developed. In numerical examples, results for the data with interval uncertainties and without the uncertainties are compared.

Chashitu is a form of Japanese architecture which originated from cha-no-yu, a Japanese art. We think that the balance of order and disorder of design in chashitsu space makes the beauty of chashitsu. The purpose of this study is to analyze the beauty of chashitsu from the rhythm in space, and to consider the effect of fractal dimension on a designer's work. The process of calculating the fractal dimension is as follows:(1)Grids are drawn up based on the detail(parts)of a chashitsu, such as fusuma, shoji, hashira piller and shikishimado. (2)Rhythm in space is written through the grids as a graph, paying attention to a change of scale on each grid. (3)An H-index is calculated from the data of the rhythm. (4)The fractal dimension of chashitsu is calculated from the H-index. We propose an analytical method of the design of chashitsu on the basis of fractal dimension.