Keywords: rough sets, rule induction, aesthetics design, kansei engineering, bridge design, classification.

Recently, the importance of aesthetics design for public structures has become apparent. In such a situation, the design that reflected the sensitivity of citizens is required. However, when some citizens participate in the design of public structures, their opinions are influenced by the advice of some engineers with enough experience and it is difficult to volunteer their own opinions for the design of the bridge. Although almost all the public structures are still designed by the engineers with enough experience, in recent years, a tendency of being designed with the influence of citizens is showing. However, there are some differences between the requests that citizens have put in and how they show up in the final design. Some citizens recognize that the irrequests are ignored in the design. So, the technique of Kansei engineering has lately attracted considerable attention. Kansei engineering, an application that is often used to poll customer ideas concerning the design in product development. However, in applying the technique proposed in the Kansei engineering to aesthetics design and its evaluation, it is necessary to measure the level of citizens care for many existing bridges through questionnaires. Such a questionnaires has a lot of points from which valuable information can be extracted. Moreover, if many images for evaluation of aesthetics design are prepared, the time for answering the questionnaire increase and it becomes hard work.

In this paper, we attempted to find a method for reducing the difficulties of answering such a questionnaires. To realize such a goal, the methods that classify the images of the bridge into some smaller groups of similarity in advance are mentioned. First, some various images are selected for learning purposes, and information like color and position are extracted from various points in these selected images. Next, the information from 4 kinds of objects such as sky, mountain, river and structures are brought in relation with the extracted information such as color and position, and the decision table is made from these results. Some decision rules that are used to determine the object are extracted from the decision table by using rough sets theory. Finally, the objects of some parts in each bridge image are determined through the extracted decision rules, and these results are evaluated.

Ninety clear images of girder bridges were selected at random from the Bridge Year Book. Out of the 90 images, five images with different distributions of RGB values, hue, chroma, and brightness were selected for learning. Each of the five images was divided into six columns by five vertical lines. The values of RGB, hue, chroma, brightness, and coordinate on the axis of ordinate were extracted as conditional attributes at every 15th pixel on each of the boundary lines. At the same time, added to the conditional attributes was information on four types of subjects of skies, mountains, rivers, and artificial structures as decision attributes. To obtain rules for the identification of objects through rough sets theory, the extracted numerical values were discretized. Various studies of discretization are being made. In this study, the RGB values were discretized into five 50-wide classes and the axis of ordinate was discretized into six 800-pixel-wide classes. The hue, chroma, and brightness were discretized respectively into five, four, and three classes by examining the tendencies of all the images and focusing on spots on which values concentrated. Then prepared were five decision tables to show the relation between RGB values, hue, chroma, brightness, and coordinate on the axis of ordinate and the four types of subjects.

By applying the concept of rough sets theory to the five decision tables, decision rules for identifying the four types of objects were derived from the decision tables. We attempted to derive, from the original decision rules, a group of a smaller number of non-contradictory decision rules covering the original decision tables completely in order to extract the characteristics based on the concise group of decision rules. In doing so, however, a combinatorial problem posed itself, and we used here genetic algorithms to deal with it.

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