This article outlines procedures that can be used to determine the boundaries and attributes associated with the resultant regions from the topological overlay of two simple polygons with indeterminate boundaries. After reviewing a definition of a simple polygon with indeterminate boundaries, this study first identifies the 10 resultant regions and 1,024 possible topological configurations from the overlay. Procedures for computing the boundaries of the 10 regions are discussed. Methods for determining the attributes associated with the 10 resultant regions are described. The effect of three typical overlay operations -intersection, difference, and unionon resultant regions is also discussed.
Due to reducing product life cycle and increasing product complexity, design chain management has become more important for industries to develop innovative products within a shorter lead-time. Selecting the design chain partners that is a key determinant of co-development success involves multiple selection criteria and constraints that are either qualitative or quantitative. Poor selection of design chain partners may cause higher development time and cost and less competitive products. This paper considers design chain partnership formation as a multi-criteria decision-making problem. Fuzzy set theory is used to represent information that is mostly imprecise and uncertain at this stage. A fuzzy hybrid decision-aid model that integrates a fuzzy multi-criteria outranking approach with a fuzzy integer programming model is proposed to tackle both qualitative and quantitative factors as well as the decision flexibility. A genetic algorithm approach is applied to select the set of partners that maximise the total performance score of the entire design chain and satisfy the constraints of target development time and cost at the same time. An example of mobile phone design chain is used to illustrate the developed concept
During the color design process, it is critical to create diversified color schemes for various consumer groups. It is also important to allow members in a design team to brainstorm for creative ideas. A theory of inspecting natural color elements was proposed in this study based on the CIE 1976 (L*,a*,b*) (CIE 1976) color space and the fuzzy c‐means clustering method. A calculation model was built to determine people's preference for colors based on a serialized system. To determine which factors affect the prediction of consumers' preference for a series of products, a gray relational color preference system was used in combination with gray relational grade so that a designer can obtain reasonable prediction results. The proposed system recommends not only the optimal colors for a product but also the optimal color scheme for a series of products.
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