At the conceptual stage of design, designers have only vague ideas of initial shapes that they gradually refine. A tool that supports conceptual design should capture such imprecise features but current CAD systems that are based on precise geometry and topology information cannot satisfy this requirement. The fuzzy set approach is particularly suitable for handling imprecise information by providing a set of solutions with different, user-specified preference degrees. We therefore choose this

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... pproach to address the imprecise design problem in a solid modelling system. Design data need to be stored in a database and accessed in later design process because of the iterative nature of design. This paper presents the representation, construction and display approaches for fuzzy shapes. We also discuss techniques for indexing and retrieving of fuzzy shapes in an object relational database with a fuzzy processing module. Design, especially in the conceptual stage, is intrinsically imprecise because of designers' vague thinking and incomplete initial information. To face with the competitive design market, the tools that support conceptual design should be human-oriented and able to capture such imprecise features. However, current Computer-Aided Design (CAD) systems that are based on precise geometry cannot satisfy this requirement. Although the parameteric and feature-based modelling approaches [20] have made current CAD systems more flexible and meaningful, they still cannot cater for the imprecise characteristics of human because of the underlying precise representation. Since people have the ability to qualitatively identify, describe, and analyse shapes and spatial relationships by a natural language, it is desirable to use words which are related to shape, position or orientation to specify shape and spatial relationship in top-down conceptual design stage. Fuzzy set theory [23] is able to deal with linguistic terms, therefore is a promising approach for simulating human behaviour in describing, locating and reasoning process in shape design. Hence, we chose this approach to address the imprecise design problem in a solid modelling system. Since fuzzy sets are generalizations of intervals and crisp values [15] , fuzzy-set-based design may be considered as a generalization of interval-based design and conventional crisp-valuebased design. On one hand, fuzzy model can describe qualitatively a system using linguistic words while on the other hand, these words are associated to fuzzy quantities represented by fuzzy sets. So, fuzzy modelling is both a qualitative and quantitative scheme. Representation of fuzzy complex shapes There exist many representation schemes for modelling 3D shapes such as point clouds [11] ; Constructive Solid Geometry (CSG), Boundary Representation (B-Rep), sweeping and cellular decomposition [12] ; NURBS [18], and parametric and feature-based modelling [20] . These modeling methods are based on underlying precise representation of geometric objects, such as vertices, edges, surfaces as well as the exact topology relationship between them. These methods are good at supporting detail design process where all design details must be represented exactly yet they are very weak to support conceptual design that is qualitative and uncertain. Qualitative shape models such as geons have been used for object recognition in the computer vision area [7] . However, qualitative models cannot provide sufficient quantitative information that is required for shape specification and manipulation in Computer-Aided Design and Manufacturing