Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

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Imprecision is uncertainty that arises because of vague or incomplete information. Preliminary design information is characteristically imprecise: specifications and requirements are subject to change, and the design description is vague and incomplete. Yet many powerful evaluation tools, including finite element models, expect precisely specified data. Thus it is common for engineers to evaluate promising designs one by one. Alternatively, optimization may be used to search for the single "best" design. These approaches focus on individual, precisely specified points in the design space and provide limited information about the full range of acceptable designs. An alternative approach would be to evaluate sets of designs. The method of imprecision uses the mathematics of fuzzy sets in order to represent imprecision as preferences among designs: . Functional requirements model the customer's direct preference on performance variables based on performance considerations: the quantifi...

The significant time, effort, and resource expenditures needed to design and develop aerospace systems motivate on-going research into developing methods for generating, evaluating, and selecting candidate system solutions that can deliver more benefit for a given cost. Compounding the problem is the multiplicity of perspectives of the many stakeholders for such systems, altering the meaning of “benefit ” and “cost ” depending on the stakeholder considered. Tradespace exploration techniques have been used in the past to generate large datasets in order to gain insights into design-value, cost-benefit tradeoffs for complex aerospace systems. Using interactive tradespace exploration to support multi-stakeholder negotiations can reveal these tradeoffs not only for individuals, but also across a group. A method is introduced and applied to two aerospace cases in order to explore the potential for interactive tradespace exploration to support stakeholder negotiations. Preliminary results indicate the method to be a rapid and beneficial technique, which generated compromise alternatives, guided the elicitation of previously unarticulated information, and resulted in increased confidence and solution buy-in of participating stakeholders. I.

A reductionist approach to inquiry in the field of design theory and methodology leads naturally to examination of the lone designer and is the foundation for the development of theories for design. Even in this simplified setting, the two `heads ' of design research emerge: describing what effective designers actually do vs. prescribing what they should do. Without partnership between the two sides there is little hope that developed theories will be applied. Another bifurcation in design occurs between the two primary cognitive activities: generating design options vs. selecting among them. These activities are interleaved; theories that isolate one from the other cannot grasp the real nature of design. This paper examines existing paths toward building design theories that extend beyond the lone designer into groups of interacting designers and further into design situated in a social environment. This analysis points to the need to develop tools that anchor successful realworld design strategies into more formal foundations, helping design teams interact in ways that are both effective and natural.

Abstract: Recent work on Imprecision in Engineering design has extended the basic methodology to negotiation among groups within the design process, and to highly computationally efficient exploration of the design space. Recent industrial applications of the Method of Imprecision have been to passenger vehicle structure design and spacecraft reentry aeroshell design. Introduction: Engineering design, the process of creating a new device to perform a desired function, intrinsically involves imprecision. This imprecision arises from the nature of the design problem, where one or more concepts are refined into a final design. At the concept stage, the designs are only vaguely, or imprecisely, described. Once the design process is complete, the design is described sufficiently precisely that it can be manufactured. During the process of the refinement of a concept into a finished design,

for all their love and sacrifice for me iii ACKNOWLEDGEMENTS This dissertation would not be possible without the immense support and encouragement from various people. First of all, I would like to thank my Ph.D. advisors Farrokh Mistree and Chris Paredis for their continuous support over the past few years. I am very fortunate to have both Farrokh and Chris as my advisors. Their different personalities and perspectives have not only provided me a broader understanding of various research topics, but also provided me reasons to think critically. It is difficult to overstate the gratitude of my mentor, Farrokh, who has been like a father for me. His enthusiasm and love for students is truly remarkable. He has a unique ability to help students realize their full potential. Farrokh has helped me by setting high goals and providing support thoughout the journey to achieve those goals. His visionary ideas and invaluable insights have always challenged me to go beyond the ‘low hanging

Many decisions need to be made based on imprecise or incomplete initial information. In such cases, decision makers are generally more interested in some sets of the most promising solutions rather than the best single solution. Therefore, in contrast to conventional optimisation approaches that aim to find exact optimal points, we aim to find optimal ranges with variable satisfaction degrees. This paper presents a fuzzy-set-based approach for representation and optimisation of practical problems with imprecise properties where evolutionary computation is used to obtain fuzzy solutions through guided searching. The representation of fuzzy sets, their initialisation, crossover, mutation, and validation, the ranking approach for fuzzy objective values, and the propagation method of fuzzy information are discussed. Several examples for illustrating the fuzzy evolutionary optimisation approach are provided.

Design is a multi-criteria decision-making process under multiple constraints. In the conceptual design stage, design is intrinsically imprecise because of designers ’ vague thinking and incomplete initial information. When exploring possible design candidates, designers are generally more interested in sets of the most promising solutions rather than the best single solution. Therefore, in contrast to conventional optimisation approaches that aim to find exact optimal points, we aim to find optimal set of alternatives with variable satisfaction degrees. A fuzzy-set-based approach for representation and optimisation of design objects is particularly suitable for solving this problem. The concept of a fuzzy shape is defined as a family of shapes with similar properties where a fuzzy solid shape is represented by a set of parameters that have fuzzy set values. Evolutionary computation is used to obtain fuzzy solutions to the fuzzy shape optimisation problem since it is the most powerful tool for supporting creative design through multiple objectives, multi-dimensional searching. The representation of fuzzy sets, its initialisation, crossover, mutation, and validation, the ranking approach for fuzzy shapes, and the propagation method of fuzzy information are discussed. A case study for illustrating this fuzzy design approach is provided.

Multi-criteria decision support methods are common in engineering design. These methods typically rely on the specification of importance weights to accomplish trade-offs among competing objectives. Such methods can have difficulties, however: they may not be able to select all possible Pareto optima, and the direct specification of importance weights can be arbitrary and ad hoc. The inability to reach all Pareto optima is shown to be surmountable by the consideration of trade-off strategy as an additional parameter of a decision. The use of indifference points to select a best solution, as an alternative to direct specification of importance weights, is presented, and a simple truss design example is used to illustrate the concepts.