## Antonsson, “Trade-Off strategies in engineering design (1991)

Venue: | Res. Eng. Design |

Citations: | 16 - 11 self |

### BibTeX

@ARTICLE{Otto91antonsson,“trade-off,

author = {Kevin N. Otto and Erik K. Antonsson},

title = {Antonsson, “Trade-Off strategies in engineering design},

journal = {Res. Eng. Design},

year = {1991},

pages = {87--103}

}

### Years of Citing Articles

### OpenURL

### Abstract

A formal method to allow designers to explicitly make trade-off decisions is presented. The methodology can be used when an engineer wishes to rate the design by the weakest aspect, or by cooperatively considering the overall performance, or a combination of these strategies. The design problem is formulated with preference rankings, similar to a utility theory or fuzzy sets approach. This approach separates the design trade-off strategy from the performance expressions. The details of the mathematical formulation are presented and discussed, along with two design examples: one from the preliminary design domain, and one from the parameter design domain. 1

### Citations

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Citation Context ...t here, in the context of selecting from a finite set of alternatives. The relationship of his developments to ours will be discussed below. An alternative to the use of imprecision is utility theory =-=[19, 29]-=-. Utility theory trades off goals by specifying utility curves on each goal, and then maximizes overall utility by aggressively combining the goals. Doing so eliminates the conservative design strateg... |

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Citation Context ... an optimization methodology [16]. Such single objective formulations have been argued to be constraining for actual design problems [32]. Instead, multi-objective function formulations could be used =-=[12, 28, 32]-=-. The methodology presented here is compatible with these multi-objective function algorithms, in that one can use them to solve the formulations presented here, when the domain has sufficient formali... |

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Citation Context ...ic, enabling direct preferential comparisons with other alternatives for which the designer may not have used the conservative design strategy. A different technique was proposed by Bellman and Zadeh =-=[4]-=- involving the fuzzy linear weighting of goals. Their formalization is not adopted because of its failure to maintain consistency with Table 1. They fail to maintain consistency with the boundary cond... |

170 |
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Citation Context ...sion can still be used, however, to determine which candidate models offer the most promise. Traditional methods used in this stage of design are matrix methods [2]. Current advanced versions are QFD =-=[1, 13]-=- and Pugh’s method [17]. The basis for the combination procedure of such matrix methods will be discussed in an example below. 2 Design Imprecision In the method of imprecision, designer preferences (... |

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Citation Context ...ed, it will be demonstrated that this combination corresponds to using a conservative design strategy. Parallel work by Dubois and Prade considers trading-off multiple goals with preference functions =-=[11]-=-. In [11], they review connectives which could be used to combine goals. However, they provide no compelling reason for selecting any of the possible candidates (as is done here: by specifying a desig... |

80 |
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Citation Context ...sion can still be used, however, to determine which candidate models offer the most promise. Traditional methods used in this stage of design are matrix methods [2]. Current advanced versions are QFD =-=[1, 13]-=- and Pugh’s method [17]. The basis for the combination procedure of such matrix methods will be discussed in an example below. 2 Design Imprecision In the method of imprecision, designer preferences (... |

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Citation Context ... in values, unless the parameterizing expressions dictate this. These first three axioms present nothing new in terms of inferencing mechanisms under uncertainty. Probability and Bayesian inferencing =-=[31]-=-, Dempster-Shafer theory [27], fuzzy sets and triangular norms in general [10], and finally utility theory [19] all conform to these 1 Throughout the paper max is used to to mean sup or least upper bo... |

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Citation Context ...ree axioms present nothing new in terms of inferencing mechanisms under uncertainty. Probability and Bayesian inferencing [31], Dempster-Shafer theory [27], fuzzy sets and triangular norms in general =-=[10]-=-, and finally utility theory [19] all conform to these 1 Throughout the paper max is used to to mean sup or least upper bound, andmin is used to mean inf or greatest lower bound.Otto & Antonsson: Tra... |

58 |
Principles of Optimal Design
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Citation Context ...nsideration, which could be the design strategy of choice in some cases. In domains involving goals with explicit expressions, one could formulate the design problem using an optimization methodology =-=[16]-=-. Such single objective formulations have been argued to be constraining for actual design problems [32]. Instead, multi-objective function formulations could be used [12, 28, 32]. The methodology pre... |

56 |
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Citation Context ...terizing expressions dictate this. These first three axioms present nothing new in terms of inferencing mechanisms under uncertainty. Probability and Bayesian inferencing [31], Dempster-Shafer theory =-=[27]-=-, fuzzy sets and triangular norms in general [10], and finally utility theory [19] all conform to these 1 Throughout the paper max is used to to mean sup or least upper bound, andmin is used to mean i... |

53 | Computations with Imprecise Parameters in Engineering Design: Background and Theory
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Citation Context ... A method for representing and manipulating uncertainties in preliminary design, to formalize the process of making these trade-off decisions, has been introduced and developed by Wood and Antonsson, =-=[34, 35, 36]-=-, called the method of imprecision. It is used to compare and contrast different objectives within a proposed design and among different design alternatives. The intent is to determine proposed candid... |

49 |
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Citation Context ...wever, to determine which candidate models offer the most promise. Traditional methods used in this stage of design are matrix methods [2]. Current advanced versions are QFD [1, 13] and Pugh’s method =-=[17]-=-. The basis for the combination procedure of such matrix methods will be discussed in an example below. 2 Design Imprecision In the method of imprecision, designer preferences (µ) are represented on a... |

37 |
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Citation Context ...ering design connectives should not be commutative. It makes no sense, for example, to require one goal’s weighting to be applicable to a different goal, which is as commutativity requires. Yager, in =-=[37]-=-, introduces some of the mathematics that we present here, in the context of selecting from a finite set of alternatives. The relationship of his developments to ours will be discussed below. An alter... |

25 | Belief functions, Non-Standard Logics for Automated Reasoning - Smets - 1988 |

23 |
Exploring the interface between hierarchies multi-objectives and fuzzy sets
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Citation Context ...e included to allow the designer to specify how much concern (or weight) should be allocated to each goal. (5)Otto & Antonsson: Trade-Off Strategies in Engineering Design 9 The reader is referred to =-=[23, 28]-=- for methods on how to specify weights; this paper will not discuss this aspect of the problem. However, it is noted that there are several reasons why weighting functions present difficulty [28, 30].... |

21 | Interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems
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Citation Context ...egies the designer may adopt. 1.3 Related Work There has been some progress in the development of optimization methods with preference functions. Diaz [7, 8, 9], Rao [20, 21, 22], and Sakawa and Yano =-=[24, 25, 26]-=- have advanced the use of “fuzzy goals” where the objective functions and constraints consist of fuzzy preference functions on different performance parameters. This paper will illustrate the implicat... |

21 |
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Citation Context ...egies in Engineering Design 2 This approach can help designers observe, justify, and direct their decision making processes. In any design scenario, there are multiple goals which need to be achieved =-=[32]-=-. Designers restrict and choose parameter values based on a combination of these concerns. This work will permit designers to directly specify a design goal trade-off strategy to specify how to trade-... |

14 | Modeling Imprecision and Uncertainty - Wood, Antonsson - 1990 |

11 |
A Modified Game Theory Approach to Multiobjective Optimization
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Citation Context ... an optimization methodology [16]. Such single objective formulations have been argued to be constraining for actual design problems [32]. Instead, multi-objective function formulations could be used =-=[12, 28, 32]-=-. The methodology presented here is compatible with these multi-objective function algorithms, in that one can use them to solve the formulations presented here, when the domain has sufficient formali... |

11 |
A Method for Representing and Manipulating Uncertainties in Preliminary Engineering Design
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Citation Context ... the scheme is to place preferences on the candidate model features, with the aim of determining an overall preference for each candidate model to determine which to pursue. The reader is referred to =-=[20, 21, 22, 33, 34, 35, 36]-=- for a discussion on how to specify preferences; this paper will not discuss this aspect of the problem. Rather, this paper will focus on the task of combining these individual preferences (of the dif... |

9 |
Design trade-offs made easy
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Citation Context ...nce µ =0), then the overall design (as a set of goals) will also not be preferred. Weighted sum multi-criteria objective formulations do not conform to this axiom, as discussed by Biegel and Pecht in =-=[5]-=-. Vincent [32] also presents this argument in the case of (non-preference) multi-objective function optimization. The second axiom is a monotonicity requirement. It states that if an individual goal’s... |

9 |
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Citation Context ...hods effectively represent different design strategies the designer may adopt. 1.3 Related Work There has been some progress in the development of optimization methods with preference functions. Diaz =-=[7, 8, 9]-=-, Rao [20, 21, 22], and Sakawa and Yano [24, 25, 26] have advanced the use of “fuzzy goals” where the objective functions and constraints consist of fuzzy preference functions on different performance... |

9 | A Strategy for Optimal Design of Hierarchical Systems Using Fuzzy Sets - Diaz - 1989 |

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Citation Context ... the scheme is to place preferences on the candidate model features, with the aim of determining an overall preference for each candidate model to determine which to pursue. The reader is referred to =-=[20, 21, 22, 33, 34, 35, 36]-=- for a discussion on how to specify preferences; this paper will not discuss this aspect of the problem. Rather, this paper will focus on the task of combining these individual preferences (of the dif... |

9 |
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Citation Context ... [23, 28] for methods on how to specify weights; this paper will not discuss this aspect of the problem. However, it is noted that there are several reasons why weighting functions present difficulty =-=[28, 30]-=-. We concur, and adopt the standard solution to the problem of specifying weights: iteration. That is, it is not assumed the designer can, apriori, specify the final goal weights, only preliminary est... |

8 |
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Citation Context ...egies the designer may adopt. 1.3 Related Work There has been some progress in the development of optimization methods with preference functions. Diaz [7, 8, 9], Rao [20, 21, 22], and Sakawa and Yano =-=[24, 25, 26]-=- have advanced the use of “fuzzy goals” where the objective functions and constraints consist of fuzzy preference functions on different performance parameters. This paper will illustrate the implicat... |

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Citation Context ...ually incomplete. The method of imprecision can still be used, however, to determine which candidate models offer the most promise. Traditional methods used in this stage of design are matrix methods =-=[2]-=-. Current advanced versions are QFD [1, 13] and Pugh’s method [17]. The basis for the combination procedure of such matrix methods will be discussed in an example below. 2 Design Imprecision In the me... |

7 |
Applications of Fuzzy Theories to Multi-Objective System Optimization,” NASA contractor report 177573
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Citation Context ... the scheme is to place preferences on the candidate model features, with the aim of determining an overall preference for each candidate model to determine which to pursue. The reader is referred to =-=[20, 21, 22, 33, 34, 35, 36]-=- for a discussion on how to specify preferences; this paper will not discuss this aspect of the problem. Rather, this paper will focus on the task of combining these individual preferences (of the dif... |

7 |
Interactive fuzzy decision making for multiobjective nonlinear programming problems
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Citation Context ...egies the designer may adopt. 1.3 Related Work There has been some progress in the development of optimization methods with preference functions. Diaz [7, 8, 9], Rao [20, 21, 22], and Sakawa and Yano =-=[24, 25, 26]-=- have advanced the use of “fuzzy goals” where the objective functions and constraints consist of fuzzy preference functions on different performance parameters. This paper will illustrate the implicat... |

7 |
A Formal Method for Representing Uncertainties in Engineering Design
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Citation Context ... A method for representing and manipulating uncertainties in preliminary design, to formalize the process of making these trade-off decisions, has been introduced and developed by Wood and Antonsson, =-=[34, 35, 36]-=-, called the method of imprecision. It is used to compare and contrast different objectives within a proposed design and among different design alternatives. The intent is to determine proposed candid... |

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Citation Context ...the search. Here the product aggressive strategy may be easier to evaluate due to differentiability. The min conservative strategy becomes a traditional maximin multiple goal optimization formulation =-=[15]-=-. In any case, iteration will almost certainly be required to ensure the final preferences and weights. Formal iterative methods (see Steuer [28] for a review) could be used. 3 Examples The first exam... |

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Citation Context ... and manipulate a design’s different concerns and uncertainties. This development is crucial, since the preliminary decision making process of any design cycle has the greatest effect on overall cost =-=[3, 6, 14]-=-. In a design decision making process, engineers must trade-off widely differing concepts to realize a result which maximizes their overall preference for a design. These concepts are usually incommen... |

5 | H.Decisions with Multiple Objectives: Preferences and Value Tradeoffs - KEENEY, RAIFFA - 1993 |

4 |
A method for integrating utility analysis into an expert system for design evaluation under uncertainty
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Citation Context ...t here, in the context of selecting from a finite set of alternatives. The relationship of his developments to ours will be discussed below. An alternative to the use of imprecision is utility theory =-=[19, 29]-=-. Utility theory trades off goals by specifying utility curves on each goal, and then maximizes overall utility by aggressively combining the goals. Doing so eliminates the conservative design strateg... |

3 |
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Citation Context ...hods effectively represent different design strategies the designer may adopt. 1.3 Related Work There has been some progress in the development of optimization methods with preference functions. Diaz =-=[7, 8, 9]-=-, Rao [20, 21, 22], and Sakawa and Yano [24, 25, 26] have advanced the use of “fuzzy goals” where the objective functions and constraints consist of fuzzy preference functions on different performance... |

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Citation Context ...s are the Analytical Hierarchy Process [23], or the marginal rate of substitution [28]. It is noted that, though theoretical issues remain with weighting functions, they are commonly used in practice =-=[1, 2, 13, 18]-=-. Assigning importance factors to goals is a relative measure: a goal’s importance is ranked relative to the rest of the goals in a design. The importance of goal j (either a design parameter or a per... |

3 |
A strategy for optimal design of hierarchial systems using fuzzy sets
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(Show Context)
Citation Context ...hods effectively represent different design strategies the designer may adopt. 1.3 Related Work There has been some progress in the development of optimization methods with preference functions. Diaz =-=[7, 8, 9]-=-, Rao [20, 21, 22], and Sakawa and Yano [24, 25, 26] have advanced the use of “fuzzy goals” where the objective functions and constraints consist of fuzzy preference functions on different performance... |

1 | The battle to build better products. Mechanical Engineering 109 - ASHLEY - 1990 |

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Citation Context ... and manipulate a design’s different concerns and uncertainties. This development is crucial, since the preliminary decision making process of any design cycle has the greatest effect on overall cost =-=[3, 6, 14]-=-. In a design decision making process, engineers must trade-off widely differing concepts to realize a result which maximizes their overall preference for a design. These concepts are usually incommen... |

1 |
The battle to build better products
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Citation Context ... and manipulate a design’s different concerns and uncertainties. This development is crucial, since the preliminary decision making process of any design cycle has the greatest effect on overall cost =-=[3, 6, 14]-=-. In a design decision making process, engineers must trade-off widely differing concepts to realize a result which maximizes their overall preference for a design. These concepts are usually incommen... |