## The method of imprecision compared to utility theory for design selection problems (1993)

Venue: | In Proceedings of the 1993 ASME Design Theory and Methodology Conference |

Citations: | 20 - 5 self |

### BibTeX

@INPROCEEDINGS{Otto93themethod,

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

title = {The method of imprecision compared to utility theory for design selection problems},

booktitle = {In Proceedings of the 1993 ASME Design Theory and Methodology Conference},

year = {1993},

pages = {167--173}

}

### Years of Citing Articles

### OpenURL

### Abstract

Two methods have been proposed for manipulating uncertainty reflecting designer choice: utility theory and the method of imprecision. Both methods represent this uncertainty across decision making attributes with zero to one ranks, higher preference modeled with a higher rank. The two methods can differ, however, in the combination metrics used to combine the ranks of the incommensurate design attributes. Utility theory resolves the multi-attributes using various well proven additive metrics. In contrast, the method of imprecision resolves by also considering non-additive metrics, such as ranking by the worst case performance or by multiplicative metrics. The axioms of utility theory are appropriate for designs where it is deemed the attributes can always be traded off, even to the point of achieving zero preference in some attributes. In the case of a design with attributes which cannot have zero preference, such as stress limits or maximum allowed cost, the method of imprecision is more appropriate: it trades off attribute levels without permitting any of them to be traded off to zero performance. 1

### Citations

1263 |
Decisions with Multiple Objectives: Preferences and Value Tradeoffs
- Keeney, Raiffa
- 1988
(Show Context)
Citation Context ...nn and Morgenstern, 1947), originally developed by von Neumann and Morgenstern (von Neumann and Morgenstern, 1947) for economic decision making, has been applied to design (Howard and Matheson, 1984; =-=Raiffa and Keeney, 1976-=-; Thurston, 1991; Thurston and Locasio, 1992; Tribus, 1969). The Method of Imprecision (Otto and Antonsson, 1991a; Wood and Antonsson, 1989), developed by Otto, Antonsson, and Wood, is a similar metho... |

230 |
The Theory of Games and Economic Behaviour
- Neumann, Morgenstern
- 1944
(Show Context)
Citation Context ... phase where a designer makes choices over particular values to use in a design model. In the design literature, two similar methods have been proposed for this particular design task. Utility theory =-=[22]-=-, originally developed by von Neumann and Morgenstern [22] for economic decision making, has been applied to design [9, 17, 18, 19, 20]. The Method of Imprecision [14, 24], developed by Otto, Antonsso... |

144 |
Decision theory: An introduction to the mathematics of rationality
- French
- 1986
(Show Context)
Citation Context ... the theory adds sufficient restrictions such that one can (even though the components of the PPS = X are not independent) make preference specifications on each component separately (Fishburn, 1982; =-=French, 1988-=-; Howard, 1968; Krantz et al., 1971; Raiffa and Keeney, 1976). That is, the different performance parameters are assumed to be such that one can make specifications of one component (say p 1 ) with th... |

80 |
The Foundations of Expected Utility
- Fishburn
- 1982
(Show Context)
Citation Context ...onents, however, the theory adds sufficient restrictions such that one can (even though the components of the PPS = X are not independent) make preference specifications on each component separately (=-=Fishburn, 1982-=-; French, 1988; Howard, 1968; Krantz et al., 1971; Raiffa and Keeney, 1976). That is, the different performance parameters are assumed to be such that one can make specifications of one component (say... |

60 |
Rational descriptions, decisions and designs
- Tribus
- 1969
(Show Context)
Citation Context ...ilar methods have been proposed for this particular design task. Utility theory [22], originally developed by von Neumann and Morgenstern [22] for economic decision making, has been applied to design =-=[9, 17, 18, 19, 20]-=-. The Method of Imprecision [14, 24], developed by Otto, Antonsson, and Wood, is a similar method developed for engineering design. This paper will analytically compare the two methods by examining th... |

53 | Computations with Imprecise Parameters in Engineering Design: Background and Theory
- Wood, Antonsson
- 1989
(Show Context)
Citation Context ...aking, has been applied to design (Howard and Matheson, 1984; Raiffa and Keeney, 1976; Thurston, 1991; Thurston and Locasio, 1992; Tribus, 1969). The Method of Imprecision (Otto and Antonsson, 1991a; =-=Wood and Antonsson, 1989-=-), developed by Otto, Antonsson, and Wood, is a similar method developed for engineering design. This paper will analytically compare the two methods by examining their basic axioms of usage and discu... |

51 |
The Cogency of Decision Analysis
- Howard
- 1992
(Show Context)
Citation Context ...ds sufficient restrictions such that one can (even though the components of the PPS = X are not independent) make preference specifications on each component separately (Fishburn, 1982; French, 1988; =-=Howard, 1968-=-; Krantz et al., 1971; Raiffa and Keeney, 1976). That is, the different performance parameters are assumed to be such that one can make specifications of one component (say p 1 ) with the remaining co... |

40 | A Formal Method for Subjective Design Evaluation With Multiple Attributes,” Res - Thurston - 1991 |

31 |
Criteria Aggregation and Ranking of Alternatives in the Framework of Fuzzy Set Theory, in Fuzzy Sets and Decision Analysis
- Dubois, Prade
- 1984
(Show Context)
Citation Context ... over [0,1] ranks as the min function. That is, ��(d) = min \Phi �� 1 ; : : : ; �� N \Psi (3) Table 2 lists a set of necessary and sufficient restrictions required to restrict P to min, as=-= proven in (Dubois and Prade, 1984-=-). If a designer believes these restrictions, then the designer must use min when making decisions. An important additional restriction used to restrict P to min is the identity restriction. If a desi... |

29 |
Sources of bias in assessment procedures for utility functions
- Hershey, Kunreuther, et al.
- 1988
(Show Context)
Citation Context ...ifically to include the iterative nature of design decision making, and initial preferences are intended to be modifiable. However, in practice, utility theory is also used iteratively (French, 1988; =-=Hershey, Kunreuther, and Schoemaker, 1988-=-). A final consideration to contrast the two methods is by their overall relevance to the complete design task. Our discussion thus far has focused on the designer's task of choosing particular design... |

21 |
Game Theory as a Design Tool
- Vincent
- 1983
(Show Context)
Citation Context ... is mathematically compensated for by large preference of another goal (such as, for example, cost). This is not reasonable for engineering design, as others have also argued (Biegel and Pecht, 1991; =-=Vincent, 1983-=-). The restrictions in Table 1 are deemed necessary for all design, but they are not sufficient to restrict P to any operator. More restrictions are needed. Consider rating a design by its most poorly... |

16 | Trade-Off Strategies in Engineering Design
- OTTO, ANTONSSON
- 1991
(Show Context)
Citation Context ...47) for economic decision making, has been applied to design (Howard and Matheson, 1984; Raiffa and Keeney, 1976; Thurston, 1991; Thurston and Locasio, 1992; Tribus, 1969). The Method of Imprecision (=-=Otto and Antonsson, 1991-=-a; Wood and Antonsson, 1989), developed by Otto, Antonsson, and Wood, is a similar method developed for engineering design. This paper will analytically compare the two methods by examining their basi... |

14 |
Fuzzy decision analysis: Some criticisms
- French
- 1984
(Show Context)
Citation Context ...r the criteria, and then optimizing the "utility, " as combined with numerical methods consistent with the initial axioms accepted. Any other way of determining a solution is said to be &quo=-=t;irrational" (French, 1984-=-, 1988). The philosophy behind the method of imprecision, on the other hand, is to let the designer select from a variety of overall combinations, to observe the results, without dictating which metri... |

14 | A Formal Representational Theory for Engineering Design
- Otto
- 1992
(Show Context)
Citation Context ...with these restrictions. Thus, if the restrictions are believed, then a designer must use utility theory when making decisions. In contrast, the method of imprecision (presented in detail previously (=-=Otto, 1992-=-; Otto, Lewis, and Antonsson, 1992; Otto and Antonsson, 1991a, 1991b; Wood, 1989; Wood and Antonsson, 1989; Wood, Otto, and Antonsson, 1990)) is a method developed to formally negotiate a design probl... |

14 |
Foundations of measurement, Volume I
- Krantz, Luce, et al.
- 1971
(Show Context)
Citation Context ...ed, if the designer can elicit the preferential ordering over Xk, (an assumption which must be met to be able to apply the method of imprecision). A rigorous method for doing so is the lottery method =-=[11]-=-, by asking the designer to first identify over all Xk the least and most preferred points xk 0 and xk 1. These are given numerical ranks 0 and 1. Then for every other point xk i in Xk, one asks a lot... |

11 |
A Method for Representing and Manipulating Uncertainties in Preliminary Engineering Design
- Wood
- 1989
(Show Context)
Citation Context ... with these restrictions. Thus, if the restrictions are believed, then a designer must use utility theory when making decisions. In contrast, the method of imprecision (presented in detail previously =-=[12, 13, 14, 15, 23, 24, 25]-=-) is a method developed to formally negotiate a design problem as desired by a designer. Originally developed as a method for providing preliminary metrics of performance [23, 24, 25], it has been exp... |

10 |
Trade-Off Strategies in the Solution of Imprecise Design Problems
- Otto, Antonsson
- 1991
(Show Context)
Citation Context ...cessary for all design, but they are not sufficient to restrict P to any operator. More restrictions are needed. Consider rating a design by its most poorly performing aspect. Such a design strategys(=-=Otto and Antonsson, 1991a) for resol-=-ving the multiple goals can be directly formalized over [0,1] ranks as the min function. That is, ��(d) = min \Phi �� 1 ; : : : ; �� N \Psi (3) Table 2 lists a set of necessary and suffici... |

9 |
Design trade-offs made easy
- BIEGEL, PECHT
- 1991
(Show Context)
Citation Context ...le, material stress) but is mathematically compensated for by large preference of another goal (such as, for example, cost). This is not reasonable for engineering design, as others have also argued (=-=Biegel and Pecht, 1991-=-; Vincent, 1983). The restrictions in Table 1 are deemed necessary for all design, but they are not sufficient to restrict P to any operator. More restrictions are needed. Consider rating a design by ... |

8 |
Determining optimal preference points with dependent variables. Fuzzy Sets and Systems
- Otto, Lewis, et al.
- 1992
(Show Context)
Citation Context ...estrictions. Thus, if the restrictions are believed, then a designer must use utility theory when making decisions. In contrast, the method of imprecision (presented in detail previously (Otto, 1992; =-=Otto, Lewis, and Antonsson, 1992-=-; Otto and Antonsson, 1991a, 1991b; Wood, 1989; Wood and Antonsson, 1989; Wood, Otto, and Antonsson, 1990)) is a method developed to formally negotiate a design problem as desired by a designer. Origi... |

7 | A Formal Method for Representing Uncertainties in Engineering Design - Wood, Otto, et al. - 1990 |

3 | Design Parameter Selection in the Presence of Noise
- Otto, Antonsson
- 1991
(Show Context)
Citation Context ...to cases of no confounding influences (noise). Therefore influences such as manufacturing errors or effects of agents other than the designer will not be considered here, and are discussed elsewhere (=-=Otto and Antonsson, 1992-=-). Utility theory (von Neumann and Morgenstern, 1947) is an analytical method for making a decision concerning an action to take, given a set of multiple criteria upon which the decision is to be base... |

2 |
Response sets and test validity
- Cronbath
- 1946
(Show Context)
Citation Context ...ly directly state preferences for goals, since many reflect customer requirements which have been expressed to the designer. While such direct methods have been shown to produce inconsistent results (=-=Cronbath, 1946-=-, 1950), it is argued that an iterative design process is iterative to eliminate such inconsistencies. A designer is free to change preference ranks in light of the implied results of the initial spec... |

2 |
Further evidence on response sets and test designs
- Cronbath
- 1950
(Show Context)
Citation Context ...ply directly state preferences for goals, since many reflect customer requirements which have been expressed to the designer. While such direct methods have been shown to produce inconsistent results =-=[2, 3]-=-, it is argued that an iterative design process is iterative to eliminate such inconsistencies. A designer is free to change preference ranks in light of the implied results of the initial specificati... |

2 |
A Method for Representing and Manipulating
- Wood
- 1989
(Show Context)
Citation Context ... must use utility theory when making decisions. In contrast, the method of imprecision (presented in detail previously (Otto, 1992; Otto, Lewis, and Antonsson, 1992; Otto and Antonsson, 1991a, 1991b; =-=Wood, 1989-=-; Wood and Antonsson, 1989; Wood, Otto, and Antonsson, 1990)) is a method developed to formally negotiate a design problem as desired by a designer. Originally developed as a method for providing prel... |

1 |
Multi-attribute optimal design of structural dynamic systems
- Thurston, Locasio
- 1992
(Show Context)
Citation Context ...eloped by von Neumann and Morgenstern (von Neumann and Morgenstern, 1947) for economic decision making, has been applied to design (Howard and Matheson, 1984; Raiffa and Keeney, 1976; Thurston, 1991; =-=Thurston and Locasio, 1992-=-; Tribus, 1969). The Method of Imprecision (Otto and Antonsson, 1991a; Wood and Antonsson, 1989), developed by Otto, Antonsson, and Wood, is a similar method developed for engineering design. This pap... |