## A Formal Representational Theory for Engineering Design (1992)

Citations: | 14 - 1 self |

### BibTeX

@TECHREPORT{Otto92aformal,

author = {Kevin N. Otto},

title = {A Formal Representational Theory for Engineering Design},

institution = {},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

3665 |
Fuzzy sets
- Zadeh
- 1965
(Show Context)
Citation Context ...some AI researchers [151]. Fuzzy sets are another example of formal modeling of informal intentions. The original motivation for fuzzy sets, as developed by Zadeh, was to represent subjective beliefs =-=[200]-=-.18 This has been developed into “linguistic variables” [76, 201] which are formal words from a considered “term set” which is the set of all words considered, out of the “universe of discourse.” Eac... |

2430 |
A Mathematical Theory of Evidence
- Shafer
- 1976
(Show Context)
Citation Context ...Work Modeling decision making with real numbers is not new. There are many formalisms developed, and their use debated. Probability and Bayesian inferencing [21, 75, 176, 186], Dempster-Shafer theory =-=[154, 159]-=-, fuzzy sets and triangular norms in general [42, 84, 85, 102, 105, 204], and finally utility theory [53, 58, 129] are all existing formal methods for representing uncertainty. The similarities betwee... |

1461 |
Decisions with Multiple Objectives: Preferences and Value Tradeoffs
- Keeney, Raiffa
- 1976
(Show Context)
Citation Context ...ormal model” will be used to refer to the interpretations and intentions of the designer. Each desire in the informal model will be called an objective, maintaining the terminology of decision theory =-=[129]-=-. Objectives are unmeasurable (generally). This formalism only discusses the designer’s intentions, not any other person’s intentions. This assumes that customer requirements are inherited by the desi... |

914 | The concept of linguistic variable and its application to approximate reasoning
- Zadeh
- 1975
(Show Context)
Citation Context ...ormal modeling of informal intentions. The original motivation for fuzzy sets, as developed by Zadeh, was to represent subjective beliefs [200].18 This has been developed into “linguistic variables” =-=[76, 201]-=- which are formal words from a considered “term set” which is the set of all words considered, out of the “universe of discourse.” Each “term” is transformed into a relation over [0, 1] ⊂ R so semanti... |

639 |
Design and analysis of experiments
- Montgomery
(Show Context)
Citation Context ...he integral of Definition 5.6 can be approximated by experimental points in the noise space; i.e., experimental design techniques can be used. These points can be chosen using a factorial method. See =-=[12, 20, 80, 98]-=- for a discussion of factorial methods and methods for determining experimental points. Alternatively, MonteCarlo simulation [66] could be used for more accuracy.124 In the situation of the DPS ≃ Rn ... |

638 |
Upper and lower probabilities induced by a multivalued mapping
- Dempster
- 1967
(Show Context)
Citation Context ...ment, Dubois and Prade also discuss expected values of fuzzy quantities in the possibilistic, probabilistic, and their necessity environments [49, 50], relying on earlier integration work by Dempster =-=[31]-=-. Such work is therefore closely related to the123 developments presented here. The full ramifications of the development, though, is lost in their presentation. There is no consideration of hybrid u... |

597 |
Fuzzy Sets and Systems: Theory and Application
- Dubois, Prade
- 1980
(Show Context)
Citation Context ...new. There are many formalisms developed, and their use debated. Probability and Bayesian inferencing [21, 75, 176, 186], Dempster-Shafer theory [154, 159], fuzzy sets and triangular norms in general =-=[42, 84, 85, 102, 105, 204]-=-, and finally utility theory [53, 58, 129] are all existing formal methods for representing uncertainty. The similarities between these methods is that all them conform to the first three restrictions... |

579 |
Methods and applications of interval analysis
- Moore
- 1995
(Show Context)
Citation Context ...be seen by Figure 6.17, even simple coupled systems can induce complex preferences. Such computations may be difficult to perform. With a non-compensating design strategy, 1 however, interval methods =-=[99]-=- can be used to calculate level sets of ν. This difficultly is a computational concern; however, the induced preference for such systems is clearly defined. 1 Also when the geometric conditions to be ... |

565 |
Theory of Probability
- Jeffreys
- 1961
(Show Context)
Citation Context ...ays enter a formal model. This represents uncertainty in the ability to determine what is true in a model relative to what it is intended to represent. Such uncertainty is historically well developed =-=[79, 150, 168]-=-. This uncertainty form shall be called probabilistic uncertainty, or random. Definition 3.5 Probabilistic uncertainty is the uncertainty in the accuracy of a model relative to what it is intended to ... |

531 |
Bayesian Inference in Statistical Analysis
- Box, Tiao
- 1973
(Show Context)
Citation Context ...nal complexity of the problem. 4.7 Related Work Modeling decision making with real numbers is not new. There are many formalisms developed, and their use debated. Probability and Bayesian inferencing =-=[21, 75, 176, 186]-=-, Dempster-Shafer theory [154, 159], fuzzy sets and triangular norms in general [42, 84, 85, 102, 105, 204], and finally utility theory [53, 58, 129] are all existing formal methods for representing u... |

463 |
Fuzzy sets as a basis for a theory of a possibility, Fuzzy Sets and Systems
- Zadeh
- 1978
(Show Context)
Citation Context ...presence of probabilistic noise [129]. 3.3 Possibility Unlike probability, there can exist other parameter forms that remain uncertain throughout a design process, but are not characterized as random =-=[50, 202]-=-. For example, the limits on choices of a manufacturing engineer (during the fabrication process) over parameters within a design model are uncertain to the designer, but these choices are not random.... |

461 |
Monte Carlo Methods
- Hammersley, Handscornb
- 1964
(Show Context)
Citation Context .... These points can be chosen using a factorial method. See [12, 20, 80, 98] for a discussion of factorial methods and methods for determining experimental points. Alternatively, MonteCarlo simulation =-=[66]-=- could be used for more accuracy.124 In the situation of the DPS ≃ Rn , probabilistic optimization methods can be used to evaluate the solution, as presented by Siddall [156, Chapter 13]. Again, it m... |

450 |
Rational Choice and the Framing of Decisions
- Tversky, Kahneman
- 1986
(Show Context)
Citation Context ...∏ denotes Cartesian product. So it is assumed the designer can specify preferences on components Xk of the parameters in the design. Techniques for eliciting preferences have been extensively studied =-=[29, 30, 58, 67, 95, 129, 140, 158, 171, 178, 204]-=-, and will not be discussed in the text. Appendix A reviews this work, discussing procedures for eliciting preferences. It remains to be shown under what conditions the designer will be able to specif... |

405 | Statistics for Experimenters
- Box, Hunter, et al.
- 1978
(Show Context)
Citation Context ...ll informally interpret any resulting formal “terms” generated. Other examples of formal models exist in which the performance metrics are not known explicitly, such as experimental design techniques =-=[20, 124]-=-. The set of parameters to choose from, the set of performance metrics, and the set of confounding influences, though, are identified. What is not known is an explicit map from the design and noise pa... |

398 |
Possibility Theory: An Approach to Computerized Processing of Uncertainty
- Dubois, Prade
- 1988
(Show Context)
Citation Context ...presence of probabilistic noise [129]. 3.3 Possibility Unlike probability, there can exist other parameter forms that remain uncertain throughout a design process, but are not characterized as random =-=[50, 202]-=-. For example, the limits on choices of a manufacturing engineer (during the fabrication process) over parameters within a design model are uncertain to the designer, but these choices are not random.... |

394 |
Fuzzy set theory and its applications
- Zimmermann
- 1991
(Show Context)
Citation Context ...∏ denotes Cartesian product. So it is assumed the designer can specify preferences on components Xk of the parameters in the design. Techniques for eliciting preferences have been extensively studied =-=[29, 30, 58, 67, 95, 129, 140, 158, 171, 178, 204]-=-, and will not be discussed in the text. Appendix A reviews this work, discussing procedures for eliciting preferences. It remains to be shown under what conditions the designer will be able to specif... |

392 | Feedback Control Theory
- Doyle, Francis, et al.
- 1991
(Show Context)
Citation Context ...n six standard deviations. This is still informal. As a formal30 example, modern control theory has developed techniques to control parameters such that the worst case noise signal can be controlled =-=[40]-=-. As a specific example, consider again the accelerometer example introduced earlier, as shown in Figure 3.1. Suppose the manufacturing errors of the spring are desired to be contained within a specif... |

362 |
Multiple Criteria Optimization: Theory, Computation & Applications
- Steuer
- 1986
(Show Context)
Citation Context ...n space, one goal indicates the designer’s satisfaction with the25 design. Strategies are formally explicit in multi-objective function formulations of optimization problems. Weighted sum techniques =-=[52, 106, 160]-=- are compensating formulations: they minimize higher valued goals simultaneously with lower valued goals. Weighted sums also usually incorporate importance weighting coefficients. Minimax formulations... |

359 |
Real Analysis
- Royden
- 1989
(Show Context)
Citation Context ...he term metric refers to a pseudo-metric. P does not form a true metric, but rather a pseudo-metric. The uniqueness condition of a true metric is not satisfied: |P(x) − P(y)| = 0 ̸⇔ x = y. See Royden =-=[139]-=- for a discussion on metrics.40 designer will be completely dissatisfied with the design. If the annihilation condition is removed, it would allow a designer to choose a design in which the designer ... |

355 |
Measure theory
- Halmos
- 1950
(Show Context)
Citation Context ...ainty measure space (NPS, B, g), is a set NPS of elements n, a σ-algebra B of sets over the NPS, and an uncertainty measure g : B → [0, 1]. An uncertainty measure is different from a Lebesgue measure =-=[64]-=- or a fuzzy measure [43, 50, 164, 165]. An uncertainty measure is a function g : B → [0, 1] intended to measure the effects of noise. Three specific measures will be developed: the probability measure... |

344 |
The Principles of Design
- Suh
- 1990
(Show Context)
Citation Context ...ess. Asimow [9] or Pugh [71, 126] describe a transition model of preliminary design through detailed design through manufacturing. Ullman [179] also presents design as refinement of descriptions. Suh =-=[166]-=- describes design as a transition from functional descriptions to form descriptions. Pahl and Beitz [121] describe a model of stages with function to form transformations. Adams [2] considers design a... |

255 | Quality Engineering using Robust Design - Phadke - 1989 |

234 |
Fuzzy sets uncertainty and information
- Klir, Folger
- 1992
(Show Context)
Citation Context ...new. There are many formalisms developed, and their use debated. Probability and Bayesian inferencing [21, 75, 176, 186], Dempster-Shafer theory [154, 159], fuzzy sets and triangular norms in general =-=[42, 84, 85, 102, 105, 204]-=-, and finally utility theory [53, 58, 129] are all existing formal methods for representing uncertainty. The similarities between these methods is that all them conform to the first three restrictions... |

226 |
The House of Quality
- Hauser, Clausing
- 1988
(Show Context)
Citation Context ...e intentions, which may or may not be “accurate.” Thus, this thesis clarifies the need for converting informal descriptions into formal models. Others also observe this need. The central theme of QFD =-=[4, 69]-=- is “voice of the customer,” meaning one must determine what the needs of the customer are, and perform all design activities to maximize customer satisfaction. Also, in the architectural design domai... |

223 |
Theory of Fuzzy Integrals and its Applications
- Sugeno
- 1974
(Show Context)
Citation Context ...iously. The trade-offs made among the satisfaction levels is not made explicit. Other decision making methods have been developed using fuzzy measures [63, 74, 165], as originally developed by Sugeno =-=[164]-=-. Here one develops a fuzzy measure space, similar to a σ-algebra (also known as a Borel field), but where the measure is not required to satisfy additivity, only monotonicity. The fuzzy measure is in... |

217 |
Decision-Making in a Fuzzy Environment
- Bellman, Zadeh
- 1970
(Show Context)
Citation Context ... when trading off goals in a non-compensating manner, and without considering importance weightings. The first paper describing the use of fuzzy sets for decision making was work by Bellman and Zadeh =-=[15]-=-. A decision was defined as a convolution of the constraints and goals, as done in this work. When such goals are equally important, then the non-compensating metric of Equation 4.5 was proposed as an... |

173 |
Differential manifolds
- Lang
- 1972
(Show Context)
Citation Context ...vector fields. X now denotes a vector field, not a subset of the DPS as was used in previous sections. This will only be true in this section. Let X ∈ X (M) and f ∈ F(M). The Lie derivative (see Lang =-=[89]-=-) of f along X will be written LXf. If (d1, . . . , dn ) are coordinates in a chart for M, and if, in this chart, the vector field X is represented by (X1(d1, . . . , dn ), . . . , Xn (d1, . . . , dn ... |

163 |
Introduction to Fuzzy Arithmetic: Theory and Applications
- Kaufmann, Gupta
- 1985
(Show Context)
Citation Context ...this work. Though these formulations have been previously determined, nowhere have the ramifications of convolving the separate theories been methodically studied, as is done here. Kaufmann and Gupta =-=[83]-=-, however, do introduce “hybrid numbers,” which are parameters with both a fuzzy and a probabilistic component, on which computations are performed. Wood [187] and Wood and Antonsson [189] extend this... |

162 |
Decision theory. An Introduction to the Mathematics of Rationality
- French
- 1986
(Show Context)
Citation Context ...∏ denotes Cartesian product. So it is assumed the designer can specify preferences on components Xk of the parameters in the design. Techniques for eliciting preferences have been extensively studied =-=[29, 30, 58, 67, 95, 129, 140, 158, 171, 178, 204]-=-, and will not be discussed in the text. Appendix A reviews this work, discussing procedures for eliciting preferences. It remains to be shown under what conditions the designer will be able to specif... |

151 |
Naive Set Theory
- Halmos
- 1974
(Show Context)
Citation Context ... Wβ ⊆ Wα = Pα. Therefore f(d) ≤ y α max, contradicting d ∈ f −1 (P α max). Thus H2 must hold.205 Appendix C Nomenclature A very brief explanation of the symbols and operations used are given. Halmos =-=[65]-=-, Royden [139], and Lang [89] provide further reading. empty set: The empty set ∅ is a set with no elements. For example, {x ∈ R | x2 = −1} = ∅. composition: The composition ◦ is used to mean µ ◦ f(d)... |

126 |
The Mechanical Design Process
- Ullman
- 2001
(Show Context)
Citation Context ...been several historical models of engineering design as a process. Asimow [9] or Pugh [71, 126] describe a transition model of preliminary design through detailed design through manufacturing. Ullman =-=[179]-=- also presents design as refinement of descriptions. Suh [166] describes design as a transition from functional descriptions to form descriptions. Pahl and Beitz [121] describe a model of stages with ... |

119 |
The algebra of probable inference
- Cox
- 1961
(Show Context)
Citation Context ...rther, the probability of either of two disjoint events occurring must equal the real additive probability of the two events.95 These restrictions are sufficient to derive an uncertainty measure P r =-=[28, 42, 43, 87, 176]-=-. Thus, for events Nj, Nk ∈ B such that Nj ∩ Nk = ∅, if g is restricted to obey: g(Nj) + g(NPS\Nj) = 1 g(Nj) + g(Nk) = g(Nj ∪ Nk) (5.12) then g is a probability measure of classical probability theory... |

107 |
Quality Function Deployment: Integrating Customer Requirements into Product Design. Translated by Glenn Mazur
- Akao, ed
- 1990
(Show Context)
Citation Context ...e intentions, which may or may not be “accurate.” Thus, this thesis clarifies the need for converting informal descriptions into formal models. Others also observe this need. The central theme of QFD =-=[4, 69]-=- is “voice of the customer,” meaning one must determine what the needs of the customer are, and perform all design activities to maximize customer satisfaction. Also, in the architectural design domai... |

107 |
Engineering Optimization Methods and Applications
- Reklaitis, Ravindran, et al.
- 1983
(Show Context)
Citation Context ...zation Other methodologies exist that do not explicitly represent preferences on parameters. For example, simple optimization formulations (linear, non-linear, integer, and mixed integer programming) =-=[3, 6, 123, 125, 137]-=- assume a relationship between preference and the objective function: the lower the function, the higher the preference. Also, a relation is assumed between preference and the constraint functions: if... |

95 |
Foundations of Expected Utility
- Fishburn
- 1982
(Show Context)
Citation Context ...debated. Probability and Bayesian inferencing [21, 75, 176, 186], Dempster-Shafer theory [154, 159], fuzzy sets and triangular norms in general [42, 84, 85, 102, 105, 204], and finally utility theory =-=[53, 58, 129]-=- are all existing formal methods for representing uncertainty. The similarities between these methods is that all them conform to the first three restrictions of Table 4.2 (boundary conditions, monoto... |

94 |
Introduction to optimum design
- Arora
- 1989
(Show Context)
Citation Context ...zation Other methodologies exist that do not explicitly represent preferences on parameters. For example, simple optimization formulations (linear, non-linear, integer, and mixed integer programming) =-=[3, 6, 123, 125, 137]-=- assume a relationship between preference and the objective function: the lower the function, the higher the preference. Also, a relation is assumed between preference and the constraint functions: if... |

85 |
Axiomatic Set Theory
- Suppes
- 1972
(Show Context)
Citation Context ...hich computations can occur. Engineering design, as desired to be modeled by this thesis, requires computations on formal models. It is proposed that a formal model can be characterized by set theory =-=[17, 65, 167]-=-, distinguishing formal models (sets) from informal characterizations, and computation (mathematical operations) from informal reasoning. After formalizing a design, informal characterizations can con... |

73 |
Optimization Theory with Applications
- Pierre
- 1965
(Show Context)
Citation Context ...zation Other methodologies exist that do not explicitly represent preferences on parameters. For example, simple optimization formulations (linear, non-linear, integer, and mixed integer programming) =-=[3, 6, 123, 125, 137]-=- assume a relationship between preference and the objective function: the lower the function, the higher the preference. Also, a relation is assumed between preference and the constraint functions: if... |

72 |
Principles of Optimal Design
- Papalambros
- 2000
(Show Context)
Citation Context ...inciple. Value analysis is a methodology to ensure that the amount of quality per amount of cost is maximized. Performance is therefore amount of quality per amount of cost. Optimization formulations =-=[123]-=- conform to the performance improvement principle. Optimization formulations determine an overall set of design parameters by minimizing an objective function, subject to additional constraint functio... |

68 |
Games against nature
- Milnor
- 1954
(Show Context)
Citation Context ...nalyses at this preliminary stage, as Pugh suggests, rather than simply accepting a weighted sum solution as “correct.” Such different methods have been analyzed by others. In a classic paper, Milnor =-=[96]-=- considers the choice among four alternatives, and demonstrates how four different strategies selected each of the four different alternatives. This is not seen as a refutation of the formalization; r... |

67 |
Introduction to Quality Engineering, Asian Productivity Organization (distributed by American Supplier Institute
- Taguchi
- 1986
(Show Context)
Citation Context ... are not formal concepts at the level of discussion intended. What is “quality?” What is “cost?” Cost in time? Cost in dollars (whose dollars)? Perhaps corporate profits? Others suggest societal loss =-=[169]-=-. These are informal concepts: they cannot be formally optimized. When a specific problem is encountered, formal performance metrics can be developed to reflect these informal terms. “Quality” and “co... |

65 |
Rational, Descriptions, Decisions and Designs
- Tribus
- 1969
(Show Context)
Citation Context ...on is a statement related to rationality. There are many different definitions of rationality. One definition is that a rational person is one who forms decisions consistent with Bayesian inferencing =-=[176]-=-. Others define rational as one who forms decisions consistent with idempotency, monotonicity, continuity, associativity, and commutativity restrictions [59]. In decision making, rational can also be ... |

64 | A class of fuzzy measures based on triangular norms - Dubois, Prade - 1982 |

60 |
Total design
- Pugh
- 1991
(Show Context)
Citation Context ...al engineering design process involves the satisfaction of needs through the development of a product. There have been several historical models of engineering design as a process. Asimow [9] or Pugh =-=[71, 126]-=- describe a transition model of preliminary design through detailed design through manufacturing. Ullman [179] also presents design as refinement of descriptions. Suh [166] describes design as a trans... |

60 |
Taguchi Techniques for Quality Engineering
- Ross
- 1998
(Show Context)
Citation Context ...aces, others have claimed that maximizing the expected value is not the only formalism to adopt. Another method might be to instead rate the design by the variance across the NPS. In Taguchi’s method =-=[26, 73, 81, 138, 157, 169, 170, 177]-=-, for example, the “quality” of a design parameter set ⃗ d is defined by the expected variation of a single performance parameter f from a target value τ. The difference between the developments is si... |

59 |
Belief functions
- Smets
- 1988
(Show Context)
Citation Context ...not so clear what formal model of uncertainty should be used to represent this. Traditionally, formal probability has been used [156], but more recent models challenge this and apply belief functions =-=[159]-=- or fuzzy sets [88] for this uncertainty. Many current formal design practices use probability. Probabilistic optimization [156] introduces noise parameters into optimization formulations, and maximiz... |

56 |
Fuzzy weighted averages and implementation of the extension principle, Fuzzy Sets and Systems 21
- Dong, Wong
- 1987
(Show Context)
Citation Context ...6) Dα is defined for all α but zero, and so define D0 as the support of µ. This definition is natural, in that Dα → D0 as α → 0. Now the Level Interval Algorithm, (LIA), as presented by Dong and Wong =-=[39]-=- (there called the “Fuzzy Weighted Average” algorithm), or as presented by Dong and Shah [38] (there called the “Vertex Method”), outlines a simple and efficient algorithm for calculating ν. A condens... |

55 | Computations with Imprecise Parameters in Engineering Design: Background and Theory," Engineering Design Research Laboratory Report 88-01, California I stitute of Technology
- Wood, Antonsson
(Show Context)
Citation Context ...c : the supremum of the combination of the preferences specified both on DPS and PPS. Since this calculation reverses the direction of usage of the induced preference, it is termed the backwards path =-=[188]-=-. 6.4.1 Definitions and Notations It is desired to combine preferences on DPS and PPS in the following manner. Let P : [0, 1] 2 → [0, 1] be monotonic in its first argument. Thus, if 0 ≤ a ≤ b ≤ 1, the... |

53 | A note on the extension principle for fuzzy set - Nguyen |

48 | Fuzzy measures and fuzzy integrals: a survey, in - Sugeno - 1977 |