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.

1.
Adby, P., and Dempster, M., 1974, Introduction to Optimization Methods, Chapman and Hall, London.
2.
Akao, Y., 1990, Quality Function Deployment: Integrating Customer Requirements into Product Design, Productivity Press, Cambridge.
3.
Alger, J., and Hays, C., 1964, Creative Synthesis in Design, Prentice Hall, Englewood Cliffs, NJ.
4.
Arora, J. S., 1989, Introduction to Optimum Design, McGraw-Hill Book Company, New York.
5.
Ashley, S., 1992, “Engineous Explores the Design Space,” Mechanical Engineering, pp. 49–52.
6.
Asimow, M., 1962, Introduction to Design, Prentice-Hall, Inc., Englewood Cliffs, NJ.
7.
Baas
S.
, and
Kwakernaak
H.
,
1977
, “
Rating and Ranking of Multiple-Aspect Alternatives Using Fuzzy Sets
,”
Automatica
, Vol.
13
, pp.
47
48
.
8.
Barker, T., 1985, Quality by Experimental Design, Marcel Dekker, Inc., New York.
9.
Bellman
R.
, and
Zadeh
L.
,
1970
, “
Decision-making in a Fuzzy Environment
,”
Management Science
, Vol.
17
, No.
4
, pp.
141
163
.
10.
Benayoun
R.
,
de Montgolfier
J.
,
Tergny
J.
, and
Laritchev
O.
,
1971
, “
Linear Programming with Multiple Objective Functions: Step Method (STEM)
,”
Mathematical Programming
, Vol.
1
, No.
3
, pp.
366
375
.
11.
Biegel
P.
, and
Pecht
M.
,
1991
, “
Design Trade-Offs Made Easy
,”
Concurrent Engineering
, Vol.
1
, No.
3
, pp.
29
40
.
12.
Box, G. E., 1978, Statistics for Experimenters, J. Wiley and Sons, New York.
13.
Byrne, D. M., and Taguchi, S., 1986, “The Taguchi Approach to Parameter Design,” Quality Congress Transaction–Anaheim, pp. 168–177, ASQC.
14.
Chen, S.-J., and Hwang, C.-L., 1992, LFuzzy Multiple Attribute Decision Making: Methods and Applications, Vol. 375 of Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, New York, in collaboration with Frank P. Hwang.
15.
Diaz, A. R., 1988, “Fuzzy Set Based Models in Design Optimization,” Rao, S. S. ed., Advances in Design Automation-1988, Vol. DE-14, pp. 477–485, New York, ASME.
16.
Diaz, A. R., 1989, “A Strategy for Optimal Design of Hierarchial Systems Using Fuzzy Sets,” Dixon, J. R. ed., The 1989 NSF Engineering Design Research Conference, pp. 537–547 College of Engineering, University of Massachusetts, Amherst. NSF.
17.
Dlesk
D. C.
, and
Liebman
J. S.
,
1983
, “
Multiple Objective Engineering Optimization
,”
Engineering Optimization
, Vol.
6
, pp.
161
175
.
18.
Dong
W. M.
, and
Wong
F. S.
,
1987
, “
Fuzzy Weighted Averages and Implementation of the Extension Principle
,”
Fuzzy Sets and Systems
, Vol.
21
, No.
2
, pp.
183
199
.
19.
Doyle, J., Francis, B., and Tannenbaum, A., 1990, Feedback Control Theory, MacMillan Publishing Co.
20.
Dubois, D., and Prade, H., 1980, Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
21.
Dubois
D.
, and
Prade
H.
,
1982
, “
A Class of Fuzzy Measures Based on Triangular Norms
,”
International Journal of General Systems
, Vol.
8
, pp.
43
61
.
22.
Efstathiou
J.
, and
Rajkovicˇ
,
1979
, “
Multiattribute Decisionmaking Using A Fuzzy Heuristic Approach
,”
IEEE Transactions on Systems, Man and Cybernetics
, Vol.
9
, No.
6
, pp.
326
333
.
23.
Eschenauer, H., Koski, J., and Osyczka, A., eds., 1990, Multicriteria Design Optimization, Springer-Verlag, Berlin.
24.
Fishburn, P., 1982, Foundations of Expected Utility, D. Reidel.
25.
Freiheit, T., and Rao, S. S., 1988, “A Modified Game Theory Approach to Multi-Objective Optimization,” Rao, S. S. ed., Advances in Design Automation-1988, Vol. DE-14, pp. 107–114, New York, ASME.
26.
French, S., 1988, Decision Theory: An Introduction to the Mathematics of Rationality, Ellis Horwood, Chichester.
27.
Gavin
J. G.
,
1994
, “
Fly Me to the Moon: An Interview with Joseph G. Gavin, Jr.
,”
Technology Review
, Vol.
97
No.
5
, pp.
61
68
.
28.
Geoffrion
A.
,
Dyer
J.
, and
Feinberg
A.
,
1972
, “
An Interactive Approach for Multicriterion Optimization, with an Application to the Operation of an Academic Department
,”
Management Science
, Vol.
19
, No.
4
, pp.
357
368
.
29.
Golden, B., Wasil, E., and Harker, P., eds., 1989, The Analytic Hierarchy Process: Applications and Studies, Springer-Verlag, New York.
30.
Hammersley, J., and Handscomb, D., 1964, Monte Carlo Methods, Methuen, London.
31.
Harker, P. T., 1989, The Art and Science of Decision Making: The Analytic Hierarchy Process, pp. 3–36, Springer-Verlag, New York.
32.
Harrington, E., 1965, “The Desirability Function,” Industrial Quality Control, pp. 494–498.
33.
Harry, M. J., 1991, “The Nature of Six Sigma Quality,” Tech. rep., Government Electronics Group, Motorola, Inc.
34.
Hauser, J., and Clausing, D., 1988, “The House of Quality,” Harvard Business Review, pp. 63–73.
35.
Holmes, M. F., 1984, “Machine Dynamics, The Need for the Greater Productivity,” Reid, K. ed., Research Needs in Mechanical Systems, pp. 140–159, New York, ASME.
36.
Hunter
J.
,
1985
, “
Statistical Design Applied to Product Design
,”
Journal of Quality Technology
, Vol.
17
, No.
4
, pp.
210
221
.
37.
Iversen, G. R., 1984, Bayesian Statistical Inference, Series No. 07-043, Sage Publications, Beverly Hills and London.
38.
Jain, R., 1976, “Decisionmaking in the Presence of Fuzzy Variables,” IEEE Transactions on Systems, Man, and Cybernetics, pp. 698–703.
39.
Jain
R.
,
1977
, “
A Procedure for Multiple-Aspect Decision Making Using Fuzzy Sets
,”
International Journal of System Science
, Vol.
8
, No.
1
, pp.
1
7
.
40.
John, P. W., 1971, Statistical Design and Analysis of Experiments, Macmillan Co.
41.
Kackar, R. N., 1985, “Off-Line Quality Control, Parameter Design, and the Taguchi Approach,” Journal of Quality Technology, Vol. 17, No. 4.
42.
Kaufmann, A., and Gupta, M. M., 1988, Fuzzy Mathematical Models in Engineering and Management Science, North Holland, Amsterdam.
43.
Klir, G. J., and Folger, T. A., 1988, Fuzzy Sets, Uncertainty, and Information, Prentice Hall, Englewood Cliffs, NJ.
44.
Korhonen, P., and Laasko, J., 1985, “A Visual Interactive Method for Solving the Multiple Criteria Problem,” European Journal of Operations Research.
45.
Law, W. S., and Antonsson, E. K., 1994a, “Implementing the Method of Imprecision: An Engineering Design Example,” Proceedings of the Third IEEE International Conference on Fuzzy Systems (FUZZ-IEEE ’94), Vol. 1, pp. 358–363, IEEE Invited paper.
46.
Law, W. S., and Antonsson, E. K., 1994b, “Including Imprecision in Engineering Design Calculations,” Design Theory and Methodology-DTM ’94, Vol. DE-68, pp. 109–114, ASME.
47.
Law, W. S., and Antonsson, E. K., 1995, “Hierarchical Imprecise Design with Weights,” Proceedings of the Fourth IEEE International Conference on Fuzzy Systems (FUZZ-IEEE/IFES ’95), IEEE.
48.
Lucas
A.
,
1992
, “
Motorola’s Kaizen Brigrade
,”
Design News
, Vol.
48
, No.
3
, pp.
98
101
.
49.
Luhandjula
M.
,
1989
, “
Fuzzy Optimization: An Appraisal
,”
Fuzzy Sets and Systems
, Vol.
30
, pp.
257
282
.
50.
Menger
K.
,
1942
, “
Statistical Metrics
,”
Proceedings of the National Academy of Sciences
, Vol.
28
, pp.
535
537
.
51.
Milnor, J., 1957, “Games Against Nature,” Thrall, R., et al., eds., Decision Processes, pp. 49–59, New York, J. Wiley and Sons.
52.
Mu¨ller, K., and Tha¨rigen, M., 1994, “Applications of Fuzzy Hierarchies and Fuzzy MADM Methods to Innovative System Design,” Proceedings of the Third IEEE International Conference on Fuzzy Systems, Vol. 1, pp. 364–367, IEEE.
53.
Negoit¸aˇ, C. V., and Ralescu, D. A., 1975, Applications of Fuzzy Sets to Systems Analysis, Halsted Press, New York.
54.
Nishiwaki, Y., 1988, “Fuzzy Optimization of Radiation Protection and Nuclear Safety,” Kacprzyk, J., and Fedrizzi, M. eds., Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making, pp. 353–273 New York, Springer-Verlag.
55.
Nova´k, V., 1989 Fuzzy Sets and Their Applications, Adam Hilger, Philadelphia, Published in English by IOP Publishing Ltd.
56.
Osycska, A., 1984, Multi-Criterion Optimization in Engineering with Fortran Examples, Halstad Press, New York.
57.
Otto
K. N.
, and
Antonsson
E. K.
,
1991
, “
Trade-Off Strategies in Engineering Design
,”
Research in Engineering Design
, Vol.
3
, No.
2
, pp.
87
104
.
58.
Otto
K. N.
, and
Antonsson
E. K.
,
1993
a, “
Extensions to the Taguchi Method of Product Design
,”
ASME Journal of Mechanical Design
, Vol.
115
, No.
1
, pp.
5
13
.
59.
Otto, K. N., and Antonsson, E. K., 1993b, “The Method of Imprecision Compared Utility Theory for Design Selection Problems,” Design Theory and Methodology-DTM ’93, pp. 167–173, ASME.
60.
Otto
K. N.
, and
Antonsson
E. K.
,
1993
c, “
Turning Parameters in Engineering Design
,”
ASME Journal of Mechanical Design
, Vol.
115
, No.
1
, pp.
14
19
.
61.
Otto
K. N.
, and
Antonsson
E. K.
,
1994
a, “
Design Parameter Selection in the Presence of Noise
,”
Research in Engineering Design
, Vol.
6
, No.
4
, pp.
234
246
.
62.
Otto, K. N., and Antonsson, E. K., 1994b, “Modeling Imprecision in Product Design,” Proceedings of the Third IEEE International Conference on Fuzzy Systems (FUZZ-IEEE ’94), Vol. 1, pp. 346–351, IEEE Invited paper.
63.
Otto
K. N.
,
Lewis
A. D.
, and
Antonsson
E. K.
,
1993
, “
Approximating α-cuts with the Vertex Method
,”
Fuzzy Sets and Systems
, Vol.
55
, No.
1
, pp.
43
50
.
64.
Papalambros, P., and Wilde, D., 1988, Principles of Optimal Design, Cambridge University Press, New York.
65.
Pierre, D., 1986, Optimization Theory with Applications, Dover Press, New York.
66.
Pugh, S., 1990, Total Design, Addison-Wesley, New York.
67.
Raiffa, H., and Keeney, R., 1993, Decision with Multiple Objectives: Preferences and Value Tradeoffs, Cambridge University Press, Cambridge, U.K.
68.
Ramaswamy, R., Ulrich, K., Kishi, N., and Tomikashi, M., 1991, “Solving Parametric Design Problems Requiring Configuration Choices,” Stauffer, L. ed., Advances in Design Automation, pp. 103–110 New York, ASME Volume DE-31.
69.
Rao
S. S.
,
1987
, “
Description and Optimum Design of Fuzzy Mechanical Systems
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
109
, pp.
126
132
.
70.
Rao, S. S., and Dhingra, A. K., 1989, “Integrated Optimal Design of Planar Mechanisms Using Fuzzy Theories,” Advances in Design Automation-1989, Vol. DE-15-2, pp. 161–168, New York, ASME.
71.
Rao, S. S., and Dhingra, A. K., 1991, “Applications of Fuzzy Theories to Multi-Objective System Optimization,” NASA contractor report 177573, NASA Ames Research Center.
72.
Rao, S. S., Dhingra, A. K., and Kumar, V., 1990, “Nonlinear Membership Functions in the Fuzzy Optimization of Mechanical and Structural Systems,” Tech. rep. 90-1175-CP, AIAA, New York.
73.
Rao
S. S.
,
Sundararju
K.
,
Prakash
B.
, and
Balakrishna
C.
,
1992
, “
Multiobjective Fuzzy Optimization Techniques for Engineering Design
,”
Computers and Structures
, Vol.
42
, No.
1
, pp.
37
44
.
74.
Reklaitis, G. V., Ravindran, A., and Ragsdell, K. M., 1983, Engineering Optimization, Methods, and Applications, Wiley, New York.
75.
Ross, P., 1988, Taguchi Techniques for Quality Engineering, McGraw Hill, New York.
76.
Saaty
T.
,
1986
, “
Axiomatic Foundation of the Analytic Hierarchy Process
,”
Management Science
, Vol.
32
, pp.
841
855
.
77.
Saaty
T. L.
,
1978
, “
Exploring the Interface Between Hierarchies, Multiple Objectives, and Fuzzy Sets
,”
Fuzzy Sets and Systems
, Vol.
1
, pp.
57
68
.
78.
Saaty, T. L., 1980, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, McGraw Hill, New York.
79.
Salukvadze, M., 1989, Vector-Valued Optimization Problems in Control Theory, Academic Press, New York.
80.
Sandgren
E.
,
1990
, “
A Multi-Objective Design Tree Approach for the Optimization of Mechanisms
,”
Mechanisms and Machine Theory
, Vol.
25
, No.
3
, pp.
257
272
.
81.
Savage, J., 1954, The Foundations of Statistics (Revised Edition, Dover Publication, 1972), Wiley, New York.
82.
Seinfeld
J.
, and
McBride
W.
,
1970
, “
Optimization with Multiple Performance Criteria
,”
Ind. Eng. Chem. Process Des. Develop.
, Vol.
9
No.
1
, pp.
53
57
.
83.
Shafer, S., 1976, A Mathematical Theory of Evidence, Princeton University Press.
84.
Siddall, J. N., 1972, Analytical Decision Making in Engineering Design, Prentice-Hall.
85.
Siddall, J. N., 1983, Probabilistic Engineering Design; Principles and Applications, Marcel Dekker, New York.
86.
Singpurwalla, N. D., 1990, “Design by Decision Theory: A Unifying Perspective on Taguchi’s Approach to Quality Engineering,” NSF Design and Manufacturing Systems Grantees Conference, Tempe Arizona, NSF, the supplement to the Proceedings.
87.
Smets, P., 1988, “Belief Functions,” Smets, P., Mamdani, E., Dubois, D., and Prade, H. eds., Non-Standard Logics for Automated Reasoning, pp. 254–286, Academic Press.
88.
Steuer, R., 1986, Multiple Criteria Optimization: Theory, Computation, and Application, J. Wiley, New York.
89.
Sullivan, L. P., 1986, “Quality Function Deployment,” Quality Progress, pp. 39–50.
90.
Taguchi, G., 1986, Introduction to Quality Engineering, Asian Productivity Organization, Unipub, White Plains, NY.
91.
Taguchi, G., and Phadke, M., 1984, “Quality Engineering Through Design Optimization,” IEEE, pp. 1106–1113.
92.
Thurston
D. L.
,
1991
, “
A Formal Method for Subjective Design Evaluation with Multiple Attributes
,”
Research in Engineering Design
, Vol.
3
, No.
2
, pp.
105
122
.
93.
Thurston
D. L.
, and
Essington
S. K.
,
1993
, “
A Tool for Optimal Manufacturing Design Decisions
,”
Manufacturing Review
, Vol.
6
No.
1
, pp.
48
59
.
94.
Thurston, D. L., and Tian, Y., 1991, “A Method for Integrating Utility Analysis into an Expert System for Design Evaluation under Uncertainty,” D’Ambrosio, B., ed., Proceedings of the Seventh Uncertainty in Artificial Intelligence Conference, pp. 398–405, San Mateo, CA, Morgan Kaufmann Publishers.
95.
Tribus, M., 1969, Rational Descriptions, Decisions, and Designs, Pergamon Press, New York.
96.
Ulrich, K. T., and Pearson, S. A., 1993, “Does Product Design Really Determine 80% of Manufacturing Cost?,” Working paper MSA 3601–93, MIT, Sloan School of Management, Cambridge, MA.
97.
Vincent
T.
,
1983
, “
Game Theory as a Design Tool
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
105
, pp.
165
170
.
98.
Ward, A., 1989, “A Theory of Quantitative Inference for Artifact Sets, Applied to a Mechanical Design Compiler,” Ph.D. thesis, MIT.
99.
Ward
A. C.
,
Lozano-Pe´rez
T.
, and
Seering
W. P.
,
1990
, “
Extending the Constraint Propagation of Intervals
,”
Artificial Intelligence in Engineering Design and Manufacturing
, Vol.
4
, No.
1
, pp.
47
54
.
100.
Ward, A. C, and Seering, W. P., 1989a, “The Performance of a Mechanical Design Compiler,” memo 1084, MIT Artificial Intelligence Laboratory.
101.
Ward, A. C, and Seering, W. P., 1989b, “Quantitative Inference in a Mechanical Design Compiler,” memo 1062, MIT Artificial Intelligence Laboratory.
102.
Ward, A. C., Liker, J. K., Sobek, D. K., and Cristiano, J. J., 1994, “Set-Based Concurrent Engineering and Toyota,” Design Theory and Methodology-DTM ’94, Vol. DE68, pp. 79–90, ASME.
103.
Whitney
D. E.
,
1988
, “
Manufacturing by Design
,”
Harvard Business Review
, Vol.
66
, No.
4
, pp.
83
91
.
104.
Winkler, R. L., 1972, An Introduction to Bayesian Inference and Decision, Holt, Rinehart and Winston Inc.
105.
Wood
K. L.
, and
Antonsson
E. K.
,
1989
, “
Computations with Imprecise Parameters in Engineering Design: Background and Theory
,”
ASME Journal of Mechanisms, Transmissions, and Automation in Design
, Vol.
111
, No.
4
, pp.
616
625
.
106.
Wood
K. L.
, and
Antonsson
E. K.
,
1990
, “
Modeling Imprecision and Uncertainty in Preliminary Engineering Design
,”
Mechanism and Machine Theory
, Vol.
25
, No.
3
, pp.
305
324
, Invited paper.
107.
Wood
K. L.
,
Otto
K. N.
, and
Antonsson
E. K.
,
1992
, “
Engineering Design Calculations with Fuzzy Parameters
,”
Fuzzy Sets and Systems
, Vol.
52
, No.
1
, pp.
1
20
.
108.
Woodson, T., 1966, Introduction to Engineering Design, McGraw-Hill, New York.
109.
Yager
R.
,
1975
, “
Decision Making with Fuzzy Sets
,”
Decision Sciences
, Vol.
6
, No.
3
, pp.
590
600
.
110.
Yager
R.
,
1978
, “
Fuzzy Decision Making Including Unequal Objectives
,”
Fuzzy Sets and Systems
, Vol.
1
, pp.
87
95
.
111.
Zadeh
L. A.
,
1965
, “
Fuzzy Sets
,”
Information and Control
, Vol.
8
, pp.
338
353
.
112.
Zadeh
L. A.
,
1978
, “
Fuzzy Sets as a Basis for a Theory of Possibility
,”
Fuzzy Sets and Systems
, Vol.
1
, pp.
3
28
.
113.
Zimmermann, H. J., 1985, Fuzzy Set Theory—and Its Applications, Management Science/Operations Research, Kluwer-Nijhoff Publishing, Boston, MA.
114.
Zimmermann, H.-J., and Sebastian, H.-J., 1993, “Optimization and Fuzziness in Problems of Design and Configuration,” Proceedings of the Second IEEE International Conference on Fuzzy Systems, pp. 1237–1240, San Francisco, CA, IEEE, Pergamon Press.
115.
Zimmermann, H.-J., and Sebastian, H.-J., 1994, “Fuzzy Design—Integration of Fuzzy Theory with Knowledge-Based System-Design,” Proceedings of the Third IEEE International Conference on Fuzzy Systems, Vol. 1, pp. 352–357, IEEE.
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