Utility copula functions (Abbas, 2009, “Multiattribute Utility Copulas,” Oper. Res., 57(6), pp. 1367–1383) construct multi-attribute utility surfaces by combining individual von-Neumann Morgenstern utility assessments for each of the attributes of a decision. Two important properties of utility copula functions guarantee consistency of the individual utility assessments with the aggregate multi-attribute utility surface: (i) the individual utility assessment for each attribute must be conducted at a specified reference value of the remaining (complement) attributes and (ii) the utility copula function must be a linear function of each attribute at some specified reference value. Preference functions (also known as aggregation functions) in engineering design construct preference surfaces to determine tradeoffs among design attributes by combining univariate utility assessments for each attribute, but they do not specify any reference value of the complement attributes for which the assessments should be made. Moreover, the preference function is not required to be a linear function of each attribute at any reference value of the complement. Consequently, the procedure used to construct some of the widely used preference functions in engineering design can result in preference surfaces that are inconsistent with the assessments used for its construction. We derive a unique form of preference functions, which allows for consistent assessments. We show that the resulting preference function is a special case of a utility copula function. With this interpretation, we also provide meaningful interpretations for the weights in preference functions to enable their appropriate assessment.
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September 2015
Technical Briefs
A Utility Copula Approach for Preference Functions in Engineering Design
Ali E. Abbas,
Ali E. Abbas
Department of Industrial and Systems Engineering,
Viterbi School of Engineering,
Viterbi School of Engineering,
University of Southern California
,Los Angeles, CA 90089
Department of Public Policy,
Price School of Public Policy,
e-mail: aliabbas@usc.edu
Price School of Public Policy,
University of Southern California
,Los Angeles, CA
90089e-mail: aliabbas@usc.edu
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Zhengwei Sun
Zhengwei Sun
Department of Management Science and Engineering,
School of Business,
e-mail: zsun4@illinois.edu
School of Business,
East China University of Science and Technology
,Shanghai 200237
, China
e-mail: zsun4@illinois.edu
Search for other works by this author on:
Ali E. Abbas
Department of Industrial and Systems Engineering,
Viterbi School of Engineering,
Viterbi School of Engineering,
University of Southern California
,Los Angeles, CA 90089
Department of Public Policy,
Price School of Public Policy,
e-mail: aliabbas@usc.edu
Price School of Public Policy,
University of Southern California
,Los Angeles, CA
90089e-mail: aliabbas@usc.edu
Zhengwei Sun
Department of Management Science and Engineering,
School of Business,
e-mail: zsun4@illinois.edu
School of Business,
East China University of Science and Technology
,Shanghai 200237
, China
e-mail: zsun4@illinois.edu
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 29, 2014; final manuscript received April 29, 2015; published online July 1, 2015. Assoc. Editor: Bernard Yannou.
J. Mech. Des. Sep 2015, 137(9): 094501 (6 pages)
Published Online: September 1, 2015
Article history
Received:
July 29, 2014
Revision Received:
April 29, 2015
Online:
July 1, 2015
Citation
Abbas, A. E., and Sun, Z. (September 1, 2015). "A Utility Copula Approach for Preference Functions in Engineering Design." ASME. J. Mech. Des. September 2015; 137(9): 094501. https://doi.org/10.1115/1.4030774
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