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Technical Brief

A Utility Copula Approach for Preference Functions in Engineering Design

[+] Author and Article Information
Ali E. Abbas

Department of Industrial and Systems Engineering,
Viterbi School of Engineering,
University of Southern California,
Los Angeles, CA 90089
Department of Public Policy,
Price School of Public Policy,
University of Southern California,
Los Angeles, CA 90089
e-mail: aliabbas@usc.edu

Zhengwei Sun

Department of Management Science and Engineering,
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 137(9), 094501 (Sep 01, 2015) (6 pages) Paper No: MD-14-1456; doi: 10.1115/1.4030774 History: Received July 29, 2014; Revised April 29, 2015; Online July 01, 2015

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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Grahic Jump Location
Fig. 1

Utility of the seven design alternatives versus the corner assessment U(14,7) when U(-3,21) = 0.5

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