A Utility Copula Approach for Preference Functions in Engineering Design

Abstract

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.