Decision Aiding On policy capturing with fuzzy measures Divakaran Liginlal a, * , Terence T. Ow b a Department of Operations and Information Management, School of Business, University of Wisconsin-Madison, 5281 Grainger Hall, 975 University Avenue, Madison, WI 53706, USA b Management Department, College of Business Administration, Marquette University, Milwaukee, WI 53201, USA Received 6 November 2002; accepted 26 February 2004 Available online 8 June 2004 Abstract Policy capturing methods generally apply linear regression analysis to model human judgment. In this paper, we examine the application of fuzzy set and fuzzy measure theories to obtain subjective descriptions of cue importance for policy capturing. At the heart of the approach is a method of learning fuzzy measures. The Shapley values associated with the fuzzy measures provide a basis for comparison with the results of linear regression. However, the fuzzy measure-theoretical approach provides additional insight into interaction effects corresponding to the nonlinear, noncompensatory nature of the underlying decision model. To illustrate the methodology, we estimated the importance of factors and the interactions among them that influence decisions related to strategic investments in telecommuni- cations infrastructure and compared the results from the fuzzy approach to those obtained from traditional statistical methods. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Fuzzy sets; Choquet integral; Judgment analysis; Fuzzy measure; Multicriteria analysis 1. Introduction Classical set theory and probability theory have provided the normative framework for formalizing uncertainty. Fuzzy measures and their integrals, first proposed by Sugeno (1974), are derived from classical measure theory. Economists use fuzzy measures to generalize the probabilistic framework of decision making and to avoid problems such as the Ellsberg paradox. The applications of the Dempster–Shafer belief measures (Shafer, 1976) and the possibility measures of Zadeh (Yager et al., 1987) are good examples. Applied to mul- tiple criteria decision making, fuzzy measures represent not only the importance of criteria but also the interactions among them, ranging from redundancy to synergy (Grabisch, 1996). As an aggregation operator, the Choquet integral is idempotent, continuous, and monotonically non- decreasing, encompassing all order statistics, such as the min (most intolerant behavior), max (most tolerant behavior), and the median (compromise). * Corresponding author. Tel.: +1-608-265-6188; fax: +1-608- 263-3142. E-mail addresses: dliginlal@bus.wisc.edu (D. Liginlal), ter- ence.ow@marquette.edu (T.T. Ow). 0377-2217/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2004.02.023 European Journal of Operational Research 167 (2005) 461–474 www.elsevier.com/locate/dsw