Multi-criteria decision-making with random parameters
Abstract
Traditionally, parameters of multiattribute utility models, representing a decision maker's judgments, are treated as deterministic. This may not be realistic, because assessments of such parameters are judgmental and potentially fraught with biases and errors. To address this issue, researchers have extensively explored the sensitivity of the aggregate utility obtained from such models regarding their parameters. We treat such parameters as stochastic and investigate theoretically how their associated errors are propagated in an additive multiattribute utility function. The rationale of modeling the imprecise assessments of decision parameters as random variables is to mitigate the decision maker's cognitive assessment demands. Our first focus is on the variance of the aggregate utility, which is relatively unexplored. Such information is useful, for example, if the difference in the means of the aggregate utilities is sufficiently large to outweigh their corresponding variances, there would be no need to further modeling. We consider a no information case, an ordinal case, and an interval case regarding the attribute weights, to model the imprecise weight information by using a uniform distribution over the corresponding feasible region for the weights. In general, the results indicate that the reliability of the aggregate utility improves, for having a smaller variance, a the number of attributes increases. We also compare the variance of the aggregate utility obtained from a decomposition to that of a holistic assessment. This provides guidelines to a decision maker as to whether he or she should decompose to obtain a smaller variance for the aggregate utility estimate. The three cases are also compared theoretically with the deterministic equal weighting model to provide insights on how errors propagate through decomposition model. Our second focus is on the joint distribution of the attribute weights and the distribution of the aggregate utility. We theoretically and empirically investigate the nature of and develop the computational procedures for determining the distribution of the aggregate utility generated by imprecise decision parameters. The objective is that if the distributions of the aggregate utility of all alternatives are known, stochastic dominance could be invoked to filter out inferior alternatives.
Degree
Ph.D.
Advisors
Tang, Purdue University.
Subject Area
Statistics|Operations research|Management
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.