Multi-attribute decision aid under incomplete information and hierarchical structure

Abstract This paper presents methods for dealing with incomplete information about both attribute weights and values under a hierarchically structured value tree. Incomplete information in this paper covers arbitrary linear inequalities and is hence to treat a more general situation than a previous restrictive definition of incomplete information that typically includes interval judgment. This may give decision makers chances that is enhanced freedom of choice and comforts of specification. We propose two techniques for prioritizing alternatives by (strict) dominance relationship. One is the extension of a previous method for operating flat-structured value trees to hierarchical ones. The other approach propagates pairwise dominance values from leaf nodes to topmost node consecutively which is also an extension of a previous method. Because the strict dominance rule fails to fully prioritize alternatives, as is usual the case under incomplete information, we suggest a new method, a measure of preference strength, which can provide decision makers with a single optimal alternative or full rank of alternatives without any further interaction with decision makers.

[1]  Gordon B. Hazen,et al.  Partial Information, Dominance, and Potential Optimality in Multiattribute Utility Theory , 1986, Oper. Res..

[2]  Rakesh K. Sarin,et al.  Ranking with Partial Information: A Method and an Application , 1985, Oper. Res..

[3]  Alan Pearman,et al.  Decision Making with Linear Partial Information (L.P.I.) , 1984 .

[4]  Martin Weber.  Decision Making with Incomplete Information , 1987 .

[5]  W. Cook,et al.  A multiple criteria decision model with ordinal preference data , 1991 .

[6]  Kyung S. Park,et al.  Tools for interactive multiattribute decisionmaking with incompletely identified information , 1997 .

[7]  Z. Kmietowicz,et al.  Decision theory, linear partial information and statistical dominance , 1984 .

[8]  Edward L. Hannan,et al.  Obtaining Nondominated Priority Vectors for Multiple Objective Decisionmaking Problems with Different Combinations of Cardinal and Ordinal Information , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Andrew P. Sage,et al.  ARIADNE: A knowledge-based interactive system for planning and decision support , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Raimo P. Hämäläinen,et al.  Preference Assessment by Imprecise Ratio Statements , 1992, Oper. Res..

[11]  Hokey Min.  International Supplier Selection , 1994 .

[12]  Andrew P. Sage,et al.  A model of multiattribute decisionmaking and trade-off weight determination under uncertainty , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  W. C. Benton,et al.  Vendor selection criteria and methods , 1991 .

[14]  Rakesh K Sarin.  Screening of multiattribute alternatives , 1977 .

[15]  Soung Hie Kim,et al.  Group decision making procedure considering preference strength under incomplete information , 1997, Comput. Oper. Res..