Abstract
The uncertain multiple attribute decision making (UMADM) problems are investigated, in which the information about attribute weights is known partly and the attribute values take the form of interval numbers, and the decision maker (DM) has uncertain multiplicative preference information on alternatives. We make the decision information uniform by using a transformation formula, and then establish an objective-programming model. The attribute weights can be determined by solving the developed model. The concept of interval positive ideal point of alternatives (IPIPA) is introduced, and an approach based on IPIPA and projection to ranking alternatives is proposed. The method can avoid comparing and ranking interval numbers, and can reflect both the objective information and the DM’s subjective preferences.
Similar content being viewed by others
References
N. Bryson A. Mobolurin (1996) ArticleTitle“An Action Learning Evaluation Procedure for Multiple Criteria Decision Making Problems” European Journal of Operational Research 96 379–386
S. J. Chen C. L. Hwang (1992) Fuzzy Multiple Attribute Decision Making Springer Berlin
Q. L. Da Z. S. Xu (2002) ArticleTitle“Single Objective Optimization Model in Uncertain Multi-attribute Decision-making” Journal of Systems Engineering 17 IssueID1 50–55
Z.P. Fan Q. Zhang (1999) ArticleTitle“The Revision for the Uncertain Multiple Attribute Decision Making Models” Systems Engineering—Theory & Practice 21 IssueID10 42–47
J. Fodor M. Roubens (1994) Fuzzy Preference Modelling and Multicriteria Decision Support Kluwer Academic Publishers Dordrecht
J. C. Harsanyi (1955) ArticleTitle“Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility” Journal of Political Economy 63 309–321
C. L. Hwang K. Yoon (1981) Multiple Attribute Decision Making Springer-Verlag Berlin
K. S. Lee K. S. Park Y. S. Eum K. Park (2001) ArticleTitle“Extended Methods for Identifying Dominance and Potential Optimality in Multi-criteria Analysis With Imprecise Information” European Journal of Operational Research 134 557–563
T. L. Saaty (1980) The Analytic Hierarchy Process McGraw-Hill New York
T. L. Saaty L. G. Vargas (1987) ArticleTitle“Uncertainty and Rank Order in the Analytic Hierarchy Process” European Journal of Operational Research 32 107–117
R. N. Xu X. Y. Zhai (1992) ArticleTitle“Extensions of the Analytic Hierarchy Process in Fuzzy Environment” Fuzzy Sets and Systems 52 251–257
Z. S. Xu (2000) “On Method for Priorities of Fuzzy Synthetic Evaluations” J. F Gu (Eds) Systems Engineering, Systems Science and Complexity Research. Research Information Ltd United kingdom 507–511
Z. S. Xu Q. L. Da (2004) ArticleTitle“An Uncertain Ordered Weighted Geometric Averaging (UOWGA) Operator and its Application” Information: An International Journal 7 75–182
Z. S. Xu (2004) Uncertain Multiple Attribute Decision Making: Methods and Applications Tsinghua University Press Beijing
R. R. Yager J. Kacprzyk (1997) The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer Norwell, MA
K. Yoon (1989) ArticleTitle“The Propagation of Errors in Multiple-attribute Decision Analysis: a Practical Approach” Journal of Operational Research Society 40 681–686
M. S. Zahir (1991) ArticleTitle“Incorporating the Uncertainty of Decision Judgements in the Analytic Hierarchy Process” European Journal of Operational Research 53 206–216
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, Z. On Method for Uncertain Multiple Attribute Decision Making Problems with Uncertain Multiplicative Preference Information on Alternatives. Fuzzy Optim Decis Making 4, 131–139 (2005). https://doi.org/10.1007/s10700-004-5869-2
Issue Date:
DOI: https://doi.org/10.1007/s10700-004-5869-2