article

A new ranking procedure by incomplete pairwise comparisons using preference subsets

Author:

Lev V. UtkinAuthors Info & Claims

Intelligent Data Analysis, Volume 13, Issue 2

Pages 229 - 241

Published: 01 April 2009 Publication History

Abstract

A method for ranking of alternatives or objects and its extensions by incomplete pairwise comparisons using random set theory are proposed in the paper. The main feature of the method is that it allows us to deal with comparisons of arbitrary groups of alternatives. The method is extended on the case of independent groups of experts. The imprecise Dirichlet model is also used to make cautious decisions in several cases. Various numerical examples illustrate the proposed method and its extensions.

References

[1]

T. Augustin. Expected utility within a generalized concept of probability - a comprehensive framework for decision making under ambiguity, Statistical Papers 43 (2002), 5-22.

[2]

J.-M. Bernard. An introduction to the imprecise Dirichlet model for multinomial data, International Journal of Approximate Reasoning 39(2-5) (2005), 123-150.

Digital Library

[3]

M. Beynon, DS/AHP method: A mathematical analysis, including an understanding of uncertainty, European Journal of Operational Research 140 (2002), 148-164.

[4]

M. Beynon, B. Curry and P. Morgan, The Dempster-Shafer theory of evidence: An alternative approach to multicriteria decision modelling, Omega 28 (2000), 37-50.

[5]

R.M. Cook, Experts in Uncertainty, Opinion and Subjective Probability in Science, Oxford University Press, New York, 1991.

[6]

A.P. Dempster, Upper and lower probabilities induced by a multi-valued mapping, Annales of Mathematical Statistics 38 (1967), 325-339.

[7]

J.Y. Halpern and R. Fagin, Two views of belief: Belief as generalized probability and belief as evidence, Artificial Intelligence 54 (1992), 275-317.

Digital Library

[8]

E. Hullermeier and J. Furnkranz, Comparison of ranking procedures in pairwise preference learning, in: Proc of the 10th International Conference on Information Processing and Management of Uncertainty in Knoweldge-Based Systems, IPMU-04, Perugua, Italy, 2004.

[9]

E. Hullermeier and J. Furnkranz, Ranking by pairwise comparison: A note on risk minimization, in: Proc of the IEEE International Conference on Fuzzy Systems, FUZZ-IEEE-04, Budapest, Hungary, July 2004.

[10]

R.D. Luce and H. Raiffa, Games and decisions, Wiley, New York, 1957.

[11]

K.-M. Osei-Bryson. Supporting knowledge elicitation and consensus building for Dempster-Shafer decision models, International Journal of Intelligent Systems 18 (2003), 129-148.

[12]

T.L. Saaty, Multicriteria Decision Making: The Analytic Hierarchy Process, McGraw Hill, New York, 1980.

[13]

J. Schubert, On ¿ in a decision-theoretic apparatus of Dempster-Shafer theory, International Journal of Approximate Reasoning 13 (1995), 185-200.

[14]

G. Shafer, A Mathematical Theory of Evidence, Princeton University Press, 1976.

[15]

T. Tervonen, R. Lahdelma and P. Salminen, A method for elicitating and combining group preferences for stochastic multicriteria acceptability analysis, TUCS Technical Report 638, Turku Centre for Computer Science, Turku, Finland, November 2004.

[16]

L.V. Utkin, Probabilities of judgments provided by unknown experts by using the imprecise Dirichlet model, Risk, Decision and Policy 9(4) (2004), 391-400.

[17]

L.V. Utkin, Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model, Fuzzy Sets and Systems 154(3) (2005), 413-431.

Digital Library

[18]

L.V. Utkin, Ranking procedures by pairwise comparison using random sets and the imprecise Dirichlet model, Applied Mathematics and Computations 183(1) (2006), 394-408.

Digital Library

[19]

L.V. Utkin and T.H. Augustin, Decision making under incomplete data using the imprecise Dirichlet model, International Journal of Approximate Reasoning 44(3) (2007), 322-338.

Digital Library

[20]

P. Walley, Inferences from multinomial data: Learning about a bag of marbles, Journal of the Royal Statistical Society, Series B 58 (1996), 3-57, with discussion.

[21]

K. Weichselberger, Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung, volume I Intervallwahr-scheinlichkeit als umfassendes Konzept, Physika, Heidelberg, 2001.

Cited By

Masson MDestercke SDenoeux T(2018)Modelling and predicting partial orders from pairwise belief functionsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-014-1553-920:3(939-950)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1007/s00500-014-1553-9
Li MHu YZhang QDeng Y(2016)A novel distance function of D numbers and its application in product engineeringEngineering Applications of Artificial Intelligence10.1016/j.engappai.2015.06.00447:C(61-67)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.engappai.2015.06.004
Huang SSu XHu YMahadevan SDeng Y(2014)A new decision-making method by incomplete preferences based on evidence distanceKnowledge-Based Systems10.5555/2842045.284236756:C(264-272)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.5555/2842045.2842367
Show More Cited By

Recommendations

Partial Ranking by Incomplete Pairwise Comparisons Using Preference Subsets
BELIEF 2014: Proceedings of the Third International Conference on Belief Functions: Theory and Applications - Volume 8764

In multi-criteria decision making the decision maker need to assign weights to criteria for evaluation of alternatives, but decision makers usually find it difficult to assign precise weights to several criteria. On the other hand, decision makers may ...
Representation of The Pairwise Comparisons in AHP Using Hesitant Cloud Linguistic Term Sets
Theory and Practice of Pairwise Comparisons

The analytic hierarchy process (AHP) is the most popular extension to the pairwise comparisons method which is based on the observation that it is much easier to rank several objects when restricted to two objects at one time. As the pairwise comparisons ...
Incomplete linguistic preference relations and their fusion

Various linguistic preference relations, including incomplete linguistic preference relation, consistent incomplete linguistic preference relation and acceptable incomplete linguistic preference relation, are introduced. Some desirable properties of the ...

Comments

Information & Contributors

Information

Published In

cover image Intelligent Data Analysis

Intelligent Data Analysis Volume 13, Issue 2

April 2009

209 pages

ISSN:1088-467X

Issue’s Table of Contents

Publisher

IOS Press

Netherlands

Publication History

Published: 01 April 2009

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

5
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 04 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Masson MDestercke SDenoeux T(2018)Modelling and predicting partial orders from pairwise belief functionsSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-014-1553-920:3(939-950)Online publication date: 30-Dec-2018
https://dl.acm.org/doi/10.1007/s00500-014-1553-9
Li MHu YZhang QDeng Y(2016)A novel distance function of D numbers and its application in product engineeringEngineering Applications of Artificial Intelligence10.1016/j.engappai.2015.06.00447:C(61-67)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.engappai.2015.06.004
Huang SSu XHu YMahadevan SDeng Y(2014)A new decision-making method by incomplete preferences based on evidence distanceKnowledge-Based Systems10.5555/2842045.284236756:C(264-272)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.5555/2842045.2842367
Schubert J(2014)Partial Ranking by Incomplete Pairwise Comparisons Using Preference SubsetsProceedings of the Third International Conference on Belief Functions: Theory and Applications - Volume 876410.1007/978-3-319-11191-9_21(190-198)Online publication date: 26-Sep-2014
https://dl.acm.org/doi/10.1007/978-3-319-11191-9_21
Boujelben MDe Smet YFrikha AChabchoub H(2011)A ranking model in uncertain, imprecise and multi-experts contextsInternational Journal of Approximate Reasoning10.1016/j.ijar.2011.06.00852:8(1171-1194)Online publication date: 1-Nov-2011
https://dl.acm.org/doi/10.1016/j.ijar.2011.06.008

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents