Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology

Optimization of the ordinal and cardinal consistency of a preference matrix in decision making

Authors
Martin Gavalec, Karel Mls, Hana Tomášková
Corresponding Author
Martin Gavalec
Available Online June 2015.
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.120How to use a DOI?
Keywords
Decision making, preference matrix, consistent preference matrix, ordinal consistency, cardinal consistency, consistent approximation, optimization, optimal consistent approximation.
Abstract

In multi-criteria decision problems the relative importance of alternatives is computed from preference matrices, which come from experience and can possibly be inconsistent. Two consistency types of preferences are studied in the paper. The ordinal consistency preserves the order in which the alternatives are arranged, and it does not allow cycles. The term ‘cyclic consistency’ is also used for this type. The second type is the cardinal consistency, when not only the order, but also the exact values of the relative importance must be consistent. In this paper efficient algorithms for computing consistent approximations of both types for a given preference matrix are described. The main result is an algorithm which combines the advantages of both particular types and computes the optimal consistent approximation of a given preference matrix in the ordinal and in the cardinal sense. The described algorithm can also be used for processing preference matrices with missing data. The performance of the algorithm is illustrated by numerical examples.

Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
Series
Advances in Intelligent Systems Research
Publication Date
June 2015
ISBN
978-94-62520-77-6
ISSN
1951-6851
DOI
https://doi.org/10.2991/ifsa-eusflat-15.2015.120How to use a DOI?
Copyright
© 2015, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Martin Gavalec
AU  - Karel Mls
AU  - Hana Tomášková
PY  - 2015/06
DA  - 2015/06
TI  - Optimization of the ordinal and cardinal consistency of a preference matrix in decision making
BT  - Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 851
EP  - 856
SN  - 1951-6851
UR  - https://doi.org/10.2991/ifsa-eusflat-15.2015.120
DO  - https://doi.org/10.2991/ifsa-eusflat-15.2015.120
ID  - Gavalec2015/06
ER  -