Title variants
Languages of publication
Abstracts
Pairwise comparison is a powerful method in multi-criteria optimiza- tion. When comparing two elements, the decision maker assigns a value from the given scale which is an Abelian linearly ordered group (Alo- group) of the real line to any pair of alternatives representing an element of the preference matrix (P-matrix). Both non-fuzzy and fuzzy mul- tiplicative and additive preference matrices are generalized. Then we focus on situations where some elements of the P-matrix are missing. We propose a general method for completing fuzzy matrix with missing elements, called the extension of the P-matrix, and investigate some im- portant particular cases of fuzzy preference matrix with missing elements. Eight illustrative numerical examples are included.
Year
Volume
Pages
124-140
Physical description
Contributors
author
References
- Alonso S., Chiclana F., Herrera F., Herrera-Viedma E., Alcala-Fdes J., Porcel C. (2008), A Consistency-based Procedure to Estimate Missing Pairwise Preference Values, Internat. J. Intelligent Syst., Vol. 23, 155-175.
- Bourbaki N. (1990), Algebra II, Springer Verlag, Heidelberg-New York-Berlin.
- Cavallo B., D'Apuzzo L. (2009), A General Uni_ed Framework for Pairwise Comparison Matrices in Multicriteria Methods, Internat. J. of Intelligent Syst., Vol. 24, No. 4, 377- 398.
- Cavallo B., D'Apuzzo L., Squillante M. (2012), About a Consistency Index for Pairwise Comparison Matrices over a Divisible Alo-Group, Internat. J. of Intelligent Syst., Vol. 27, 153-175.
- Chiclana F., Herrera-Viedma E., Alonso S. (2009), A Note on Two Methods for Estimating Pairwise Preference Values, IEEE Transactions Syst. Man and Cybernetics, Vol. 39, No. 6, 1628-1633.
- Gavalec M., Ramik J., Zimmermann K. (2014), Decision Making and Optimization: Special Matrices and Their Applications in Economics and Management, Springer Internat. Publ. Switzerland, Cham-Heidelberg-New York-Dordrecht-London.
- Herrera-Viedma E., Herrera F., Chiclana F., Luque M. (2004), Some Issues on Consistency of Fuzzy Preference Relations, European J. Operat. Res., Vol. 154, 98-109.
- Herrera F., Herrera-Viedma E., Chiclana F. (2001), Multiperson Decision Making Based on Multiplicative Preference Relations, European J. Operat. Res., Vol. 129, 372-385.
- Kim S.H., Choi S.H., Kim J.K. (1999), An Interactive Procedure for Multiple Attribute Group Decision Making with Incomplete Information: Range-based Approach, European J. Operat. Res., Vol. 118, 139-152.
- Ma J. et al. (2006), A Method for Repairing the Inconsistency of Fuzzy Preference Relations, Fuzzy Sets and Systems, Vol. 157, 20-33.
- Ramik J. (2014), Incomplete Fuzzy Preference Matrix and Its Application to Ranking of Alternatives, Internat. J. of Intelligent Syst., Vol. 28, No. 8, 787-806.
- Saaty T.L. (1980), The Analytic Hierarchy Process, McGraw-Hill, New York.
- Xu Z.S. (2004), Goal Programming Models for Obtaining the Priority Vector of Incomplete Fuzzy Preference Relation, Int. J. Approx. Reasoning, Vol. 36, 261-270.
- Xu Z.S., Da Q.L. (2005), A Least Deviation Method to Obtain a Priority Vector of a Fuzzy Preference Relation, European J. of Operat. Res., Vol. 164, 206-216.
Document Type
Publication order reference
Identifiers
ISSN
2084-1531
YADDA identifier
bwmeta1.element.cejsh-d50fa4b2-5d3f-4d1a-8bd0-01ee29fc2ca4