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  1. 2 Multiple Criteria Decision Making

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  1. 1 2015

  2. 1 2013

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  1. 2 Ramik J.

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Incomplete Pairwise Comparison Matrix and Its Application to Ranking of Alternatives

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Ramik J.
Multiple Criteria Decision Making
|
2013
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vol. 8
114-128
EN
A fuzzy preference matrix is the result of pairwise comparison - a powerful method in multi-criteria optimization. When comparing two elements, the decision maker assigns a value between 0 and 1 to any pair of alternatives representing the element of the fuzzy preference matrix. Here, we investigate relations between transitivity and consistency of fuzzy preference matrices and multiplicative preference ones. The results obtained are applied to decision situations where some elements of the fuzzy preference matrix are missing. We propose a new method for completing the fuzzy preference matrix with missing elements called the extension of the fuzzy preference matrix and investigate an important particular case of the fuzzy preference matrix with missing elements. Next, using the eigenvector of the transformed matrix we obtain the corresponding priority vector. Illustrative numerical examples are supplied.
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Incomplete Preference Matrix on Alo-Group and Its Application to Ranking of Alternatives

100%
Ramik J.
Multiple Criteria Decision Making
|
2015
|
vol. 10
124-140
EN
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.
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