Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem
Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focu...
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| Veröffentlicht in: | Journal of global optimization Jg. 75; H. 1; S. 143 - 161 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Springer US
01.09.2019
Springer Springer Nature B.V |
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. The paper deals with a crucial step in multi-criteria decision analysis, that is to obtain coherent weights for alternatives/criteria that are compared by means of a PCM. Firstly, we provide a condition ensuring coherent weights. Then, we provide and solve a mixed-integer linear programming problem in order to obtain the closest PCM, to a given PCM, having coherent weights. Isomorphisms and the mixed-integer linear programming problem allow us to solve an infinity of optimization problems, among them optimization problems concerning additive, multiplicative and fuzzy PCMs. |
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| AbstractList | Pairwise comparison matrices (PCMs) have been a long standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision making methods. In order to obtain general results, suitable for several kinds of PCMs proposed in the literature, we focus on PCMs defined over a general unifying framework, that is an Abelian linearly ordered group. The paper deals with a crucial step in multi-criteria decision analysis, that is to obtain coherent weights for alternatives/criteria that are compared by means of a PCM. Firstly, we provide a condition ensuring coherent weights. Then, we provide and solve a mixed-integer linear programming problem in order to obtain the closest PCM, to a given PCM, having coherent weights. Isomorphisms and the mixed-integer linear programming problem allow us to solve an infinity of optimization problems, among them optimization problems concerning additive, multiplicative and fuzzy PCMs. |
| Audience | Academic |
| Author | Cavallo, Bice |
| Author_xml | – sequence: 1 givenname: Bice orcidid: 0000-0002-5102-3232 surname: Cavallo fullname: Cavallo, Bice email: bice.cavallo@unina.it organization: Department of Architecture, University of Naples Federico II |
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| CitedBy_id | crossref_primary_10_1007_s10203_020_00291_x crossref_primary_10_1515_ms_2021_0038 crossref_primary_10_1016_j_ins_2022_10_030 crossref_primary_10_1007_s10203_020_00289_5 crossref_primary_10_1007_s10479_023_05753_0 crossref_primary_10_1007_s12597_023_00641_4 crossref_primary_10_1109_TFUZZ_2021_3073238 crossref_primary_10_1016_j_ijar_2019_10_010 crossref_primary_10_1016_j_fss_2022_04_020 crossref_primary_10_1080_01605682_2023_2259935 |
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| Keywords | Mixed-integer linear programming problem Isomorphism Coherent weights Pairwise comparison matrix |
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