A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers
In group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These relative importance values can be treat...
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MDPI AG
2025-02-01
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| author | József Dombi Jenő Fáró Tamás Jónás |
| author_facet | József Dombi Jenő Fáró Tamás Jónás |
| author_sort | József Dombi |
| collection | DOAJ |
| description | In group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These relative importance values can be treated as weights. In a group decision making situation, it is not only the weighted aggregate output that matters, but also the weighted measure of the group consensus. Noting that weighted group consensus measures have not yet been intensely studied, in this study, based on well-known requirements for non-weighted consensus measures, we define six reasonable requirements for the weighted case. Then, we propose a function family and prove that it satisfies the above requirements for a weighted consensus measure. Hence, the proposed measure can be used in group decision making situations where the decision-makers have various weight values that reflect the relative importance of their opinions. The proposed weighted consensus measure is based on the fuzziness degree of the decumulative distribution function of the input scores, taking into account the weights. Hence, it may be viewed as a weighted adaptation of the so-called fuzziness measure-based consensus measure. The novel weighted consensus measure is determined by a fuzzy entropy function; i.e., this function may be regarded as a generator of the consensus measure. This property of the proposed weighted consensus measure family makes it very versatile and flexible. The nice properties of the proposed weighted consensus measure family are demonstrated by means of concrete numerical examples. |
| format | Article |
| id | doaj-art-d1e81760426748bc9ec431c4a4a55ea1 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-d1e81760426748bc9ec431c4a4a55ea12025-08-20T03:12:35ZengMDPI AGMathematics2227-73902025-02-0113352610.3390/math13030526A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-MakersJózsef Dombi0Jenő Fáró1Tamás Jónás2HUN-REN SZTE, Research Group on Artificial Intelligence, 6701 Szeged, HungaryFaculty of Economics, Eötvös Loránd University, 1053 Budapest, HungaryFaculty of Economics, Eötvös Loránd University, 1053 Budapest, HungaryIn group decision making, the knowledge, skills, and experience of the decision-makers may not be at the same level. Hence, the need arises to take into account not only the opinion, but also the relative importance of the opinion of each decision-maker. These relative importance values can be treated as weights. In a group decision making situation, it is not only the weighted aggregate output that matters, but also the weighted measure of the group consensus. Noting that weighted group consensus measures have not yet been intensely studied, in this study, based on well-known requirements for non-weighted consensus measures, we define six reasonable requirements for the weighted case. Then, we propose a function family and prove that it satisfies the above requirements for a weighted consensus measure. Hence, the proposed measure can be used in group decision making situations where the decision-makers have various weight values that reflect the relative importance of their opinions. The proposed weighted consensus measure is based on the fuzziness degree of the decumulative distribution function of the input scores, taking into account the weights. Hence, it may be viewed as a weighted adaptation of the so-called fuzziness measure-based consensus measure. The novel weighted consensus measure is determined by a fuzzy entropy function; i.e., this function may be regarded as a generator of the consensus measure. This property of the proposed weighted consensus measure family makes it very versatile and flexible. The nice properties of the proposed weighted consensus measure family are demonstrated by means of concrete numerical examples.https://www.mdpi.com/2227-7390/13/3/526decision supportgroup decision makingfuzziness measureweighted consensus measures |
| spellingShingle | József Dombi Jenő Fáró Tamás Jónás A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers Mathematics decision support group decision making fuzziness measure weighted consensus measures |
| title | A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers |
| title_full | A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers |
| title_fullStr | A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers |
| title_full_unstemmed | A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers |
| title_short | A Group Consensus Measure That Takes into Account the Relative Importance of the Decision-Makers |
| title_sort | group consensus measure that takes into account the relative importance of the decision makers |
| topic | decision support group decision making fuzziness measure weighted consensus measures |
| url | https://www.mdpi.com/2227-7390/13/3/526 |
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