Measuring criteria weights by means of Dimension Theory
| dc.contributor.author | Gómez González, Daniel | |
| dc.contributor.author | Montero De Juan, Francisco Javier | |
| dc.contributor.author | Yáñez Gestoso, Francisco Javier | |
| dc.date.accessioned | 2023-06-20T10:50:40Z | |
| dc.date.available | 2023-06-20T10:50:40Z | |
| dc.date.issued | 2006 | |
| dc.description.abstract | Measuring criteria weights in multicriteria decision making is a key issue in order to amalgamate information when reality is being described from several different points of view. In this paper we propose a method for evaluating those weights taking advantage of Dimension Theory, which allows the representation of the set of alternatives within a real space, provided that decision maker preferences satisfy certain consistency conditions. Such a representation allows a first information about possible underlying criteria in decision maker’s mind. In particular, we propose to measure the importance of those underlying criteria by means of all possible representations associated to the dimension of the binary preference relations between criteria, each one being understood as a linear order of the set of alternatives. | en |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Gobierno de España | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/29070 | |
| dc.identifier.issn | 1134-5632 | |
| dc.identifier.officialurl | http://dmle.cindoc.csic.es/revistas/detalle.php?numero=4359 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51325 | |
| dc.issue.number | 3 | |
| dc.journal.title | Mathware & Soft Computing | |
| dc.language.iso | eng | |
| dc.page.final | 188 | |
| dc.page.initial | 173 | |
| dc.publisher | European Society for Fuzzy Logic and Technology | |
| dc.relation.projectID | TIN2006-0619 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 515.12 | |
| dc.subject.keyword | Multicriteria Decision Analysis | |
| dc.subject.keyword | Valued Preference Relations | |
| dc.subject.keyword | Dimension Theory | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Measuring criteria weights by means of Dimension Theory | en |
| dc.type | journal article | |
| dc.volume.number | 13 | |
| dcterms.references | [1] A. Amo, D. Gomez, J. Montero and G. Biging. Relevance and redundancy in fuzzy classification systems. Mathware and Soft Computing 8, 203-216 (2001). [2] A. Amo, J. Montero and E. Molina. Representation of consistent recursive rules. European Journal of Operational Research 130, 29-53 (2001). [3] A. Amo, J. Montero, G. Biging and V. Cutello. Fuzzy classification systems. European Journal of Operational Research 156, 459-507 (2004). [4] T. Calvo, G. Mayor and R. Mesiar, eds. Aggregation operators. Physica-Verlag, Heidelberg (2002). [5] V. Cutello and J. Montero. Recursive connective rules. Intelligent Systems 14,3-20 (1999). [6] J.P. Doignon and J. Mitas. Dimension of valued relations. European Journal of Operational Research 125, 571-587 (2000). [7] B. Dushnik and E.W. Miller. Partially ordered sets. American Journal of Mathematics 63, 600-610 (1941). [8] J. Figueira and B. Roy: Determining the weights of criteria in the ELECTRE type methods with a revised Simon’s procedure. European Journal Of Operational Research 139, 317-326 (2002). [9] J.C. Fodor and M. Roubens. Structure of valued binary relations. Mathematical Social Sciences 30, 71-94 (1995). [10] D. G´omez, J. Montero and J. Yañez. A dimension-based representation in multicriteria decision making. Proceedings EUSFLAT’05 Conference (UPC Press, Barcelona), pp. 910-915. [11] D. G´omez, J. Montero, J. Yañez, J. Gonzalez-Pachon and V. Cutello. Crisp dimension theory and valued preference relations. International Journal of General Systems 33, 115-131 (2004). [12] D. G´omez, J. Montero and J. Yañez. A coloring algorithm for image classifi-cation. Information Sciences 176, 3645-3657 (2006). [13] D. Gomez, J. Montero, J. Yañez, C. Poidomani. A graph coloring algorithm approach for image segmentation. Omega 35, 173-183 (2007). [14] J. Gonzalez-Pachon, D. Gomez, J. Montero and J.Yañez. Searching for the dimension of binary valued preference relations. International Journal of Approximate Reasoning 33, 133-157 (2003). [15] J. Gonzalez-Pachon, D. Gomez, J. Montero and J. Yañez. Soft dimension theory. Fuzzy Sets and Systems 137, 137-149 (2003). [16] R. L. Keeny and H. Raiffa. Decision with multiple objetives- preferences and valued tradeoffs. Cambridge U iversity Press, Cambridge (1993). [17] B. Roy. Decision aid and decision making. European Journal of Operational Research 45, 324-331 (1990). [18] T. L. Saaty. The analytic hierarchy process, MacGraw Hill, New York (1980). [19] J. Simos. L’evaluation environnementale: Un processus cognitif negocie These de doctorat, DGF-EPFL, Lausanne. (1990). [20] E. Szpilrajn. Sur l’extension de l’ordre partiel. Fundamenta Mathematicae 16,386-389 (1930). [21] W.T. Trotter. Combinatorics and Partially Ordered Sets. Dimension Theory. The Johns Hopkins University Press, Baltimore and London (1992). [22] M. Yannakakis. On the complexity of the partial order dimension problem. SIAM Journal of Algebra and Discrete Mathematics 3, 351-358 (1982). [23] J. Yañez and J. Montero. A poset dimension algorithm. Journal of Algorithms 30, 185-208 (2000). | |
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