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Some Properties of Consistency in the Families of Aggregation Operators

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dc.book.titleEurofuse 2011:Workshop on Fuzzy Methods for Knowledge-Based Systems
dc.contributor.authorRojas Patuelli, Karina
dc.contributor.authorGómez González, Daniel
dc.contributor.authorRodríguez González, Juan Tinguaro
dc.contributor.authorMontero De Juan, Francisco Javier
dc.contributor.editorMelero Pinto, Pedro
dc.contributor.editorCouto, P.
dc.contributor.editorSerôdio, Carlos
dc.contributor.editorFodor, János
dc.contributor.editorBaets de, Bernard
dc.date.accessioned2023-06-20T05:44:42Z
dc.date.available2023-06-20T05:44:42Z
dc.date.issued2011
dc.description.abstractProperties related with aggregation operators functions have been widely studied in literature. Nevertheless, few efforts have been dedicated to analyze those properties related with the family of operators in a global way. What should be the relationship among the members of a family of aggregation operators? Is it possible to build the aggregation of n data with aggregation operators of lower dimension? Should it exist some consistency in the family of aggregation operators? In this work, we analyze two properties of consistency in a family of aggregation operators: Stability and Structural Relevance. The stability property for a family of aggregation operators tries to force a family to have a stable/continuous definition in the sense that the aggregation of,, items should be similar to the aggregation of n + 1 items if the last item is the aggregation of the previous n items. Following this idea some definitions and results are given. The second concept presented in this work is related with the construction of the aggregation operator when the data that have to be aggregated has an inherent structure. The Structural Relevance property tries to give some ideas about the construction of the aggregation operator when the items are related by means of a graph.en
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.facultyInstituto de Matemática Interdisciplinar (IMI)
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/17818
dc.identifier.citationRojas, K., Gómez, D., Rodríguez, J.T., Montero, J.: Some Properties of Consistency in the Families of Aggregation Operators. En: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., y De Baets, B. (eds.) Eurofuse 2011. pp. 169-176. Springer Berlin Heidelberg, Berlin, Heidelberg (2011)
dc.identifier.doi10.1007/978-3-642-24001-0_17
dc.identifier.isbn978-3-642-24000-3
dc.identifier.officialurlhttps//doi.org/10.1007/978-3-642-24001-0_17
dc.identifier.relatedurlhttps://springerlink3.metapress.com/content/r76k55u82216671n/resource-secured/?target=fulltext.pdf&sid=gtovfdpyjxo5e0bshdgo55ss&sh=www.springerlink.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/45384
dc.issue.number107
dc.language.isoeng
dc.page.final176
dc.page.initial169
dc.page.total424
dc.publication.placeBerlin
dc.publisherSpringerLink
dc.relation.ispartofseriesAdvances in intelligent and Soft Computing
dc.rights.accessRightsrestricted access
dc.subject.cdu004.8
dc.subject.keywordComputational Intelligence
dc.subject.keywordArtificial Intelligence (incl. Robotics)
dc.subject.ucmInteligencia artificial (Informática)
dc.subject.unesco1203.04 Inteligencia Artificial
dc.titleSome Properties of Consistency in the Families of Aggregation Operatorsen
dc.typebook part
dcterms.referencesAmo, A., Montero, J., Molina, E.: Representation of consistent recursive rules. European Journal of Operational Research 130, 29–53 (2001) Beliakov, G., Pradera, A., Calvo, T.: Aggregation Functions, a Guide to Practitioners. Springer, Berlin (2007) Bustince, H., Barrenechea, E., Fernández, J., Pagola, M.,Montero, J., Guerra, C.: Aggregation of neighbourhood information by means of interval type 2 fuzzy relations Calvo, T., Kolesarova, A., Komornikova, M., Mesiar, R.:Aggregation operators, properties, classes and construction methods. In: Calvo, T., et al. (eds.) Aggregation Operators New trends ans Aplications, pp. 3–104. Physica-Verlag, Heidelberg (2002) Calvo, T., Mayor, G., Torrens, J., Suñer, J., Mas, M.,Carbonell, M.: Generation of weighting triangles associated with aggregation fuctions. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 8(4),417–451 (2000) Carlsson, C.H., Fuller, R.: Fuzzy reaasoning in decision making and optimization. Heidelberg, Springfield-Verlag (2002) Cutello, V., Montero, J.: Hierarchical aggregation of OWA operators: basic measures and related computational problems. Uncertainty, Fuzzinesss and Knowledge-Based Systems 3, 17–26 (1995) Cutello, V., Montero, J.: Recursive families of OWA operators. In: Proceedings FUZZ-IEEE Conference, pp. 1137–1141. IEEE Press, Piscataway (1994) Cutello, V., Montero, J.: Recursive connective rules.International Journal of Intelligent Systems 14, 3–20 (1999) Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade,H.: Terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets. Fuzzy Sets and Systems 156, 485–491 (2005) Fung, L.W., Fu, K.S.: An axiomatic approach to rational decision making in a fuzzy environment. In: Zadeh, L.A. (ed.) Fuzzy Sets and their Applications to Cognitive and Decision Processes, pp. 227–256. Academic Press, London (1975) Gómez, D., Montero, J.: A discussion of aggregation functions. Kybernetika 40, 107–120 (2004) Gómez, D., Montero, J., Yáñez, J., Poidomani, C.: A graph coloring algorithm approach for image segmentation. Omega 35, 173–183 (2007) Gómez, D., Montero, J., Yánez, J.: A coloring algorithm for image classification. Information Sciences 176, 3645–3657 (2006) Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation Functions, Encyclopedia of Mathematics and its Applications (2009) Kolesárová, A.: Sequential aggregation. In: González, M., et al. (eds.) Proceedings of the Fifth International Summer School on Aggregation Operators, AGOP, Universitat de les Illes Balears, Palma de Mallorca, pp. 183–187 (2009) López, V., Garmendia, L., Montero, J., Resconi, G.: Specification and computing states in fuzzy algorithms. Uncertainty, Fuzziness and Knowledge-Based Systems 16, 301–336 (2008) López, V., Montero, J.: Software engineering specification under fuzziness. Multiple-Valued Logic and Soft Computing 15, 209–228 (2009) López, V., Montero, J., Tinguaro Rodriguez, J.: Formal Specification and implementation of computational aggregation Functions. In: Computational Intelligence,Foundations and Applications Proceedings of the 9th International FLINS Conference 2010, pp. 523–528 (2010) Montero, J.: A note on Fung-Fu‘s theorem. Fuzzy Sets and Systems 13, 259–269 (1985) Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets and Systems 158, 2429–2442 (2007) Montero, J., López, V., Gómez, D.: The role of fuzziness in decision making. Studies in Fuzziness and Soft Computing 215, 337–349 (2007) Yager, R.R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems, Man and Cybernetics 18, 183–190 (1988) Yager, R.R., Rybalov, A.: Nonconmutative self-identity aggregation. Fuzzy Sets and Systems 85, 73–82 (1997)
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