Generalized theory of aggregation and its applications

Period: 1.1.2018 - 31.12.2020

Principal investigator: Anna Kolesárová

Scientific co-workers: Zdenko Takáč, Ľubomíra Horanská, Peter Viceník, Martin Nehéz

Goals: The aim of the project is not only to bring a deeper knowledge of aggregation functions in their standard framework of real-valued intervals – primarily proposals of new construction methods, definitions of new properties of aggregation functions and construction of aggregation functions with the introduced properties, but also to extend/generalize the notion of aggregation functions allowing processing data represented by real values or by fuzzy sets and their generalizations, for example, by interval-valued fuzzy sets, type-2 fuzzy sets or, in general, by elements of lattices, and to develop the basis of the theory of generalized aggregation functions. The project will also deal with construction and possible applications of some generalized aggregation functions (fusion functions) defined on real scales, and on particular or general lattice structures as well. The aims of the project also include implementation of some theoretical results in real applications, primarily in image processing.

Keywords:Aggregation function, information fusion, uncertainty modelling.

Annotation:The project is focused on a deeper investigation of standard aggregation functions on real-valued scales, with the emphasis on the proposals of new construction methods and introducing new types of aggregation functions, including the proposals for extending/generalizing the notion of aggregation functions, and on developing the theory of generalized aggregation functions and their applications. The attention is also devoted to aggregation on lattice structures.



  1. Ľ. HoranskáZ. Takáč: Relations between classes of k-Choquet integrals. Editor(s): Miroslav Hrubý, Pavlína Račková, In Matematika, informační technologie a aplikované vedy (MITAV 2018), Univerzita obrany v Brne, pp. 33–34, 2018.
  2. Ľ. HoranskáZ. Takáč: Characterization of k-Choquet Integrals, In Modeling Decisions for Artificial Intelligence 15th International Conference, Mallorca, Spain, October 15–18, 2018, Editor(s): V. Torra, I. Aguiló, Y. Narukawa, M. González-Hidalgo, Springer Nature Switzerland AG, pp. 64–76, 2018.
  3. R. Mesiar – A. Kolesárová: On the fuzzy set theory and aggregation functions: History and some recent advances. Iranian Journal of Fuzzy Systems, no. 7, vol. 15, pp. 1–12, 2018.
  4. M. Minárová – D. Paternain – A. Jurio – J. Ruiz-Aranguren – Z. Takáč – H. Bustince: Modifying the gravitational search algorithm: A functional study. Information Sciences, vol. 430-431, pp. 87–103, 2018.
  5. Z. Takáč – M. Minárová – L. De Miguel – J. Fernandez – H. Bustince: Interval-valued entropies and p-entropies. Editor(s): Radko Mesiar, Susanne Saminger-Platz, Peter Struk, In Abstracts of the Fourteenth International Conference on Fuzzy Set Theory and Applications, Printing House of the Armed Forces Academy of General M. R. Štefánik in Liptovský Mikuláš, pp. 97–98, 2018.
  6. Z. Takáč – M. Minárová – J. Montero – E. Barrenechea – J. Fernandez – H. Bustince: Interval-valued fuzzy strong S-subsethood measures, interval-entropy and P-interval-entropy. Information Sciences, vol. 451-452, pp. 97–115, 2018.
  7. P. Viceník: Strictly increasing additive generators of the second kind of associative binary operations. In Abstracts of the 32nd International Summer Conference on Real Functions Theory, Stará Lesná, Slovakia, September 2-7, C-Press, Košice, pp. 42–42, 2018.

Responsibility for content: doc. RNDr. Zdenko Takáč, PhD.
Last update: 07.11.2018 14:07
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