Project number:
VEGA 1/0614/18
Title of the project:
Generalized theory of aggregation and its applications
Project type:
VEGA Research Projects
Project duration (start):
Project duration (end):

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. Horanská: Extensions of Fuzzy Measures Based on Double Generalization of the Lovász Extension Formula, In Computational Intelligence and Mathematics for Tackling Complex Problems 3., Editor(s): Harmati I.Á., Kóczy L.T., Medina J., Ramírez-Poussa E., Springer Nature Switzerland AG, Cham, no. 959, pp. 81–88, 2022.


  1. F. Bardozzo – B. de la Osa – Ľ. Horanská – J. Fumanal – M. delli Priscoli – L. Troiano – R. Tagliaferri – J. Fernandez – H. Bustince: Sugeno integral generalization applied to improve adaptive image binarization. Information Fusion, vol. 68, pp. 37–45, 2021.


  1. H. Bustince – C. Marco-Detchart – J. Fernandez – C. Wagner – J. Garibaldi – Z. Takáč: Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders. Fuzzy Sets and Systems, vol. 390, pp. 23–47, 2020.
  2. H. Bustince – R. Mesiar – J. Fernandez – D. Paternain – Z. Takáč: Dissimilarity based Choquet integrals. In Abstracts of the Fifteenth International Conference on Fuzzy Set Theory and Applications, pp. 27–28, 2020.
  3. H. Bustince – R. Mesiar – A. Kolesárová – G. P. Dimuro – J. Fernandez – I. Diaz – S. Montes: On some classes of directionally monotone functions. Fuzzy Sets and Systems, vol. 386, pp. 161–178, 2020.
  4. J. Fernandez – H. Bustince – Ľ. Horanská – R. Mesiar – A. Stupňanová: A Generalization of the Choquet Integral Defined in Terms of the Möbius Transform. IEEE Transactions on Fuzzy Systems, no. 10, vol. 28, pp. 2313–2319, 2020.
  5. Ľ. Horanská: On Compatibility of Two Approaches to Generalization of the Lovász Extension Formula, In Information Processing and Management of Uncertainty in Knowledge-Based Systems, Springer, pp. 426–434, 2020.
  6. Ľ. Horanská – H. Bustince – J. Fernandez – R. Mesiar: On some generalizations of decomposition integrals. In Abstracts of the Fifteenth International Conference on Fuzzy Set Theory and Applications, pp. 43–44, 2020.
  7. Ľ. Horanská – H. Bustince – J. Fernandez – R. Mesiar: Generalized decomposition integral. Information Sciences, vol. 538, pp. 415–427, 2020.
  8. Ľ. Horanská – P. Sarkoci: A note on the copulas invariant with respect to (a,b)-transformation. Fuzzy Sets and Systems, vol. 378, pp. 157–164, 2020.
  9. A. Kolesárová – R. Mesiar: A Note on Aggregation of Intuitionistic Values. Editor(s): M.-J. Lesot et al., In 18th Int. Conference IPMU'2020, part of the Communications in Computer and Information Science, vol. 1238, Springer Nature Switzerland AG, pp. 411–418, 2020.
  10. R. Mesiar – A. Kolesárová: Copulas and fuzzy implications. International Journal of Approximate Reasoning, vol. 117, pp. 52–59, 2020.
  11. R. Mesiar – A. Kolesárová: Quasi-Copulas, Copulas and Fuzzy Implicators. International Journal of Computational Intelligence Systems, no. 1, vol. 13, pp. 681–689, 2020.
  12. S. Saminger-Platz – A. Kolesárová – R. Mesiar – E. Klement: The key role of convexity in some copula costructions. European Journal of Mathematics, no. 2, vol. 6, pp. 533–560, 2020.
  13. P. Viceník: The constructions of non-continuous additive generators of t-conorms based on discrete addtive generators of discrete t-conorms. Fuzzy Sets and Systems, vol. 378, pp. 1–22, 2020.


  1. A. H. Altalhi – J. I. Forcén – M. Pagola – E. Barrenechea – H. Bustince – Z. Takáč: Moderate deviation and restricted equivalence functions for measuring similarity between data. Information Sciences, vol. 501, pp. 19–29, 2019.
  2. H. Bustince – J. Fernandez – Ľ. Horanská – R. Mesiar – A. Stupňanová: On Some Generalizations of the Choquet Integral, In New Trends in Aggregation Theory, Springer International Publishing, vol. 981, 2019.
  3. H. Bustince – J. Fernandez – I. Rodriguez – B. de la Osa – C. Marco-Detchart – J. A. S. Delgado – Z. Takáč: A New Axiomatic Approach to Interval-Valued Entropy. In Fuzzy Techniques: Theory and Applications, Springer International Publishing, pp. 3–12, 2019.
  4. A. Kolesárová – F. Kouchakinejad – R. Mesiar: Additive Aggregation Functions: Generalizations and Modifications of Additivity. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 27, pp. 39–58, 2019.
  5. A. Kolesárová – S. Massanet – R. Mesiar – J. V. Riera – J. Torrens: Polynomial constructions of fuzzy implication functions: The quadratic case. Information Sciences, vol. 494, pp. 60–79, 2019.
  6. A. Kolesárová – R. Mesiar: Fuzzy implicators related to (quasi-)copulas. Editor(s): M. Štepnička, In Proceedings of the 2019 Conference of the International Fuzzy Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019), Atlantis Press, vol. 1, pp. 235–240, 2019.
  7. R. Mesiar – A. Kolesárová: On a construction of fuzzy implication functions. Editor(s): U. Bentkowska et al., In The 4th International Symposium on Fuzzy Sets, Uncertainty Modelling, ISFS 2019, WYDAWNICTVO UNIWERSYTETU RZESZOWSKIEGO, pp. 15–16, 2019.
  8. R. Mesiar – A. Kolesárová: Construction of Fuzzy Implication Functions Based on F-chains. In New Trends in Aggregation Theory, Springer International Publishing, vol. 981, pp. 315–326, 2019.
  9. R. Mesiar – A. Kolesárová: Utility Functions and Constrained Additivity. In 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT), IEEE, pp. 274–278, 2019.
  10. R. Mesiar – A. Kolesárová – D. Gómez – J. Montero: Set-based extended aggregation functions. International Journal of Intelligent Systems, no. 9, vol. 34, pp. 2039–2054, 2019.
  11. R. Mesiar – A. Kolesárová – A. Stupňanová – R. R. Yager: Normed Utility Functions: Some Recent Advances, In New Perspectives in Multiple Criteria Decision Making, Springer Nature Switzerland AG, pp. 133–150, 2019.
  12. R. Mesiar – A. Kolesárová – A. Šeliga – J. Montero – D. Gómez: Set-based extended functions. Editor(s): V. Torra et al., In Modeling Decisions for Artificial Intelligence, LNAI, Springer Nature Switzerland AG, vol. 11 676, pp. 41–51, 2019.
  13. H. Santos – I. Couso – B. Bedregal – Z. Takáč – M. Minárová – A. Asiain – E. Barrenechea – H. Bustince: Similarity measures, penalty functions, and fuzzy entropy from new fuzzy subsethood measures. International Journal of Intelligent Systems, vol. 36, pp. 1281–1302, 2019.
  14. Z. Takáč – H. Bustince – J. Fernandez – G. P. Dimuro – T. Asmus – A. Castillo: Interval-Valued EN-functions and Similarity Measures. In New Trends in Aggregation Theory, Springer International Publishing, vol. 981, pp. 140–150, 2019.
  15. Z. Takáč – H. Bustince – J. M. Pintor – C. Marco-Detchart – I. Couso: Width-Based Interval-Valued Distances and Fuzzy Entropies. IEEE Access, vol. 11, pp. 14044–14057, 2019.
  16. Z. Takáč – J. Fernandez – J. Fumanal – C. Marco-Detchart – I. Couso – G. P. Dimuro – H. Santos – H. Bustince: Distances between Interval-valued Fuzzy Sets Taking into Account the Width of the Intervals. In 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2019.
  17. Z. Takáč – M. Minárová – H. Bustince – J. Fernandez: Restricted Similarity Functions, Distances and Entropies with Intervals Using Total Orders. In Integrated Uncertainty in Knowledge Modelling and Decision Making, Springer Nature Switzerland, pp. 432–442, 2019.
  18. P. Viceník: Strictly increasing additive generators of the second kind of associative binary operations. Tatra Mountains Mathematical Publications, no. 74, pp. 159–176, 2019.


  1. Ľ. Horanská: On some properties of aggregation-based extensions of fuzzy measures. Tatra Mountains Mathematical Publications, vol. 72, pp. 43–54, 2018.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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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