Project number:
VEGA 1/0198/09
Title of the project:
Completion of partial information under uncertainty
Project type:
VEGA Research Projects
Project duration (start):
00.00.2009
Project duration (end):
00.00.2011

Number: VEGA 1/0198/09

Period: 1.1.2009-31.12.2011

Principal investigator: Prof. RNDr. Anna Kolesárová, CSc.

Scientific co-workers:

RNDr. Milan Jasem, CSc., Doc. RNDr. P. Volauf, CSc., FEI STU; Doc. RNDr. J. Dobrakovová, CSc., Mgr. A. Stupňanová, PhD., SvF STU; Mgr. J. Mordelová, PhD., SvF STU.

Goals:

  1. Extension of aggregation functions from a partially given information on an aggregation process. Especially, aggregation functions used in probability and statistics, in applications of fuzzy logic in inference processes and in multicriteria decision making.
  2. Completion of a partially given information on an aggregation process by means of various types of fuzzy integrals, primarily, by means of the level dependent Choquet and Sugeno integrals, but also by generalized fuzzy integrals based on pseudo-operations.
  3. Modeling and construction of fuzzy nearness and similarity relations by means of aggregation functions, investigation of relationships between various types of fuzzy relations and examination of their properties.
  4. Investigation in the area of generalized MV-algebras and lattice ordered monoids.

Keywords: Aggregation function, extension, fuzzy measure, fuzzy integral, fuzzy nearness and similarity relations, generalized many-valued algebras

Anotation: The extensions of various types of aggregation functions from a partially given information on subsets of the domain, and construction of the best possible bounds under given conditions, especially in the case of copulas, quasi-copulas and semi-copulas. A detailed examination of properties of the Choquet and Sugeno integrals defined with respect to level dependent fuzzy measures and proposals of new types of generalized fuzzy integrals with respect to level dependent fuzzy measures. Completion of a partial information on an aggregation process by fuzzy integrals. Definition of utility functions by means of generalized level dependent integrals enabling building preference structures and orderings of considered alternatives. The study and construction of fuzzy nearness and similarity relations based on new aggregation techniques. Investigation in the area of MV-algebras and lattice ordered monoids.

Publications

2012

  1. H. Bustince – J. Fernandez – A. Jurio – R. Mesiar – A. Kolesárová – B. Benjamin: Multicriteria decision making using the intreval-valued Choquet integral (in Spanish). Editor(s): Gregorio I. Sainz Palmero et al., In Actas del XVI Congreso Espanol sobre Tecnologías y Lógica Fuzzy, Valadolid, pp. 230–234, 2012.
  2. M. Jasem: A Cauchy completion of dually residuated lattice ordered semigroups. Editor(s): M. Kováčová, In Aplimat 2012, Faculty of Mechanical Engineering STU, vol. 11, pp. 55–62, 2012.
  3. M. Jasem: A Cauchy completion of dually residuated lattice ordered semigroups. Journal of Applied Mathematics, no. 3, vol. 5, pp. 15–23, 2012.
  4. A. Kolesárová – A. Stupňanová: Non-standard Moebius transform-based extensions of Boolean utility functions. Editor(s): E.P. Klement et al., In Abstracts of the 11th Int. Conference on Fuzzy Set Theory and Applications, Printing House of the Armed Forces Academy of gen. M.R. Štefánik, Lipt. Mikuláš, pp. 77, 2012.
  5. A. Kolesárová – A. Stupňanová – J. Beganová: Aggregation-based extensions of fuzzy measures. Fuzzy Sets and Systems, vol. 194, pp. 1–14, 2012.

2011

  1. H. Bustince – J. Fernandez – J. Sans – M. Galar – R. Mesiar – A. Kolesárová: Multicriteria decision making by means of interval valued Choquet integrals. In Advances in Intelligent and Soft Computing, Editor(s): P. Melo-Pinto, P. Couto, C. Serodio, J. Fodor, B. De Baets, Springer, no. 107, pp. 269–278, 2011.
  2. M. Jasem: On Isometries in GMV-Algebras. Mathematica Slovaca, no. 5, vol. 61, pp. 827–833, 2011.
  3. M. Jasem: On Convergence with a Fixed Regulator in Riesz Groups. Editor(s): O. Šedivý, D. Vallo, K. Vidermanová, In ACTA MATHEMATICA 14, UKF v NITRE, vol. 14, pp. 95–100, 2011.
  4. M. Jasem: Relatively Uniform Convergence in Dually Residuated Lattice Ordered Semigroups. Editor(s): M. Kováčová, In Aplimat 2011, Faculty of Mechanical Engineering STU, vol. 10, pp. 129–135, 2011.
  5. M. Jasem: On convergence with a fixed regulator in dually residuated lattice ordered semigroups. Editor(s): D. Andrejsová, J. Hozman, In Proceedings of International Conference Presentation of Mathematics'11, Technická univerzita v Liberci, pp. 69–77, 2011.
  6. M. Jasem: Weak relatively uniform convergence in dually residuated lattice ordered semigroups. In Contributions to general algebra, Verlag Johannes Heyn, Klagenfurt, vol. 20, pp. 39–49, 2011.
  7. M. Jasem: Relatively uniform convergence in dually residuated lattice ordered semigroups. Journal of Applied Mathematics, no. 2, vol. 4, pp. 77–83, 2011.
  8. A. Kolesárová – J. Beganová – A. Stupňanová: Aggregation-based extensions of utility functions. Editor(s): M. Drmota, In OMG-TAGUNG CSACS 2011, Abstract Book, Osterreichische Mathematische Gesellschaft, Wien, pp. 86–86, 2011.
  9. A. Kolesárová – A. Stupňanová: On some extension methods for normed utility functions. Editor(s): B. De Baets, R. Mesiar, L. Troiano, In Proceedings of the 6th International Summer School on Aggregation Operators, Benevento, Italy, pp. 169–174, 2011.
  10. A. Kolesárová – A. Stupňanová: On the structure of associative n-dimensional copulas. Editor(s): M. Drmota, In OMG-TAGUNG CSACS 2011, Abstract Book, Osterreichische Mathematische Gesellschaft, Wien, pp. 88–88, 2011.
  11. A. Kolesárová – A. Stupňanová – J. Beganová: On extension of fuzzy measures to aggregation functions. Editor(s): Galichet,S., Montero, J., Mauris,G., In Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology, Atlantis Press, Aix-Les-Bains, France, pp. 28–32, 2011.
  12. A. Stupňanová – A. Kolesárová: Associative n-dimensional copulas. Kybernetika, no. 1, vol. 49, pp. 93–99, 2011.
  13. A. Stupňanová – A. Kolesárová: Associative n-dimensional aggregation functions. Editor(s): B. De Baets, R. Mesiar, L. Troiano, In Proceedings of the 6th International Summer School on Aggregation Operators, Benevento, Italy, pp. 139–144, 2011.
  14. Z. Takáč: Intersection and union of type-2 fuzzy sets and connection to (α1,α2)-double cuts. Editor(s): Galichet, Sylvie / Montero, Javier / Mauris, Gilles, In Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011, pp. 1052–1059, 2011.

2010

  1. M. Jasem: Relatively Uniform Convergence in Riesz Groups. Editor(s): M. Kováčová, In Aplimat 2010, STU, vol. 9, pp. 57–61, 2010.
  2. M. Jasem: Weak relatively uniform convergence in Riesz groups. In Contributions to General Algebra 19, Verlag Johannes Heyn, Klagenfurt, pp. 127–138, 2010.
  3. E. Klement – A. Kolesárová – R. Mesiar – A. Stupňanová: Lipschitz continuity of discrete universal integrals based on copulas. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, no. 1, vol. 18, pp. 39–52, 2010.
  4. E. Klement – A. Kolesárová – A. Stupňanová: Chebyshev stability of discrete universal integrals based on copulas. Editor(s): E.P.Klement, R. Mesiar, P. Struk, E. Drobná, In Abstracts of the Tenth Internat. Conference on Fuzzy Set Theory and Applications FSTA 2010, Armed Forces of General M.R. Štefánik, Lipt. Mikuláš, pp. 78, 2010.
  5. A. Kolesárová – R. Mesiar: Lipschitzian De Morgan triplets of fuzzy connectives. Information Sciences, no. 18, vol. 180, pp. 3488–3496, 2010.
  6. A. Kolesárová – J. Mordelová – A. Stupňanová: Aggregation functions as extensions of fuzzy measures. Editor(s): E.P.Klement, R. Mesiar, P. Struk, E. Drobná, In Abstracts of the Tenth Internat. Conference on Fuzzy Set Theory and Applications FSTA 2010, Armed Forces of General M.R. Štefánik, Lipt. Mikuláš, pp. 80, 2010.

2009

  1. E. Klement – A. Kolesárová – R. Mesiar – A. Stupňanová: Universal integrals based on level dependent capacities. In Proceedings IFSA-EUSFLAT 2009, pp. 114–118, 2009.
  2. A. Kolesárová: Sequential aggregation. Editor(s): M. Gonzáles, G. Mayor, J Suner, J. Torrens, In Proceedings of the Fifth International Summer School on Aggregation Operators, Full papers, Edicions UIB. Cas Jai. Campus Universitari, Palma, Illes Balears, pp. 183–187, 2009.
  3. A. Kolesárová – R. Mesiar: Lipschitzian De Morgan triplets with strong negations. Editor(s): U. Bodenhofer, B. De Baets, E.P. Klement, S. Saminger-Platz, In 30th Linz Seminar on Fuzzy Set Theory, Universitatsdirektion, Johannes Kepler Universitat, A-4040 Linz, pp. 64–69, 2009.
  4. A. Kolesárová – J. Mordelová – A. Stupňanová: Aggregation-based extensions of fuzzy measures. Editor(s): P. Burillo, H. Bustince, B. De Baets, J. Fodor, In EUROFUSE Workshop 09 Prefernce Modelling and Decision Analysis, Public University of Navarra, Universidad Pública de Navarra, Pamplona, Navarra, pp. 141–146, 2009.

Investigators

Facebook / Youtube

Facebook / Youtube

RSS