Project number:
VEGA 1/3012/06
Title of the project:
Conjunctive aggregation operators
Project type:
VEGA Research Projects
Project duration (start):
00.00.2006
Project duration (end):
00.00.2008

Title: Conjunctive aggregation operators

Number: VEGA 1/3012/06

Period: 1.1.2006-31.12.2008

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

Scientific co-workers: Ing. P. Sarkoci (2006-2007), Ing. D. Zelisková (2006), Doc. RNDr. P.Volauf, CSc. (FEI), Doc. RNDr. J. Dobrakovová , CSc. (SjF), Doc. RNDr. M. Kalina, CSc. (SvF), Mgr. J. Mordelová, PhD. (SvF)

Goals:

  • Fuzzy topologies based on fuzzy nearness relations
  • Construction of binary 1-Lipschitz aggregation operators or their best possible bounds from a partial information on subdomains in general, and consequences of these results for some special classes of aggregation operators, including copulas and quasi-copulas
  • Investigation of the structure and properties of discrete quasi-copulas
  • Introducing discrete copulas, investigation of their properties, structure, statistical meaning and also possibility of their application for modeling the dependence structure of discrete random variables
  • Identification of copulas from observed data, software for computer-assisted evaluation
  • Study of dominantion in special classes of triangular norms
  • Construction of more dimensional 1-Lipschitz aggregation operators or their best possible bounds from known values on subdomains in special classes of 1-Lipschitz aggregation operators
  • Study of k-Lipschitz aggregation operators
  • Study of the relationship between properties of copulas and various measures of association of stochastic variables
  • Investigation of the transitivity of dominantion
  • Investigation of the structure of the set of all solutions to the Mulholland functional inequality
  • Dominantion of discrete t-norms
  • Applications of aggregation operators and dominantion in building fuzzy topologies

Keywords:

Aggregation operator, copula, quasi-copula, triangular norm, dominantion, fuzzy topology

Anotation:

Construction of 1-Lipschitz aggregation operators or their best possible bounds from partial information on subdomains. Results in special classes of 1-Lipschitz aggregation operators, including quasi-copulas and copulas. Study of more dimensional cases. Introducing discrete copulas and a deep investigation of their properties, structure and possible applications in mathematical statistics and stochastic processes. Proposal of a method for identification of copulas from observed data, including a software program, and application of obtained results for investigation of the dependence structure of random variables. Study of the relationship between properties of copulas and various measures of association of stochastic variables. Investigation of the domination of triangular norms and general aggregation operators. Application of aggregation operators and dominance for building topologies based on fuzzy nearness relations in environment of logical uncertainty.

Publications

2009

  1. A. Kolesárová – R. Mesiar: Parametric characterization of aggregation functions. Fuzzy Sets and Systems, no. 6, vol. 160, pp. 816–831, 2009.

2008

  1. I. Garaj: Non-Central T-Distribution and Confidence Interval for Non-Centrality Parameter (in Slovak). Forum Statisticum Slovacum, no. 1, vol. 4, pp. 40–45, 2008.

2007

  1. F. Durante – A. Kolesárová – R. Mesiar – C. Sempi: Copulas with given values on a horizontal and a vertical section. Kybernetika, no. 4, vol. 43, pp. 209–220, 2007.
  2. F. Durante – A. Kolesárová – R. Mesiar – C. Sempi: Copulas with given diagonal sections: novel constructions and applications. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, no. 4, vol. 15, pp. 397–410, 2007.
  3. A. Kolesárová: Best possible bounds for 1-Lipschitz aggregation functions determined from a partial information, and consequences for quasi-copulas and copulas. pp. 23–31, 2007.
  4. A. Kolesárová: Fuzzy utility functions. pp. 21–27, 2007.
  5. R. Mesiar – A. Kolesárová – M. Komorníková – T. Calvo: A review of aggregation functions. pp. 121–144, 2007.
  6. J. Mordelová – A. Kolesárová: Some results on discrete copulas. pp. 145–150, 2007.

Investigators

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