Fuzzy transforms, korovkin theorems and the durrmeyer operator

Barnabas Bede, I. Rudas

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform's framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions are shown to include, for example the Bernstein basis polynomials. The F-transform considered with the Bernstein basis polynomials as atoms of a fuzzy partition, is shown to be the classical Durrmeyer operator.

Original languageEnglish
Title of host publication2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings
Pages760-762
Number of pages3
Publication statusPublished - 2009
EventJoint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009 - Lisbon, Portugal
Duration: Jul 20 2009Jul 24 2009

Other

OtherJoint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009
CountryPortugal
CityLisbon
Period7/20/097/24/09

Fingerprint

Mathematical transformations
Polynomials
Atoms

Keywords

  • Bernstein polynomial
  • Durrmeyer operator
  • F-transform
  • Korovkin theorems

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Information Systems

Cite this

Bede, B., & Rudas, I. (2009). Fuzzy transforms, korovkin theorems and the durrmeyer operator. In 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings (pp. 760-762)

Fuzzy transforms, korovkin theorems and the durrmeyer operator. / Bede, Barnabas; Rudas, I.

2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings. 2009. p. 760-762.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bede, B & Rudas, I 2009, Fuzzy transforms, korovkin theorems and the durrmeyer operator. in 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings. pp. 760-762, Joint 2009 International Fuzzy Systems Association World Congress, IFSA 2009 and 2009 European Society of Fuzzy Logic and Technology Conference, EUSFLAT 2009, Lisbon, Portugal, 7/20/09.
Bede B, Rudas I. Fuzzy transforms, korovkin theorems and the durrmeyer operator. In 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings. 2009. p. 760-762
Bede, Barnabas ; Rudas, I. / Fuzzy transforms, korovkin theorems and the durrmeyer operator. 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings. 2009. pp. 760-762
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