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A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice

Yıl 2017, Cilt: 5 Sayı: 2, 1 - 9, 30.03.2017

Öz

In this paper, a way to obtain 2-uninorm on bounded lattice
from U1 disjunctive uninorm on [0, k] and U2   conjunctive uninorm on [k,1] is presented.
When the conditions disjunctive of U
 or conjunctive of U2    drop, it is showed that this method is
invalid. Additionally, some properties of this construction method are
investigated.

Kaynakça

  • P. Akella, C-sets of n-uninorms, Fuzzy Sets and Systems, 160 (2009), 1-21.
  • P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
  • G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
  • P. Dryga´s, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 2016 (291), 82-97.
  • U. Ertu˘grul, F. Karac¸al, R. Mesiar, Modified ordinal sums o ¨ f triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
  • U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d on uninorms, Information Sciences, 330 (2016), 315-327.
  • U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d 2-uninorms on bounded lattices, New Trends in Mathematical Sciences, in press.
  • J. Fodor, R. Yager, and A. Rybalov, Structure of uninorms, Internata. J. Uncertain. Fuzziness Knowledge-Based Systems, 5 (1997), 411-427.
  • M. Grabisch, J.-L. Marichal, R. Mesiar, E. Pap, Aggregation Functions, Cambridge University Press, 2009.
  • F. Karac¸al, M.A. ˙Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
  • F. Karac¸al, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
  • R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.
  • R. R. Yager, Uninorms in fuzzy system modelling, Fuzzy Sets and Systems, 122 (2001), 167-175.
Yıl 2017, Cilt: 5 Sayı: 2, 1 - 9, 30.03.2017

Öz

Kaynakça

  • P. Akella, C-sets of n-uninorms, Fuzzy Sets and Systems, 160 (2009), 1-21.
  • P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
  • G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
  • P. Dryga´s, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 2016 (291), 82-97.
  • U. Ertu˘grul, F. Karac¸al, R. Mesiar, Modified ordinal sums o ¨ f triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
  • U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d on uninorms, Information Sciences, 330 (2016), 315-327.
  • U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d 2-uninorms on bounded lattices, New Trends in Mathematical Sciences, in press.
  • J. Fodor, R. Yager, and A. Rybalov, Structure of uninorms, Internata. J. Uncertain. Fuzziness Knowledge-Based Systems, 5 (1997), 411-427.
  • M. Grabisch, J.-L. Marichal, R. Mesiar, E. Pap, Aggregation Functions, Cambridge University Press, 2009.
  • F. Karac¸al, M.A. ˙Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
  • F. Karac¸al, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
  • R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.
  • R. R. Yager, Uninorms in fuzzy system modelling, Fuzzy Sets and Systems, 122 (2001), 167-175.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Umit Ertugrul

Yayımlanma Tarihi 30 Mart 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 2

Kaynak Göster

APA Ertugrul, U. (2017). A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice. New Trends in Mathematical Sciences, 5(2), 1-9.
AMA Ertugrul U. A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice. New Trends in Mathematical Sciences. Mart 2017;5(2):1-9.
Chicago Ertugrul, Umit. “A Way to Obtain 2-Uninorm on Bounded Lattice from Uninorms Defined on Subintervals of Bounded Lattice”. New Trends in Mathematical Sciences 5, sy. 2 (Mart 2017): 1-9.
EndNote Ertugrul U (01 Mart 2017) A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice. New Trends in Mathematical Sciences 5 2 1–9.
IEEE U. Ertugrul, “A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice”, New Trends in Mathematical Sciences, c. 5, sy. 2, ss. 1–9, 2017.
ISNAD Ertugrul, Umit. “A Way to Obtain 2-Uninorm on Bounded Lattice from Uninorms Defined on Subintervals of Bounded Lattice”. New Trends in Mathematical Sciences 5/2 (Mart 2017), 1-9.
JAMA Ertugrul U. A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice. New Trends in Mathematical Sciences. 2017;5:1–9.
MLA Ertugrul, Umit. “A Way to Obtain 2-Uninorm on Bounded Lattice from Uninorms Defined on Subintervals of Bounded Lattice”. New Trends in Mathematical Sciences, c. 5, sy. 2, 2017, ss. 1-9.
Vancouver Ertugrul U. A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice. New Trends in Mathematical Sciences. 2017;5(2):1-9.