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Ordering based 2-uninorm on bounded lattice

Yıl 2017, Cilt: 5 Sayı: 1, 287 - 293, 01.01.2017

Öz




In this paper, an order induced by 2-uninorm on
bounded lattices is given and some properties of the order are discussed. By
defining such an order on bounded lattice, the T-partial order, S-partial order
and V-partial order are extended to a more general form.




Kaynakça

  • P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
  • G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
  • P. Drygaś, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 2016 (291), 82-97.
  • Ü. Ertuğrul, F. Karaçal, R. Mesiar, Modified ordinal sums of triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
  • Ü. Ertuğrul, M. N. Kesicioğlu, F. Karaçal, Ordering based on uninorms, Information Sciences, 330 (2016), 315-327.
  • 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.
  • D. Hline ̆ná, M. Kalina, P. Král, Pre-orders and orders generated by conjunctive uninorms, Information Processing and Management of Uncertainty in Knowledge-Based Systems Communications in Computer and Information Science, 444 (2014), 307-316.
  • F. Karaçal, M.A. İnce, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
  • F. Karaçal, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
  • F. Karaçal, M. N. Kesicioğlu, A T-partial order obtained from t-norms, Kybernetika, 47(2011), 300-314.
  • M. N. Kesicioğlu, F. Karaçal, R. Mesiar, Order-equivalent triangular norms, Fuzzy Sets and Systems, 268 (2015), 59-71.
  • M. N. Kesicioğlu, R. Mesiar, Ordering based on implications, Information Sciences, 276 (2014), 377-386.
  • M. N. Kesicioğlu, On the property of T-distributivity, Fixed Point Theory and Applications, 2013, 2013:32.
  • 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: 1, 287 - 293, 01.01.2017

Öz

Kaynakça

  • P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
  • G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
  • P. Drygaś, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 2016 (291), 82-97.
  • Ü. Ertuğrul, F. Karaçal, R. Mesiar, Modified ordinal sums of triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
  • Ü. Ertuğrul, M. N. Kesicioğlu, F. Karaçal, Ordering based on uninorms, Information Sciences, 330 (2016), 315-327.
  • 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.
  • D. Hline ̆ná, M. Kalina, P. Král, Pre-orders and orders generated by conjunctive uninorms, Information Processing and Management of Uncertainty in Knowledge-Based Systems Communications in Computer and Information Science, 444 (2014), 307-316.
  • F. Karaçal, M.A. İnce, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
  • F. Karaçal, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
  • F. Karaçal, M. N. Kesicioğlu, A T-partial order obtained from t-norms, Kybernetika, 47(2011), 300-314.
  • M. N. Kesicioğlu, F. Karaçal, R. Mesiar, Order-equivalent triangular norms, Fuzzy Sets and Systems, 268 (2015), 59-71.
  • M. N. Kesicioğlu, R. Mesiar, Ordering based on implications, Information Sciences, 276 (2014), 377-386.
  • M. N. Kesicioğlu, On the property of T-distributivity, Fixed Point Theory and Applications, 2013, 2013:32.
  • 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 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Umit Ertugrul Bu kişi benim

Mucahide Nesibe Kesicioglu Bu kişi benim

Funda Karacal Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 1

Kaynak Göster

APA Ertugrul, U., Kesicioglu, M. N., & Karacal, F. (2017). Ordering based 2-uninorm on bounded lattice. New Trends in Mathematical Sciences, 5(1), 287-293.
AMA Ertugrul U, Kesicioglu MN, Karacal F. Ordering based 2-uninorm on bounded lattice. New Trends in Mathematical Sciences. Ocak 2017;5(1):287-293.
Chicago Ertugrul, Umit, Mucahide Nesibe Kesicioglu, ve Funda Karacal. “Ordering Based 2-Uninorm on Bounded Lattice”. New Trends in Mathematical Sciences 5, sy. 1 (Ocak 2017): 287-93.
EndNote Ertugrul U, Kesicioglu MN, Karacal F (01 Ocak 2017) Ordering based 2-uninorm on bounded lattice. New Trends in Mathematical Sciences 5 1 287–293.
IEEE U. Ertugrul, M. N. Kesicioglu, ve F. Karacal, “Ordering based 2-uninorm on bounded lattice”, New Trends in Mathematical Sciences, c. 5, sy. 1, ss. 287–293, 2017.
ISNAD Ertugrul, Umit vd. “Ordering Based 2-Uninorm on Bounded Lattice”. New Trends in Mathematical Sciences 5/1 (Ocak 2017), 287-293.
JAMA Ertugrul U, Kesicioglu MN, Karacal F. Ordering based 2-uninorm on bounded lattice. New Trends in Mathematical Sciences. 2017;5:287–293.
MLA Ertugrul, Umit vd. “Ordering Based 2-Uninorm on Bounded Lattice”. New Trends in Mathematical Sciences, c. 5, sy. 1, 2017, ss. 287-93.
Vancouver Ertugrul U, Kesicioglu MN, Karacal F. Ordering based 2-uninorm on bounded lattice. New Trends in Mathematical Sciences. 2017;5(1):287-93.