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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 Araştırma Makalesi
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 (Ocak2017), 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.