Araştırma Makalesi
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An order UV obtained by uninorm and nullnorm

Yıl 2017, Cilt: 5 Sayı: 2, 47 - 52, 30.03.2017

Umit Ertugrul

Öz

Uninorms and nullnorms are hot topics to study nowadays. In this paper, a new order definition on bounded lattice is given using the uninorm and nullnorm on sub-interval of bounded lattice order defined on. Some interesting properties of the order are investigated. It is posed that even if L chain with order defined on, L may not be chain with the order UV.

Anahtar Kelimeler

Uninorm nullnorm

Kaynakça

  • E. Asici, An order induced by nullnorms and its properties, Fuzzy Sets and Systems http://dx.doi.org/10.1016/j.fss.2016.12.004.
  • G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
  • T. Calvo, B. DeBaets, J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorm, Fuzzy Sets and Systems 120 (2001) 385-394.
  • G. D. Cayli, F. Karacal, R.Mesiar, On a new class of uninorms on bounded lattices, Information Sciences 367-368 (2016) 221-231.
  • U. Ertugrul, F. Karacal, R. Mesiar, Modified ordinal sums of triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
  • U. Ertugrul, M. N. Kesicioglu, F. Karac¸al, Ordering based on uninorms, Information Sciences, 330 (2016), 315-327.
  • U. Ertugrul,M. N. Kesicioglu, F. Karac¸al, Ordering based 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. Karacal, U. Ertugrul, R. Mesiar, Characterization of uninorms on bounded lattices, Fuzzy Sets and Systems, 308 (2017) 54-71.
  • F. Karacal, M.A. Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences 325 (2015) 277-236.
  • F. Karacal, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
  • F. Karacal, M. N. Kesicioglu, A T-partial order obtained from t-norms, Kybernetika, 47(2011), 300-314.
  • M. N. Kesicioglu, F. Karacal, R. Mesiar, Order-equivalent triangular norms, Fuzzy Sets and Systems, 268 (2015), 59-71.
  • M. Mas, G. Mayor, J. Torens, t-operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7 (1999) 31-50.
  • R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.

Yıl 2017, Cilt: 5 Sayı: 2, 47 - 52, 30.03.2017

Umit Ertugrul

Öz

Kaynakça

  • E. Asici, An order induced by nullnorms and its properties, Fuzzy Sets and Systems http://dx.doi.org/10.1016/j.fss.2016.12.004.
  • G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
  • T. Calvo, B. DeBaets, J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorm, Fuzzy Sets and Systems 120 (2001) 385-394.
  • G. D. Cayli, F. Karacal, R.Mesiar, On a new class of uninorms on bounded lattices, Information Sciences 367-368 (2016) 221-231.
  • U. Ertugrul, F. Karacal, R. Mesiar, Modified ordinal sums of triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
  • U. Ertugrul, M. N. Kesicioglu, F. Karac¸al, Ordering based on uninorms, Information Sciences, 330 (2016), 315-327.
  • U. Ertugrul,M. N. Kesicioglu, F. Karac¸al, Ordering based 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. Karacal, U. Ertugrul, R. Mesiar, Characterization of uninorms on bounded lattices, Fuzzy Sets and Systems, 308 (2017) 54-71.
  • F. Karacal, M.A. Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences 325 (2015) 277-236.
  • F. Karacal, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
  • F. Karacal, M. N. Kesicioglu, A T-partial order obtained from t-norms, Kybernetika, 47(2011), 300-314.
  • M. N. Kesicioglu, F. Karacal, R. Mesiar, Order-equivalent triangular norms, Fuzzy Sets and Systems, 268 (2015), 59-71.
  • M. Mas, G. Mayor, J. Torens, t-operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7 (1999) 31-50.
  • R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Umit Ertugrul

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

Kaynak Göster

APA Ertugrul, U. (2017). An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences, 5(2), 47-52.
AMA Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences. Mart 2017;5(2):47-52.
Chicago Ertugrul, Umit. “An order UV obtained by uninorm and nullnorm”. New Trends in Mathematical Sciences 5, sy. 2 (Mart 2017): 47-52.
EndNote Ertugrul U (01 Mart 2017) An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences 5 2 47–52.
IEEE U. Ertugrul, “An order UV obtained by uninorm and nullnorm”, New Trends in Mathematical Sciences, c. 5, sy. 2, ss. 47–52, 2017.
ISNAD Ertugrul, Umit. “An order UV obtained by uninorm and nullnorm”. New Trends in Mathematical Sciences 5/2 (Mart2017), 47-52.
JAMA Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences. 2017;5:47–52.
MLA Ertugrul, Umit. “An order UV obtained by uninorm and nullnorm”. New Trends in Mathematical Sciences, c. 5, sy. 2, 2017, ss. 47-52.
Vancouver Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences. 2017;5(2):47-52.