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.