Research Article
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An order UV obtained by uninorm and nullnorm

Year 2017, Volume: 5 Issue: 2, 47 - 52, 30.03.2017
https://izlik.org/JA38DY99EM

Abstract

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.

References

  • 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.

Year 2017, Volume: 5 Issue: 2, 47 - 52, 30.03.2017
https://izlik.org/JA38DY99EM

Abstract

References

  • 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.
There are 16 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Umit Ertugrul

Publication Date March 30, 2017
IZ https://izlik.org/JA38DY99EM
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Ertugrul, U. (2017). An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences, 5(2), 47-52. https://izlik.org/JA38DY99EM
AMA 1.Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences. 2017;5(2):47-52. https://izlik.org/JA38DY99EM
Chicago Ertugrul, Umit. 2017. “An Order UV Obtained by Uninorm and Nullnorm”. New Trends in Mathematical Sciences 5 (2): 47-52. https://izlik.org/JA38DY99EM.
EndNote Ertugrul U (March 1, 2017) An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences 5 2 47–52.
IEEE [1]U. Ertugrul, “An order UV obtained by uninorm and nullnorm”, New Trends in Mathematical Sciences, vol. 5, no. 2, pp. 47–52, Mar. 2017, [Online]. Available: https://izlik.org/JA38DY99EM
ISNAD Ertugrul, Umit. “An Order UV Obtained by Uninorm and Nullnorm”. New Trends in Mathematical Sciences 5/2 (March 1, 2017): 47-52. https://izlik.org/JA38DY99EM.
JAMA 1.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, vol. 5, no. 2, Mar. 2017, pp. 47-52, https://izlik.org/JA38DY99EM.
Vancouver 1.Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences [Internet]. 2017 Mar. 1;5(2):47-52. Available from: https://izlik.org/JA38DY99EM