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

Umit Ertugrul

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.

Keywords

Uninorm nullnorm

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

Umit Ertugrul

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
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.
AMA Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences. March 2017;5(2):47-52.
Chicago Ertugrul, Umit. “An Order UV Obtained by Uninorm and Nullnorm”. New Trends in Mathematical Sciences 5, no. 2 (March 2017): 47-52.
EndNote Ertugrul U (March 1, 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, vol. 5, no. 2, pp. 47–52, 2017.
ISNAD Ertugrul, Umit. “An Order UV Obtained by Uninorm and Nullnorm”. New Trends in Mathematical Sciences 5/2 (March2017), 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, vol. 5, no. 2, 2017, pp. 47-52.
Vancouver Ertugrul U. An order UV obtained by uninorm and nullnorm. New Trends in Mathematical Sciences. 2017;5(2):47-52.