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Ordering based 2-uninorm on bounded lattice

Year 2017, Volume: 5 Issue: 1, 287 - 293, 01.01.2017

Abstract




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.




References

  • 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.
Year 2017, Volume: 5 Issue: 1, 287 - 293, 01.01.2017

Abstract

References

  • 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.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Umit Ertugrul This is me

Mucahide Nesibe Kesicioglu This is me

Funda Karacal This is me

Publication Date January 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

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. January 2017;5(1):287-293.
Chicago Ertugrul, Umit, Mucahide Nesibe Kesicioglu, and Funda Karacal. “Ordering Based 2-Uninorm on Bounded Lattice”. New Trends in Mathematical Sciences 5, no. 1 (January 2017): 287-93.
EndNote Ertugrul U, Kesicioglu MN, Karacal F (January 1, 2017) Ordering based 2-uninorm on bounded lattice. New Trends in Mathematical Sciences 5 1 287–293.
IEEE U. Ertugrul, M. N. Kesicioglu, and F. Karacal, “Ordering based 2-uninorm on bounded lattice”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 287–293, 2017.
ISNAD Ertugrul, Umit et al. “Ordering Based 2-Uninorm on Bounded Lattice”. New Trends in Mathematical Sciences 5/1 (January 2017), 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 et al. “Ordering Based 2-Uninorm on Bounded Lattice”. New Trends in Mathematical Sciences, vol. 5, no. 1, 2017, pp. 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.