Research Article
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Year 2019, Volume: 48 Issue: 2, 439 - 450, 01.04.2019

Emel Aşıcı

Abstract

References

  • E. Aşıcı, An order induced by nullnorms and its properties, Fuzzy Sets Systs. 325, 35-46, 2017.
  • E. Aşıcı, On the properties of the $F$-partial order and the equivalence of nullnorms, Fuzzy Sets Systs. 346, 72-84, 2018, doi: 10.1016/j.fss.2017.11.008.
  • E. Aşıcı, Some notes on the $F$-partial order, in: Advances in Fuzzy Logic and Tech- nology 2017, Kacprzyk J., Szmidt E., Zadroźny S., Atanassov K., Krawczak M. (eds), IWIFSGN 2017, EUSFLAT 2017, Advances in Intelligent Systems and Computing 641, 78-84, Springer, Cham, 2018.
  • E. Aşıcı, On the migrativity property for uninorms and nullnorms, in: Information Processing and Management of Uncertainty in Knowledge-Based Systems, Medina J. et al. (eds), Theory and Foundations, IPMU 2018, Communications in Computer and Information Science 853, 319-328, Springer, Cham, 2018.
  • E. Aşıcı and F. Karaçal On the $T$-partial order and properties, Inf. Sci. 267, 323-333, 2014.
  • T. Calvo, B. De Baets and J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets Systs. 120, 385-394, 2001.
  • J. Casasnovas and G. Mayor, Discrete $t$-norms and operations on extended multisets, Fuzzy Sets Systs. 159, 1165-1177, 2008.
  • G.D. Çaylı, On a new class of $t$-norms and $t$-conorms on bounded lattices, Fuzzy Sets Systs. 332, 129-143, 2018, doi: 10.1016/j.fss.2017.07.015.
  • G.D. Çaylı and P. Drygaś, Some properties of idempotent uninorms on a special class of bounded lattices, Inf. Sci. 422, 352-363, 2018.
  • G.D. Çaylı and F. Karaçal, Construction of uninorms on bounded lattices, Kyber- netika 53, 394-417, 2017.
  • G.D. Çaylı, F. Karaçal and R. Mesiar, On a new class of uninorms on bounded lattices, Inf. Sci. 367-368, 221-231, 2016.
  • B. De Baets and R. Mesiar, Triangular norms on product lattices, Fuzzy Sets Systs. 104, 61-75, 1999.
  • B. De Baets and R. Mesiar, Triangular norms on the real unit square, Proceedings of the 1999 EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca, Spain, 351-354, 1999.
  • J. Drewniak, P. Drygaś and E. Rak, Distributivity between uninorms and nullnorms, Fuzzy Sets Systs. 159, 1646-1657, 2008.
  • P. Drygaś and E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets Systs. 291, 82-97, 2016.
  • D. Dubois and H. Prade, Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Boston 2000.
  • U. Ertuğrul, M.N. Kesicioğlu and F. Karaçal, Ordering based on uninorms, Inf. Sci. 330, 315-327, 2016.
  • J.C. Fodor, R.R. Yager and A. Rybalov, Structure of uninorms, Int. J. Uncertain. Fuzziness Knowl-Based Syst. 5, 411-427, 1997.
  • S. Gottwald, A treatise on many-valued logic, Studies in Logic and Computation, Research Studies Press, Baldock, 2001.
  • M. Grabisch, J.L. Marichal, R. Mesiar and E. Pap, Aggregation Functions, Cambridge University Press, 2009.
  • F. Karaçal and E. Aşıcı, Some notes on $T$-partial order, J. Inequal. Appl. 2013, 219, 2013.
  • F. Karaçal and M.N. Kesicioğlu, A $T$-partial order obtained from $t$-norms, Kyber- netika 47, 300-314, 2011.
  • E.P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000.
  • M. Mas, G. Mayor and J. Torrens, The distributivity condition for uninorms and $t$-operators, Fuzzy Sets Systs. 128, 209-225, 2002.
  • S. Saminger, On ordinal sums of triangular norms on bounded lattices, Fuzzy Sets Systs. 157, 1403-1413, 2006.
  • R.R. Yager, Uninorms in fuzzy system modeling, Fuzzy Sets Systs. 122, 167-175, 2001.
  • R.R. Yager and A. Rybalov, Uninorm aggregation operators, Fuzzy Sets Systs. 80, 111-120, 1996.

The equivalence of uninorms induced by the $U$-partial order

Year 2019, Volume: 48 Issue: 2, 439 - 450, 01.04.2019

Emel Aşıcı

Abstract

In this paper, some properties of an order induced by uninorms are investigated. In this aim, the set of incomparable elements with respect to the $U$-partial order for any uninorm is introduced and studied. Also, by defining such an order, an equivalence relation on the class of uninorms is defined and this equivalence is deeply investigated. Finally, another set of incomparable elements with respect to the $U$-partial order for any uninorm is introduced and studied.

Keywords

uninorm partial order equivalence

References

  • E. Aşıcı, An order induced by nullnorms and its properties, Fuzzy Sets Systs. 325, 35-46, 2017.
  • E. Aşıcı, On the properties of the $F$-partial order and the equivalence of nullnorms, Fuzzy Sets Systs. 346, 72-84, 2018, doi: 10.1016/j.fss.2017.11.008.
  • E. Aşıcı, Some notes on the $F$-partial order, in: Advances in Fuzzy Logic and Tech- nology 2017, Kacprzyk J., Szmidt E., Zadroźny S., Atanassov K., Krawczak M. (eds), IWIFSGN 2017, EUSFLAT 2017, Advances in Intelligent Systems and Computing 641, 78-84, Springer, Cham, 2018.
  • E. Aşıcı, On the migrativity property for uninorms and nullnorms, in: Information Processing and Management of Uncertainty in Knowledge-Based Systems, Medina J. et al. (eds), Theory and Foundations, IPMU 2018, Communications in Computer and Information Science 853, 319-328, Springer, Cham, 2018.
  • E. Aşıcı and F. Karaçal On the $T$-partial order and properties, Inf. Sci. 267, 323-333, 2014.
  • T. Calvo, B. De Baets and J. Fodor, The functional equations of Frank and Alsina for uninorms and nullnorms, Fuzzy Sets Systs. 120, 385-394, 2001.
  • J. Casasnovas and G. Mayor, Discrete $t$-norms and operations on extended multisets, Fuzzy Sets Systs. 159, 1165-1177, 2008.
  • G.D. Çaylı, On a new class of $t$-norms and $t$-conorms on bounded lattices, Fuzzy Sets Systs. 332, 129-143, 2018, doi: 10.1016/j.fss.2017.07.015.
  • G.D. Çaylı and P. Drygaś, Some properties of idempotent uninorms on a special class of bounded lattices, Inf. Sci. 422, 352-363, 2018.
  • G.D. Çaylı and F. Karaçal, Construction of uninorms on bounded lattices, Kyber- netika 53, 394-417, 2017.
  • G.D. Çaylı, F. Karaçal and R. Mesiar, On a new class of uninorms on bounded lattices, Inf. Sci. 367-368, 221-231, 2016.
  • B. De Baets and R. Mesiar, Triangular norms on product lattices, Fuzzy Sets Systs. 104, 61-75, 1999.
  • B. De Baets and R. Mesiar, Triangular norms on the real unit square, Proceedings of the 1999 EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca, Spain, 351-354, 1999.
  • J. Drewniak, P. Drygaś and E. Rak, Distributivity between uninorms and nullnorms, Fuzzy Sets Systs. 159, 1646-1657, 2008.
  • P. Drygaś and E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets Systs. 291, 82-97, 2016.
  • D. Dubois and H. Prade, Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Boston 2000.
  • U. Ertuğrul, M.N. Kesicioğlu and F. Karaçal, Ordering based on uninorms, Inf. Sci. 330, 315-327, 2016.
  • J.C. Fodor, R.R. Yager and A. Rybalov, Structure of uninorms, Int. J. Uncertain. Fuzziness Knowl-Based Syst. 5, 411-427, 1997.
  • S. Gottwald, A treatise on many-valued logic, Studies in Logic and Computation, Research Studies Press, Baldock, 2001.
  • M. Grabisch, J.L. Marichal, R. Mesiar and E. Pap, Aggregation Functions, Cambridge University Press, 2009.
  • F. Karaçal and E. Aşıcı, Some notes on $T$-partial order, J. Inequal. Appl. 2013, 219, 2013.
  • F. Karaçal and M.N. Kesicioğlu, A $T$-partial order obtained from $t$-norms, Kyber- netika 47, 300-314, 2011.
  • E.P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht 2000.
  • M. Mas, G. Mayor and J. Torrens, The distributivity condition for uninorms and $t$-operators, Fuzzy Sets Systs. 128, 209-225, 2002.
  • S. Saminger, On ordinal sums of triangular norms on bounded lattices, Fuzzy Sets Systs. 157, 1403-1413, 2006.
  • R.R. Yager, Uninorms in fuzzy system modeling, Fuzzy Sets Systs. 122, 167-175, 2001.
  • R.R. Yager and A. Rybalov, Uninorm aggregation operators, Fuzzy Sets Systs. 80, 111-120, 1996.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Emel Aşıcı 0000-0002-7692-5937

Publication Date April 1, 2019
Published in Issue Year 2019 Volume: 48 Issue: 2

Cite

APA Aşıcı, E. (2019). The equivalence of uninorms induced by the $U$-partial order. Hacettepe Journal of Mathematics and Statistics, 48(2), 439-450.
AMA Aşıcı E. The equivalence of uninorms induced by the $U$-partial order. Hacettepe Journal of Mathematics and Statistics. April 2019;48(2):439-450.
Chicago Aşıcı, Emel. “The Equivalence of Uninorms Induced by the $U$-Partial Order”. Hacettepe Journal of Mathematics and Statistics 48, no. 2 (April 2019): 439-50.
EndNote Aşıcı E (April 1, 2019) The equivalence of uninorms induced by the $U$-partial order. Hacettepe Journal of Mathematics and Statistics 48 2 439–450.
IEEE E. Aşıcı, “The equivalence of uninorms induced by the $U$-partial order”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, pp. 439–450, 2019.
ISNAD Aşıcı, Emel. “The Equivalence of Uninorms Induced by the $U$-Partial Order”. Hacettepe Journal of Mathematics and Statistics 48/2 (April 2019), 439-450.
JAMA Aşıcı E. The equivalence of uninorms induced by the $U$-partial order. Hacettepe Journal of Mathematics and Statistics. 2019;48:439–450.
MLA Aşıcı, Emel. “The Equivalence of Uninorms Induced by the $U$-Partial Order”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, 2019, pp. 439-50.
Vancouver Aşıcı E. The equivalence of uninorms induced by the $U$-partial order. Hacettepe Journal of Mathematics and Statistics. 2019;48(2):439-50.

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