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2-Uninormlar Üzerinde Denklik Bağıntısı ve Kıyaslanamayan Elemanların Kümesi

Year 2018, , 309 - 317, 31.07.2018
https://doi.org/10.17714/gumusfenbil.365920

Abstract

Uninormlar, üçgensel normları, üçgensel konormları kapsayan
birleştirme fonksiyonlarının bir sınıfıdır. 2-Uninormlar ise uninormları ve
nullnormları kapsayan çok daha genel bir sınıftır. Uninormlardan elde edilen
kısmen sıralama bağıntısı ve özellikleri üzerine yapılan çalışmalar, onların
daha genel bir sınıfı olan 2-uninormlar için de bu tip özelliklerin
araştırılmasını oldukça doğal kılar. Bu çalışmada, 2-uninormlardan elde edilen
sıralama bağıntısı göz önüne alınarak, 2-uninormların sınıfı üzerinde bir
denklik bağıntısı tanımlanmış ve bazı özellikleri araştırılmıştır. İlaveten,
2-uninormlardan elde edilen sıralama bağıntısına göre kıyaslanamayan
elemanların kümesi karakterize edilmiştir.

References

  • Akella, P., 2007. Structure of n-Uninorms, Fuzzy Sets and Systems, 158, 1631-1651.
  • Beliakov, G., Pradera, A. ve Calvo, T., 2007, Aggregation Functions: A Guide for Practitioners, in: Studies in Fuzziness and Soft Computing, 221, Springer, Berlin, Heidelberg, 361p.
  • Birkhoff G., 1967, Lattice Theory, 3 rd edition, Providence, Rhode Island, 418p.
  • Ertuğrul, Ü., 2017a. Some properties of orders generated by uninorm and 2-uninorm, New Trends in Mathematical Sciences, 1, 278-286.
  • Ertuğrul, Ü., 2017b. A Way to Obtain 2-Uninorm on Bounded Lattice from Uninorms Defined on Subintervals of Bounded Lattice, New Trends in Mathematical Sciences, 2, 1-9.
  • Ertuğrul, Ü., 2018. Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms, Fuzzy Sets and Systems, https://doi.org/10.1016/j.fss.2017.07.020.
  • Ertuğrul, Ü., Kesicioğlu, M.N. ve Karaçal, F., 2016. Ordering Based on Uninorms, Information Sciences, 330, 315-327.
  • Ertuğrul, Ü., Kesicioğlu, M.N. ve Karaçal, F., 2017. Ordering Based on 2-Uninorms on Bounded Lattices, New Trends in Mathematical Sciences, 1, 287-293.
  • Grabish, M., Marichal, J.-L., Mesiar, R. ve Pap, E., 2009, Aggregation Functions, Cambridge University Press, 460p.
  • Hlinĕná, D., Kalina, M. ve Král P., 2014. Pre-orders and Orders Generated by Conjunctive Uninorms, Inf. Proc. Manage. Uncert. Knowl. Based Syst., 30, 807-817.
  • Karaçal, F., Ertuğrul, Ü. ve Mesiar, R., 2017. Characterization of Uninorms on Bounded Lattices, Fuzzy Sets and Systems, 308, 54-71.
  • Karaçal, F. ve Kesicioğlu, M.N., 2011. A T-partial Order Obtained From T-norms, Kybernetika, 47, 300-314.
  • Karaçal, F. ve Mesiar, R., 2015. Uninorms on Bounded Lattices, Fuzzy Sets and Systems, 261, 33-43.
  • Kesicioğlu, M.N., Ertuğrul, Ü. ve Karaçal, F., 2017. An Equivalence Relation Based On The U-Partial Order, Information Sciences, 411, 39-51.
  • Kesicioğlu, M.N., Karaçal, F. ve Mesiar, R., 2015. Order-equivalent Triangular Norms, Fuzzy Sets and Systems, 268, 59-71.
  • Kesicioğlu, M.N. ve Mesiar, R., 2014. Ordering Based on Implications, Information Sciences, 276, 377-386.
  • Yager, R.R. ve Rybalov, A., 1996. Uninorm Aggregation Operators, Fuzzy Sets and Systems, 80, 111-120.

Equivalence Relation on 2-Uninorms and The Set of Incomparable Elements

Year 2018, , 309 - 317, 31.07.2018
https://doi.org/10.17714/gumusfenbil.365920

Abstract

Uninorms are a class
of aggregation functions involving triangular norms and triangular conorms.
2-Uninorms are a much more general class that includes uninorms and nullnorms.
Studies on partial order obtained from uninorms and their properties make it
very natural to investigate such properties for their more general class
2-uninorms. In this study, an equivalence relation is defined on the class of
2-uninorms and some properties are investigated, taking into account the order
relation obtained from 2-uninorms. In addition, the set of incomparable
elements according to the ordering relation obtained from 2-uninorms is
characterized.

References

  • Akella, P., 2007. Structure of n-Uninorms, Fuzzy Sets and Systems, 158, 1631-1651.
  • Beliakov, G., Pradera, A. ve Calvo, T., 2007, Aggregation Functions: A Guide for Practitioners, in: Studies in Fuzziness and Soft Computing, 221, Springer, Berlin, Heidelberg, 361p.
  • Birkhoff G., 1967, Lattice Theory, 3 rd edition, Providence, Rhode Island, 418p.
  • Ertuğrul, Ü., 2017a. Some properties of orders generated by uninorm and 2-uninorm, New Trends in Mathematical Sciences, 1, 278-286.
  • Ertuğrul, Ü., 2017b. A Way to Obtain 2-Uninorm on Bounded Lattice from Uninorms Defined on Subintervals of Bounded Lattice, New Trends in Mathematical Sciences, 2, 1-9.
  • Ertuğrul, Ü., 2018. Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms, Fuzzy Sets and Systems, https://doi.org/10.1016/j.fss.2017.07.020.
  • Ertuğrul, Ü., Kesicioğlu, M.N. ve Karaçal, F., 2016. Ordering Based on Uninorms, Information Sciences, 330, 315-327.
  • Ertuğrul, Ü., Kesicioğlu, M.N. ve Karaçal, F., 2017. Ordering Based on 2-Uninorms on Bounded Lattices, New Trends in Mathematical Sciences, 1, 287-293.
  • Grabish, M., Marichal, J.-L., Mesiar, R. ve Pap, E., 2009, Aggregation Functions, Cambridge University Press, 460p.
  • Hlinĕná, D., Kalina, M. ve Král P., 2014. Pre-orders and Orders Generated by Conjunctive Uninorms, Inf. Proc. Manage. Uncert. Knowl. Based Syst., 30, 807-817.
  • Karaçal, F., Ertuğrul, Ü. ve Mesiar, R., 2017. Characterization of Uninorms on Bounded Lattices, Fuzzy Sets and Systems, 308, 54-71.
  • Karaçal, F. ve Kesicioğlu, M.N., 2011. A T-partial Order Obtained From T-norms, Kybernetika, 47, 300-314.
  • Karaçal, F. ve Mesiar, R., 2015. Uninorms on Bounded Lattices, Fuzzy Sets and Systems, 261, 33-43.
  • Kesicioğlu, M.N., Ertuğrul, Ü. ve Karaçal, F., 2017. An Equivalence Relation Based On The U-Partial Order, Information Sciences, 411, 39-51.
  • Kesicioğlu, M.N., Karaçal, F. ve Mesiar, R., 2015. Order-equivalent Triangular Norms, Fuzzy Sets and Systems, 268, 59-71.
  • Kesicioğlu, M.N. ve Mesiar, R., 2014. Ordering Based on Implications, Information Sciences, 276, 377-386.
  • Yager, R.R. ve Rybalov, A., 1996. Uninorm Aggregation Operators, Fuzzy Sets and Systems, 80, 111-120.
There are 17 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Ümit Ertuğrul 0000-0003-0672-8134

Publication Date July 31, 2018
Submission Date December 14, 2017
Acceptance Date April 4, 2018
Published in Issue Year 2018

Cite

APA Ertuğrul, Ü. (2018). 2-Uninormlar Üzerinde Denklik Bağıntısı ve Kıyaslanamayan Elemanların Kümesi. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 8(2), 309-317. https://doi.org/10.17714/gumusfenbil.365920