Araştırma Makalesi
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Building A Different Family of Nullnorms on Lattices

Yıl 2019, Cilt: 19 Sayı: 1, 103 - 113, 28.05.2019
https://doi.org/10.35414/akufemubid.422010

Öz



In this paper, we introduce a new method for obtaining nullnorms on l having an annihilator based on the existence of triangular norms and nullnorms acting on a subinterval of a bounded lattice L Some basic properties concerning this construction method are investigated. Furthermore, it is exemplified the fact that the proposed method differs from the existing methods for constructing nullnorms on bounded lattices.


Kaynakça

  • Birkhoff, G., 1967. Lattice Theory. American Mathematical Society Colloquium Publishers, Providence, RI.
  • Calvo, T., De Baets, B. and Fodor, J., 2001. The mappingal equations of Frank and Alsina for uninorms and nullnorm. Fuzzy Sets and Systems, 120, 385-394.
  • Çaylı, G.D., Karaçal, F. and Mesiar, R., 2016. On a new class of uninorms on bounded lattices. Information Sciences, 367–368, 221–231.
  • Çaylı, G.D. and Karaçal, F., 2018. Idempotent nullnorms on bounded lattices. Information Sciences, 425, 154-163.
  • Çaylı, G.D., 2018. On a new class of triangular norms and triangular conorms on bounded lattices. Fuzzy Sets and Systems, 332, 129-143.
  • Drygaś, P., 2004a. A characterization of idempotent nullnorms. Fuzzy Sets and Systems, 145, 455-461.
  • Drygaś, P., 2004b. Isotonic operations with annihilator in bounded lattices. in: K. Atanassov, O. Hryniewicz, J. Kacprzyk (Eds.), Soft Computing Foundations and Theoretical Aspect, EXIT Warszawa, 181–190.
  • Drygaś, P., Qin, F. and Rak, E., 2017. Left and right distributivity equations for semi-t-operators and uninorms. Fuzzy Sets and Systems, 325, 21-34.
  • Dubois, D. and Prade, H., 2000. Fundamentals of Fuzzy Sets. Kluwer Academic Publishers, Boston, MA.
  • Ertuğrul, Ü., Karaçal, F. and Mesiar, R., 2015. Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. International Journal of Intelligent Systems, 30, 807-817.
  • Ertuğrul, Ü., 2018. Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms. Fuzzy Sets and Systems, 334, 94–109.
  • Grabisch, M., Marichal, J.L., Mesiar, R. and Pap, E., 2009. Aggregation Operations. Cambridge University Press Cambridge.
  • Karaçal, F., İnce, M.A. and Mesiar, R., 2015. Nullnorms on bounded lattices. Information Sciences, 325, 227–236.
  • Klement, E.P., Mesiar, R. and Pap, E., 2000. Triangular Norms. Kluwer Academic Publishers, Dordrecht.
  • Takács, M., 2008. Uninorm-based models for FLC systems. Journal of Intelligent & Fuzzy Systems, 19, 65-73.
  • Mas, M., Mayor, G. and Torrens, J., 1999. t-operators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7, 31-50.
  • Mas, M., Mayor, G. and Torrens, J., 2002. The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems, 128, 209-225.
  • Sun, F., Wang, X.P. and Qu, X.B., 2017. Uni-nullnorms and null-uninorms. Journal of Intelligent & Fuzzy Systems, 32, 1969-1981.

Kafesler Üzerinde Nullnormların Bir Farklı Ailesinin İnşaası

Yıl 2019, Cilt: 19 Sayı: 1, 103 - 113, 28.05.2019
https://doi.org/10.35414/akufemubid.422010

Öz

Bu çalışmada sınırlı bir L kafesinin bir alt aralığı üzerinde hareket eden nulnormlar ve üçgensel normlar temel alınarak L üzerinde bir yutan elemanlı nullnormları elde etmek için yeni bir inşaa yöntemi önerilmektedir. Bu inşaa yöntemi ile ilgili bazı temel özellikler araştırılmaktadır. Ayrıca, önerilen  yöntemin sınırlı kafesler üzerinde nullnormları inşa eden mevcut yöntemlerden farklı olduğu örnekle gösterilmektedir.

Kaynakça

  • Birkhoff, G., 1967. Lattice Theory. American Mathematical Society Colloquium Publishers, Providence, RI.
  • Calvo, T., De Baets, B. and Fodor, J., 2001. The mappingal equations of Frank and Alsina for uninorms and nullnorm. Fuzzy Sets and Systems, 120, 385-394.
  • Çaylı, G.D., Karaçal, F. and Mesiar, R., 2016. On a new class of uninorms on bounded lattices. Information Sciences, 367–368, 221–231.
  • Çaylı, G.D. and Karaçal, F., 2018. Idempotent nullnorms on bounded lattices. Information Sciences, 425, 154-163.
  • Çaylı, G.D., 2018. On a new class of triangular norms and triangular conorms on bounded lattices. Fuzzy Sets and Systems, 332, 129-143.
  • Drygaś, P., 2004a. A characterization of idempotent nullnorms. Fuzzy Sets and Systems, 145, 455-461.
  • Drygaś, P., 2004b. Isotonic operations with annihilator in bounded lattices. in: K. Atanassov, O. Hryniewicz, J. Kacprzyk (Eds.), Soft Computing Foundations and Theoretical Aspect, EXIT Warszawa, 181–190.
  • Drygaś, P., Qin, F. and Rak, E., 2017. Left and right distributivity equations for semi-t-operators and uninorms. Fuzzy Sets and Systems, 325, 21-34.
  • Dubois, D. and Prade, H., 2000. Fundamentals of Fuzzy Sets. Kluwer Academic Publishers, Boston, MA.
  • Ertuğrul, Ü., Karaçal, F. and Mesiar, R., 2015. Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. International Journal of Intelligent Systems, 30, 807-817.
  • Ertuğrul, Ü., 2018. Construction of nullnorms on bounded lattices and an equivalence relation on nullnorms. Fuzzy Sets and Systems, 334, 94–109.
  • Grabisch, M., Marichal, J.L., Mesiar, R. and Pap, E., 2009. Aggregation Operations. Cambridge University Press Cambridge.
  • Karaçal, F., İnce, M.A. and Mesiar, R., 2015. Nullnorms on bounded lattices. Information Sciences, 325, 227–236.
  • Klement, E.P., Mesiar, R. and Pap, E., 2000. Triangular Norms. Kluwer Academic Publishers, Dordrecht.
  • Takács, M., 2008. Uninorm-based models for FLC systems. Journal of Intelligent & Fuzzy Systems, 19, 65-73.
  • Mas, M., Mayor, G. and Torrens, J., 1999. t-operators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7, 31-50.
  • Mas, M., Mayor, G. and Torrens, J., 2002. The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems, 128, 209-225.
  • Sun, F., Wang, X.P. and Qu, X.B., 2017. Uni-nullnorms and null-uninorms. Journal of Intelligent & Fuzzy Systems, 32, 1969-1981.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Gül Deniz Çaylı

Yayımlanma Tarihi 28 Mayıs 2019
Gönderilme Tarihi 8 Mayıs 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 19 Sayı: 1

Kaynak Göster

APA Çaylı, G. D. (2019). Building A Different Family of Nullnorms on Lattices. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 19(1), 103-113. https://doi.org/10.35414/akufemubid.422010
AMA Çaylı GD. Building A Different Family of Nullnorms on Lattices. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. Mayıs 2019;19(1):103-113. doi:10.35414/akufemubid.422010
Chicago Çaylı, Gül Deniz. “Building A Different Family of Nullnorms on Lattices”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 19, sy. 1 (Mayıs 2019): 103-13. https://doi.org/10.35414/akufemubid.422010.
EndNote Çaylı GD (01 Mayıs 2019) Building A Different Family of Nullnorms on Lattices. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 19 1 103–113.
IEEE G. D. Çaylı, “Building A Different Family of Nullnorms on Lattices”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 19, sy. 1, ss. 103–113, 2019, doi: 10.35414/akufemubid.422010.
ISNAD Çaylı, Gül Deniz. “Building A Different Family of Nullnorms on Lattices”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 19/1 (Mayıs 2019), 103-113. https://doi.org/10.35414/akufemubid.422010.
JAMA Çaylı GD. Building A Different Family of Nullnorms on Lattices. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2019;19:103–113.
MLA Çaylı, Gül Deniz. “Building A Different Family of Nullnorms on Lattices”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, c. 19, sy. 1, 2019, ss. 103-1, doi:10.35414/akufemubid.422010.
Vancouver Çaylı GD. Building A Different Family of Nullnorms on Lattices. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2019;19(1):103-1.