Abstract
Nullnorms have been produced from triangular norms and triangular conorms and they have several applications in fuzzy logic. The main purpose of this paper is to study the order induced by nullnorms on bounded lattices. We discuss the relationship between the natural order and the order induced by a nullnorm on bounded lattice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aşıcı, E.: An order induced by nullnorms and its properties. Fuzzy Sets Syst. (in press). doi:10.1016/j.fss.2016.12.004
Aşıcı, E., Karaçal, F.: On the \(T\)-partial order and properties. Inf. Sci. 267, 323–333 (2014)
Aşıcı, E., Karaçal, F.: Incomparability with respect to the triangular order. Kybernetika 52, 15–27 (2016)
Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1967)
Calvo, T., De Baets, B., Fodor, J.: The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets Syst. 120, 385–394 (2001)
Casasnovas, J., Mayor, G.: Discrete t-norms and operations on extended multisets. Fuzzy Sets Syst. 159, 1165–1177 (2008)
De Baets, B., Mesiar, R.: Triangular norms on the real unit square. In: Proceedings of the 1999 EUSFLAT-ESTYLF Joint Conference, Palma de Mallorca, Spain, pp. 351–354 (1999)
Çaylı, G.D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices. Inf. Sci. 367–368, 221–231 (2016)
Çaylı, G.D., KaraÇal, F.: Construction of uninorms on bounded lattices. Kybernetika 53, 394–417 (2017)
Çaylı, G.D.: On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets Syst. (in press) doi:10.1016/j.fss.2017.07.015
Drewniak, J., Drygaś, P., Rak, E.: Distributivity between uninorms and nullnorms. Fuzzy Sets Syst. 159, 1646–1657 (2008)
Drygaś, P.: A characterization of idempotent nullnorms. Fuzzy Sets Syst. 145, 455–461 (2004)
Karaçal, F., Ince, M.A., Mesiar, R.: Nullnorms on bounded lattice. Inf. Sci. 325, 227–236 (2015)
Karaçal, F., Kesicioğlu, M.N.: A T-partial order obtained from t-norms. Kybernetika 47, 300–314 (2011)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)
Liang, X., Pedrycz, W.: Logic-based fuzzy networks: a study in system modeling with triangular norms and uninorms. Fuzzy Sets Syst. 160, 3475–3502 (2009)
Mas, M., Mayor, G., Torrens, J.: t-operators. Int. J. Uncertain. Fuzz Knowl.-Based Syst. 7, 31–50 (1999)
Mas, M., Mayor, G., Torrens, J.: The distributivity condition for uninorms and t-operators. Fuzzy Sets Syst. 128, 209–225 (2002)
Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. 8, 535–537 (1942)
Mitsch, H.: A natural partial order for semigroups. Proc. Am. Math. Soc. 97, 384–388 (1986)
Saminger, S.: On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets Syst. 157, 1403–1416 (2006)
Xie, A., Liu, H.: On the distributivity of uninorms over nullnorms. Fuzzy Sets Syst. 211, 62–72 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Aşıcı, E. (2018). Some Notes on the F-partial Order. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 641. Springer, Cham. https://doi.org/10.1007/978-3-319-66830-7_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-66830-7_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66829-1
Online ISBN: 978-3-319-66830-7
eBook Packages: EngineeringEngineering (R0)