Previous |  Up |  Next


principal topology; bounded lattice; generating method; uninorm; triangular norm
In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.
[1] Alexandroff, P.: Diskrete Räume. Mat. Sb. (N.S.) 2 (1937), 501-518.
[2] Birkhoff, G.: Lattice Theory. American Mathematical Society, New York 1948. Zbl 0537.06001
[3] Chen, X.: Cores of Alexandroff spaces.
[4] Çaylı, G. D., Ertuğrul, Ü., Köroğlu, T., Karaçal, F.: Notes on locally internal uninorm on bounded lattices. Kybernetika 53 (2017), 911-921. DOI 
[5] Dahane, I., Lazaar, S., Richmond, T., Turki, T.: On resolvable primal spaces. Quaestiones Mathematicae (2018), 15-35. DOI 
[6] Dixmier, J.: General Topology. Springer-Verlag, 1984.
[7] Echi, O.: Quasi-homeomorphisms, Goldspectral spaces and Jacspectral spaces. Boll Unione Mat. Ital. Sez. B Artic. Ric. Mat. 8 (2003), 489-507.
[8] Echi, O.: The category of flows of Set and Top. Topol. Appl. 159 (2012), 2357-2366. DOI 
[9] Ertuğrul, Ü., Kesicioğlu, M. N., Karaçal, F.: Ordering based on uninorms. Inform. Sci. 330 (2016), 315-327. DOI 
[10] Ertuğrul, Ü., Karaçal, F., Mesiar, R.: Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. Int. J. Intell. Systems 30 (2015), 807-817. DOI 
[11] Fodor, J., Yager, R., Rybalov, A.: Structure of uninorms. Int. J. Uncertain. Fuzziness Knowledge-Based Systems 5 (1997), 411-427. DOI 10.1142/S0218488597000312 | Zbl 1232.03015
[12] Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, 2009. MR 2538324 | Zbl 1206.68299
[13] Karaçal, F., Köroğlu, T.: An Alexandroff Topology Obtained from Uninorms. Submitted (2019).
[14] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices. Fuzzy Sets and Systems 261 (2015), 33-43. DOI 
[15] Katsevich, A., Mikusiński, P.: Order of spaces of pseudoquotients. Top. Proc. 44 (2014), 21-31.
[16] Kelley, J. L.: General Topology. Springer, New York 1975.
[17] Kesicioğlu, M. N., Ertuğrul, Ü., Karaçal, F.: Some notes on U-partial order. Kybernetika 55 (2019), 3, 518-530. DOI 
[18] Lai, H., Zhang, D.: Fuzzy preorder and fuzzy topology. Fuzzy Sets Systems 157 (2006), 14, 1865-1885. DOI 
[19] Lazaar, S., Richmond, T., Houssem, S.: The autohomeomorphism group of connected homogeneous functionally Alexandroff spaces. Comm. Algebra (2019). DOI 
[20] Lazaar, S., Richmond, T., Turki, T.: Maps generating the same primal space. Quaest. Math. 40 (2017), 17-28. DOI 
[21] Ma, Z., Wu, W. M.: Logical operators on complete lattices. Information Sciences 55 (1991), 77-97. DOI  | Zbl 0741.03010
[22] Steiner, A. K.: The lattice of topologies: Structure and complementation. Trans. Amer. Math. Soc. 122 (1969), 379-398. DOI 10.1090/S0002-9947-1966-0190893-2
[23] Walden, P.: Effective topology from spacetime tomography. J. Physics: Conference Series 68 (2007), 12-28.
[24] Yager, R. R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets Systems 80 (1996), 111-120. DOI  | Zbl 0871.04007
[25] Zhang, H.-P., Pérez.-Fernández, R., Baets, B. De: Topologies induced by the representatiton of a betweenness relation as a family of order relations. Topol. Appl. 258 (2019), 100-114. DOI 
Partner of
EuDML logo