L-fuzzy closure operator

  • Yueli Yue Beijing Institute of Technology.
  • Fu-Gui Shi Ocean University of China.
Palabras clave: L-fuzzy co-topology, fuzzy remote neighborhood system, L-fuzzy closure operator, co-topología L-difusa, sistema difuso remoto de vecindad, operador de clausura L-difuso.


The aim of this paper is to study L-fuzzy closure operator in Lfuzzy topological spaces. We introduce two kinds of L-fuzzy closure operators from different point view and prove that both L-TFCS–the category of topological L-fuzzy closure spaces–and L-PTFCS–the category of topological pointwise L-fuzzy closure spaces–are isomorphic to L-CTOP.

Biografía del autor

Yueli Yue, Beijing Institute of Technology.
Department of Mathematics.
Fu-Gui Shi, Ocean University of China.
Department of Mathematics.


[1] J. Adamek, H. Herrlich, G.E. Strecker, Abstract and Concrete Categories, JohnWiley and Sons, Inc., (1990).

[2] C. L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl. 24, pp. 182-193, (1968).

[3] K. C. Chattopadhyay, S. K. Samanta, Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness, Fuzzy Sets and Systems 54, pp. 207-212, (1993).

[4] Gierz, et al., A Compendium of Continuous Lattices, Springer, Berlin, (1980).

[5] U. Höhle, Upper semicontinuous fuzzy sets and applications, J.Math.Anal.Appl. 78, pp. 659-673, (1980).

[6] U. Höhle, A.P. Sostak, Axiomatic foundations of fixed-basis fuzzy topology, Chapter 3 in: U. Höhle, S.E. Rodabaugh (Eds), Mathematics of Fuzzy Sets-Logic, Topology, and Measure Theory, Kluwer Academic Publishers (Boston/Dordrecht/London), pp. 123-272, (1999).

[7] Y. C. Kim, Initial L-fuzzy closure spaces, Fuzzy Sets and Systems 133, pp. 277-297, (2003).

[8] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, (1985).

[9] Y. Liu, M. Luo, Fuzzy Topology, World Scientific Publishing Co.Pte.Ltd, Singapore, (1997).

[10] S. E. Rodabaugh, Powerset operator foundations for poslat fuzy set theories and topologies, Chapter 2 in [6].

[11] S. E. Rodabaugh, Categorical foundations of variable-basis fuzzy topology, Chapter 4 in [6].

[12] A. P. Sostak, On a fuzzy topological structure, Rendiconti Ciecolo Matematico Palermo (Suppl.Ser.II) 11, pp. 89-103, (1985).

[13] A.P. Sostak,, Basic structures of fuzzy topology, J. Math. Sci. 78 (6), pp. 662-701, (1996).

[14] R. Lowen, L. Xu, Alternative characterizations of FNCS, Fuzzy Sets and Systems, 104, pp. 381-391, (1999).

[15] Y. Yue , J. Fang , Categories isomorphic to the Kubiak-Sostak extension of TML, Fuzzy Sets and Systems, 157, pp. 832-842 (2006).
Cómo citar
Yue, Y., & Shi, F.-G. (2017). L-fuzzy closure operator. Proyecciones. Revista De Matemática, 25(3), 237-247. https://doi.org/10.4067/S0716-09172006000300002