L-Topological Spaces Based on Residuated Lattices

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DOI: 10.4236/apm.2012.21010   PDF   HTML     3,771 Downloads   7,668 Views   Citations

Abstract

In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.

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Z. Wang and X. Liu, "L-Topological Spaces Based on Residuated Lattices," Advances in Pure Mathematics, Vol. 2 No. 1, 2012, pp. 41-44. doi: 10.4236/apm.2012.21010.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] K. Blount and C. Tsinakis, “The Structure of Residuated Lattices,” International Journal of Algebra and Computation, Vol. 13, No. 4, 2003, pp. 437-461.
[2] N. Galatos, P. Jipsen, T. Kowalski and H. One, “Residuated Lattices: An Algebraic Glimpse at Substructural Logics,” Elsevier, Amsterdam, 2007.
[3] L. Z. Liu and K. T. Li, “Boolean Filters and Positive Implicative Filters of Residuated Lattices,” Information Sciences, Vol. 177, No. 24, 2007, pp. 5725-5738. doi:10.1016/j.ins.2007.07.014
[4] Z. D. Wang and J. X. Fang, “On v-Filters and Normal v-Filters of a Residuated Lattice with a Weak vt-Opera- tor,” Information Sciences, Vol. 178, No. 17, 2008, pp. 3465-3473. doi:10.1016/j.ins.2008.04.003
[5] U. Hohle, “Commutative, Residuated L-Monoids,” In: U. Hohle and E. P. Klement, Eds., Non-Classical Logics and Their Applications to Fuzzy Subsets, Kluwer Academic Publishers, Boston, Dordrecht, 1995, pp. 53-106.
[6] A. M. Radzikowska and E. E. Kerre, “Fuzzy Rough Sets Based on Residuated Lattices,” In: J. F. Peter et al., Eds., Transactions on Rough Sets II, LNCS 3135, 2004, pp. 278-296.
[7] Z. D. Wang and Y. D. Yu, “Pseudo-t-Norms and Implication Operators on a Complete Brouwerian Lattice,” Fuzzy Sets and Systems, Vol. 132, No. 1, 2002, pp. 113-124. doi:10.1016/S0165-0114(01)00210-X
[8] Z. D. Wang and J. X. Fang, “Residual Operations of Left and Right Uninorms on a Complete Lattice,” Fuzzy Sets and Systems, Vol. 160, No. 1, 2009, pp. 22-31. doi:10.1016/j.fss.2008.03.001
[9] Y. M. Liu and M. K. Luo, “Fuzzy Topology,” World Scientific Publishing, Singapore, 1997.

  
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