<i>L</i>-Topological Spaces Based on Residuated Lattices

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.

KeywordsResiduated LatticeL-Topological SpaceInterior OperatorLeft (Right) Closure Operator

K. Blount and C. Tsinakis, “The Structure of Residuated Lattices,” International Journal of Algebra and Computation, Vol. 13, No. 4, 2003, pp. 437-461.
N. Galatos, P. Jipsen, T. Kowalski and H. One, “Residuated Lattices: An Algebraic Glimpse at Substructural Logics,” Elsevier, Amsterdam, 2007.
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
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
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.
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.
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
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
Y. M. Liu and M. K. Luo, “Fuzzy Topology,” World Scientific Publishing, Singapore, 1997.

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<i>L</i>-Topological Spaces Based on Residuated Lattices

Abstract

References (9)