Korean J. Math. Vol. 27 No. 2 (2019) pp.475-485
DOI: https://doi.org/10.11568/kjm.2019.27.2.475

$L$-fuzzy bi-closure systems and $L$-fuzzy bi-closure operators

Main Article Content

Jung Mi Ko
Yong Chan Kim

Abstract

In this paper, we introduced the notions of right and left closure systems on generalized residuated lattices. In particular, we study the relations between right (left) closure (interior) operators and right (left) closure (interior) systems. We give their examples.


Article Details

Supporting Agencies

Research Institute of Natural Science of Gangneung-Wonju National University.

References

[1] R. BVelohl avek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002. Google Scholar

[2] R. BVelohl avek, Fuzzy Galois connection, Math. Log. Quart., 45 (2000), 497-504. Google Scholar

[3] R. BVelohl avek, Fuzzy closure operator, J. Math. Anal. Appl. 262 (2001), 473-486. Google Scholar

[4] R. BVelohl avek, Lattices of fixed points of Galois connections, Math. Logic Quart. 47 (2001), 111-116. Google Scholar

[5] L. Biacino and G.Gerla, Closure systems and L-subalgebras, Inf. Sci. 33 (1984), 181–195. Google Scholar

[6] L. Biacino and G.Gerla, An extension principle for closure operators, J. Math. Anal. Appl. 198 (1996), 1–24. Google Scholar

[7] G.Gerla, Graded consequence relations and fuzzy closure operators, J. Appl. Non-classical Logics 6 (1996), 369–379. Google Scholar

[8] Jinming Fang and Yueli Yue, L-fuzzy closure systems, Fuzzy Sets and Systems 161 (2010), 1242–1252. Google Scholar

[9] G. Georgescu and A. Popescue, Non-commutative Galois connections, Soft Computing 7 (2003), 458–467. Google Scholar

[10] G. Georgescu and A. Popescue, Non-dual fuzzy connections, Arch. Math. Log. 43 (2004), 1009–1039. Google Scholar

[11] P. H ajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. Google Scholar

[12] U. H ̈ohle and E. P. Klement, Non-classical logic and their applications to fuzzy subsets , Kluwer Academic Publisher, Boston, 1995. Google Scholar

[13] U. H ̈ohle and S.E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series 3, Kluwer Academic Publishers, Boston, 1999. Google Scholar

[14] H. Lai and D. Zhang, Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory, Int. J. Approx. Reasoning 50 (2009), 695–707. Google Scholar

[15] C.J. Mulvey, Quantales, Suppl. Rend. Cric. Mat. Palermo Ser.II 12,1986,99-104. Google Scholar

[16] M. Ward and R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), 335–354. Google Scholar

[17] E. Turunen, Mathematics Behind Fuzzy Logic, A Springer-Verlag Co., 1999. Google Scholar