## $$L$$-fuzzy bi-closure systems and $$L$$-fuzzy bi-closure operators.(English)Zbl 1477.06042

Summary: 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.

### MSC:

 06D72 Fuzzy lattices (soft algebras) and related topics 03E72 Theory of fuzzy sets, etc. 03G10 Logical aspects of lattices and related structures 06A15 Galois correspondences, closure operators (in relation to ordered sets)
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### References:

 [1] R. Bˇelohl ́avek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002. [2] R. Bˇelohl ́avek, Fuzzy Galois connection, Math. Log. Quart., 45 (2000), 497-504. [3] R. Bˇelohl ́avek, Fuzzy closure operator, J. Math. Anal. Appl. 262 (2001), 473-486. [4] R. Bˇelohl ́avek, Lattices of fixed points of Galois connections, Math. Logic Quart. 47 (2001), 111-116. [5] L. Biacino and G.Gerla, Closure systems and L-subalgebras, Inf. Sci. 33 (1984), 181-195. · Zbl 0562.06004 [6] L. Biacino and G.Gerla, An extension principle for closure operators, J. Math. Anal. Appl. 198 (1996), 1-24. · Zbl 0855.54007 [7] G.Gerla, Graded consequence relations and fuzzy closure operators, J. Appl. Non-classical Logics 6 (1996), 369-379. · Zbl 0872.03012 [8] Jinming Fang and Yueli Yue, L-fuzzy closure systems, Fuzzy Sets and Systems 161 (2010), 1242-1252. · Zbl 1195.54015 [9] G. Georgescu and A. Popescue, Non-commutative Galois connections, Soft Computing 7 (2003), 458-467. · Zbl 1024.03025 [10] G. Georgescu and A. Popescue, Non-dual fuzzy connections, Arch. Math. Log. 43 (2004), 1009-1039. · Zbl 1060.03042 [11] P. H ́ajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998. [12] U. H ̈ohle and E. P. Klement, Non-classical logic and their applications to fuzzy subsets , Kluwer Academic Publisher, Boston, 1995. [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. [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. · Zbl 1191.68658 [15] C.J. Mulvey, Quantales, Suppl. Rend. Cric. Mat. Palermo Ser.II 12,1986,99-104. [16] M. Ward and R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), 335-354. [17] E. Turunen, Mathematics Behind Fuzzy Logic, A Springer-Verlag Co., 1999. · Zbl 0940.03029
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