Bi-closure systems and bi-closure operators on generalized residuated lattices
Pages 2631 - 2643
Abstract
In this paper, we introduce 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.
References
[1]
R. Bëlohlövek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
[2]
R. Bëlohlövek, Fuzzy galois connection, Math Log Quart 45 (2000), 497–504.
[3]
R. Bëlohlövek, Fuzzy closure operator, J Math Anal Appl 262 (2001), 473–486.
[4]
R. Bëlohlövek, 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.
[6]
L. Biacino and G. Gerla, An extension principle for closure operators, J Math Anal Appl 198 (1996), 1–24.
[7]
G. Gerla, Graded consequence relations and fuzzy closure operators, J Appl Non-classical Logics 6 (1996), 369–379.
[8]
L. Guo, G.Q. Zhang and Q. Li, Fuzzy closure systems on Lordered sets, Math Log Quart 57(3) (2011), 281–291.
[9]
J. Fang and Y. Yue, L-fuzzy closure systems, Fuzzy Sets and Systems 161 (2010), 1242–1252.
[10]
G. Georgescu and A. Popescue, Non-commutative Galois connections, Soft Computing 7 (2003), 458–458.
[11]
G. Georgescu and A. Popescue, Non-dual fuzzy connections, Arch Math Log 43 (2004), 1009–1009.
[12]
P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
[13]
U. Höhle and E.P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publisher, Boston, 1995.
[14]
U. Höhle 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.
[15]
H. Lai and D. Zhang, Concept lattices of fuzzy contexts: Formal concept analysis vs. rough set theory. Int J Approx Reasoning 50 (2009), 695–695.
[16]
J. Li, C. Mei and Y. Lv, Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge redution, Int J Approx Reasoning 54(1) (2013), 149–149.
[17]
C.J. Mulvey, Quantales, Suppl Rend Cric Mat Palermo Ser II 12 (1986), 99–99.
[18]
P.K. Singh, C.A. Kumar and J. Li, Knowledge representation using interval-valued fuzzy formal conceptlattices, Soft Computing 20(4) (2016), 1485–1485.
[19]
E. Turunen, Mathematics Behind Fuzzy Logic, A Springer Verlag Co., 1999.
[20]
M. Ward and R.P. Dilworth, Residuated lattices, Trans Amer Math Soc 45 (1939), 335–335.
[21]
J. Xie, M. Yang, J. Li and Z. Zheng, Rule acquisition and optimal scale selection in multi-scale formal decision contexts and applications to smart city, Future Generation Comp Syst 83 (2018), 564–564.
Index Terms
- Bi-closure systems and bi-closure operators on generalized residuated lattices
Index terms have been assigned to the content through auto-classification.
Recommendations
Generalized state operators on residuated lattices
We give a definition of a generalized state operator (g-state operator) $$\sigma $$ź on a residuated lattice X and a g-state residuated lattice $$(X,\sigma )$$(X,ź), by which the class of all g-state residuated lattices is proved to be a variety, and ...
Various operations and right completeness in generalized residuated lattices
In this paper, based on generalized residuated lattices as an extension of Zhang’s complete residuated lattices, there are two types of structures: bi-partially orders, right (left) joins, right (left) complete lattices and right (left) Alexandrov ...
The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey
Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)Closure systems (i.e. families of subsets of a set S containing S and closed by set intersection) or, equivalently, closure operators and full implicational systems appear in many fields in pure or applied mathematics and computer science. We present a ...
Comments
Information & Contributors
Information
Published In
© 2019 – IOS Press and the authors. All rights reserved.
Publisher
IOS Press
Netherlands
Publication History
Published: 01 January 2019
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 11 Aug 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in