A lattice-valued information system is an important model in the field of artificial intelligence and the notion of homomorphisms between lattice-valued information systems is a kind of tools to study data compression in a lattice-valued information system. This paper investigates invariant characterizations of information structures in a lattice-valued information system under homomorphisms based on data compression. Information structures in a lattice-valued information system is first proposed by using set vectors. Then, dependence and independence between information structures in the same lattice-valued information system is characterized by the inclusion degree. Finally, a complex massive lattice-valued information system can be compressed into a relatively small-scale lattice-valued information system by means of homomorphisms and it is proved that some characterizations of information structures in a lattice-valued information system under homomorphisms based on data compression are invariant, that is, some of the same data structures are obtained.
DaveyB.A. and PriestleyH.A., Introduction to lattices and order, Cambridge University Press, Cambridge, 1990.
2.
BlaszczynskiJ., SlowinskiR. and SzelagM., Sequential covering rule induction algorithm for variable consistency rough set approaches, Information Sciences181(5) (2011), 987–1002.
3.
CornelisC., JensenR., MartinG.H. and SlezakD., Attribute selection with fuzzy decision reducts, Information Sciences180 (2010), 209–224.
4.
DuboisD. and PradeH., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems17 (1990), 191–209.
5.
Grzymala-BusseJ.W., Algebraic properties of knowledge representation systems, Proc of the ACM SIGART International Symposium on Methodologies for Intelligent Systems, Knoxville, Tennessee, 1986, pp. 432–440.
6.
Grzymala-BusseJ.W. and SedelowW.A., On rough sets, and information system homomorphism, Bulletin of the Polish Academy of Technology Science36 (1988), 233–239.
7.
HuQ., PedryczW., YuD. and LangJ., Selecting discrete and continuous features based on neighborhood decision error minimization, IEEE Transactions on Systems, Man and Cybernetics (Part B)40 (2010), 137–150.
8.
JensenR. and ShenQ., Semantics-preserving dimensionality reduction: Rough and fuzzy rough based approaches, IEEE Transactions on Knowledge and Data Engineering16 (2004), 1457–1471.
9.
JensenR. and ShenQ., New approaches to fuzzy-rough feature selection, IEEE Transactions on Fuzzy Systems17 (2009), 824–838.
10.
KryszkiewiczM., Rules in incomplete information systems, Information Sciences113 (1999), 271–292.
11.
LinT.Y., Granular computing on binary relations I: Data mining and neighborhood systemsąś, In: Rough Sets In Knowledge Discovery,
SkowronA. and PolkowskiL. (eds.), Physica-Verlag, 1998, pp. 107–121.
12.
LinT.Y., Granular computing on binary relations II: Rough set representations and belief functions, In: Rough Sets In Knowledge Discovery,
SkowronA. and PolkowskiL. (eds), Physica-Verlag, 1998, pp. 121–140.
13.
LinT.Y., Granular computing: Practices, theories, and future directions, in Encyclopedia of Complexity and Systems Science,
MeyersR.A., Ed., Berlin, Heidelberg: Springer, 2009, pp. 4339–4355.
14.
LinT.Y., Granular computing I: The concept of granulation and its formal model, Int J Granular Comput, Rough Sets Intell Syst1(1) (2009), 21–42.
15.
LinT.Y., Deductive data mining using granular computing, Encyclopedia of Database Systems (2009), 772–778.
16.
LiZ. and CuiR., Similarity of fuzzy relations based on fuzzy topologies induced by fuzzy rough approximation operators, Information Sciences305 (2015), 219–233.
17.
LiZ. and CuiR., T-similarity of fuzzy relations and related algebraic structures, Fuzzy Sets and Systems275 (2015), 130–143.
18.
LiangJ., DangC., ChinK. and
RichardC.M.am, A new method for measuring uncertainty and fuzziness in rough set theory, International Journal of General Systems31 (2002), 331–342.
19.
LewelerD.A. and HirschbergD.S., Data compression, ACM Computing Surveys19(3) (1987), 261–296.
20.
LiZ., LiuY., LiQ. and QinB., Relationships between knowledge bases and related results, Knowledge and Information Systems49 (2016), 171–195.
21.
LiZ., LiQ., ZhangR. and XieN., Knowledge structures in a knowledge base, Expert Systems33(6) (2016), 581–591.
22.
LiD. and MaY., Invariant characters of information systems under some homomorphisms, Information Sciences129 (2000), 211–220.
23.
LiangJ. and QianY., Information granules and entropy theory in information systems, Science in China (Series F)51 (2008), 1427–1444.
24.
MajiP., Rough hypercuboid approach for feature selection in approximation spaces, IEEE Transactions on Knowledge and Data Engineering99 (2012), 1–14.
25.
PawlakZ., Rough sets, International Journal of Computer and Information Science11 (1982), 341–356.
26.
PawlakZ., Rough sets: Theoretical aspects of reasoning about data, Kluwer Academic Publishers, Dordrecht, 1991.
27.
PedryczW. and VukovichG., Granular worlds: Representation and communication problems, International Journal of Intelligent Systems15 (2000), 1015–1026.
28.
QianY., LiangJ. and DangC., Knowledge structure, knowledge granulation and knowledge distance in a knowledge base, International Journal of Approximate Reasoning50 (2009), 174–188.
29.
QianY., ZhangH., LiF., HuQ. and LiangJ., Set-based granular computing: A lattice model, International Journal of Approximate Reasoning55 (2014), 834–852.
30.
StorerJ.A., Data Compression: Methods and Theory, Computer Science Press, 1988.
31.
SwiniarskiR.W. and SkowronA., Rough set methods in feature selection and recognition, Pattern Recognition Letters24 (2003), 833–849.
32.
SlowinskiR. and VanderpootenD., A generalized definition of rough approximations based on similarity, IEEE Transactions on Knowledge and Data Engineering12 (2000), 331–336.
33.
WangC., QiY., ShaoM., HuQ., ChenD., QianY. and LinY., A fitting model for feature selection with fuzzy rough sets, IEEE Transaction on Fuzzy Systems25(4) (2017), 741–753.
34.
WangC., ShaoM., HeQ., QianY. and QiY., Feature subset selection based on fuzzy neighborhood rough sets, Knowledge-Based Systems111 (2016), 173–179.
35.
WangC., WuC., ChenD. and DuW., Some properties of relation information systems under homomorphisms, Applied Mathematics Letters21 (2008), 940–945.
36.
WangC., WuC., ChenD., HuQ. and WuC., Communicating between information systems, Information Sciences178 (2008), 3228–3239.
37.
WangC., ChenD., WuC. and HuQ., Data compression with homomorphism in covering information systems, International Journal of Approximate Reasoning52 (2011), 519–525.
38.
WangX., TsangE.C.C., ZhaoS., ChenD. and YeungD., Learning fuzzy rules from fuzzy samples based on rough set technique, Information Sciences177 (2007), 4493–4514.
39.
XuW., LiuS. and ZhangW., Lattice-valued information systems based on dominance relation, International Journal of Machine Learning and Cybernetics4 (2013), 245–257.
40.
YaoY.Y., Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences111 (1998), 239–259.
41.
YaoY.Y., Information granulation and rough set approximation, International Journal of Intelligent Systems16 (2001), 87–104.
42.
YaoY.Y., A partition model of granular computing, LNCS Transactions on Rough Sets I (2004), 232–253.
43.
ZadehL.A., Fuzzy logic equals computing with words, IEEE Transactions on Fuzzy Systems4 (1996), 103–111.
44.
ZadehL.A., Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems90 (1997), 111–127.
45.
ZadehL.A., Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information / intelligent systems, Soft Computing2 (1998), 23–25.
46.
ZadehL.A., A new direction in AI-Toward a computational theory of perceptions, Ai Magazine22(1) (2001), 73–84.
47.
ZhangX., Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras, Journal of Intelligent & Fuzzy Systems33 (2017), 1767–1774.
48.
ZhangX., DaiJ. and YuY., On the union and intersection operations of rough sets based on various approximation spaces, Information Sciences292 (2015), 214–229.
49.
ZhangX., MiaoD., LiuC. and LeM., Constructive methods of rough approximation operators and multigranulation rough sets, Knowledge-Based Systems91 (2016), 114–125.
50.
ZhangW. and QiuG., Uncertain decision making based on rough sets, Tsinghua University Publishers, Beijing, 2005.
