This paper focuses on fuzzy relational structures. In order to collect the knowledge that has been acquired with regard to fuzzy relational structures, the concept of collective relations is proposed and characterizations of collective relations are investigated. A method on computing the largest collective relation is further given. Moreover, based on substructures of fuzzy relational structures, a decomposition theorem of collective relations is obtained and weak collective relations and strong collective relations are put forward. Finally, the fuzzy rough set analysis of fuzzy relational structures is discussed.
BĕlohlávekR., Fuzzy Relational Systems: Foundations and Principles. Kluwer, New York. 2002.
2.
BĕlohlávekR., VychodilV., Fuzzy Equational Logic, Studies in Fuzziness and Soft Computing. Springer, Berlin, Heidelberg. 2005.
3.
BoixaderD., JacasJ. and RecasensJ., Upper and lower approximations of fuzzy sets, International Journal of General Systems29 (1999), 555–568.
4.
CírićM., IgnjatovićJ., DamljanovićN. and BašićM., Bisimulations for fuzzy automata, Fuzzy Sets and Systems186 (2012), 100–139.
5.
CírićM., StamenkovićA., IgnjatovićJ. and PetkovićT., Fuzzy relation equations and reduction of fuzzy automata, Journal of Computer and System Sciences76 (2010), 609–633.
6.
DuY.B. and ZhuP., Fuzzy approximations of fuzzy relational structures, International Journal of Approximate Reasoning, submitted for publication.
7.
DuboisD. and PradeH., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems17 (1990), 191–209.
8.
D’eerL., VerbiestN., CornelisC. and GodoL., A comprehensive study of implicator-conjunctor-based and noise-tolerant fuzzy rough sets: Definitions, properties and robustness analysis, Fuzzy Sets and Systems275 (2015), 1–38.
9.
FanT.F., Rough set analysis of relational structures, Information Sciences221 (2013), 230–244.
10.
HuB.Q. and HuangZ.H., (⊥, ⊤)-Generalized Fuzzy Rough Sets Based on Fuzzy Composition Operations, CaoB.-Y., ZhangC.-Y., LiT.-F., (Eds.), Fuzzy Info and Engineering, ASC 54, Springer-VerlagBerlin, Heidelberg, 2009, pp. 647–659.
11.
KlirG.J. and YuanB., Fuzzy Sets and Fuzzy, Logic Theory and Application, Prentice-Hall.Englewood Cliffs, NJ, 1995.
12.
LiauC. and LinT., Reasoning about relational granulation in modal logics, in Proceedings of the First IEEE International Conference on Granular Computing, IEEE Press, 2005, pp. 534–538.
13.
MiJ.S., LeungY., ZhaoH.Y. and FengT., Generalized fuzzy rough sets determined by a triangular norm, Information Sciences178 (2008), 3203–3213.
14.
ScottJ., Social Network Analysis: A Handbook, second ed., SAGE Publications, 2000.
15.
WuW.Z., MiJ.S. and ZhangW.X., Generalized fuzzy rough sets, Information Sciences151 (2003), 263–282.
16.
WuW.Z., LeungY. and MiJ.S., On characterizations of (ℐℑ)-fuzzy rough approximation operators, Fuzzy Sets and Systems154(1) (2005), 76–102.
17.
ZhangX., MeiC.L., ChenD.G. and LiJ.H., Feature selection in mixed data: A method using a novel fuzzy rough set-based information entropy, Pattern Recognition56 (2016), 1–15.
