## Homomorphisms between fuzzy information systems.(English)Zbl 1179.94090

Summary: The information system is one of the most important mathematical models in the field of artificial intelligence, and the concept of mapping is a useful tool for studying the communication between two information systems. In this work, the concepts of fuzzy relation mapping and inverse fuzzy relation mapping are first introduced and their properties are studied. Then, the notions of homomorphisms of information systems based on fuzzy relations are proposed, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the condition of homomorphism.

### MSC:

 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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### References:

 [1] Pedrycz, W.; Vukovich, G., Granular worlds: representation and communication problems, International journal of intelligent systems, 15, 1015-1026, (2000) · Zbl 0960.68146 [2] J.W. Graymala-Busse, Algebraic properties of knowledge representation systems, in : Proceedings of the ACM SIGART International Symposium on Methodologies for Intelligent Systems. Knoxville, 1986, pp. 432-440 [3] Graymala-Busse, J.W.; Sedelow, W.A., On rough sets and information system homomorphism, Bulletin of the Polish Academy of science, technical science, 36, 233-239, (1988) · Zbl 0691.68093 [4] Li, D.Y.; Ma, Y.C., Invariant characters of information systems under some homomorphisms, Information sciences, 129, 211-220, (2000) · Zbl 0980.68110 [5] T.Y. Lin, Neighborhood systems and relational database, in: Proceedings of 1988 ACM Sixteenth Annual ComputerScience Conference, 1988, February, pp. 23-25 [6] P. Pagliani, Transforming information systems, in: Proceedings of the 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, Canada, 2005, pp. 660-670 · Zbl 1134.68551 [7] D. Slezak, Searching for dynamic reducts in inconsistent decision tables, in: Proceedings of IPMU’ 98, France, 1998, l.2: pp. 1362-1369 [8] Wang, C.Z.; Wu, C.X.; Chen, D.G., A systematic study on attribute reduction with rough sets based on general binary relations, Information sciences, 178, 2237-2261, (2008) · Zbl 1136.68051 [9] Wang, X.; Tsang, E.C.C.; Zhao, S.Y.; Chen, D.G.; Yeung, D.S., Learning fuzzy rules from fuzzy samples based on rough set technique, Information sciences, 177, 4493-4514, (2007) · Zbl 1129.68069 [10] Wang, C.; Wu, C.; Chen, D.; Du, W., Some properties of relation information systems under homomorphisms, Applied mathematics letters, 21, 940-945, (2008) · Zbl 1152.68635 [11] Wang, C.; Wu, C.; Chen, D.; Hu, Q.; Wu, C., Communication between information systems, Information sciences, 178, 3228-3239, (2008) · Zbl 1154.68558 [12] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International journal of general systems, 17, 2-3, 191-209, (1990) · Zbl 0715.04006 [13] Wu, Wei-Zhi; Mi, Ju-Sheng; Zhang, Wen-Xiu, Generalized fuzzy rough sets, Information sciences, 151, 263-282, (2003) · Zbl 1019.03037 [14] Yeung, D.S.; Chen, D.G.; Tsang, E.; Lee, J.; Wang, X.Z., On the generalization of fuzzy rough sets, IEEE transactions on fuzzy systems, 13, 343-361, (2005) [15] Zadeh, L.A., The concept of a linguistic variable and its applications in approximate reasoning, Information sciences, 8, 199-251, (1975) · Zbl 0397.68071
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