##
**Homomorphisms of approximation spaces.**
*(English)*
Zbl 1243.68281

Summary: The notion of a homomorphism of approximation spaces is introduced. Some properties of such homomorphisms are investigated and some characterizations are given. Furthermore, the notion of an approximation subspace is introduced. Relations between approximation subspaces and homomorphisms are studied.

### MSC:

68T37 | Reasoning under uncertainty in the context of artificial intelligence |

PDF
BibTeX
XML
Cite

\textit{Z. Wang} et al., J. Appl. Math. 2012, Article ID 185357, 18 p. (2012; Zbl 1243.68281)

Full Text:
DOI

### References:

[1] | Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341-356, 1982. · Zbl 0501.68053 |

[2] | Z. Pawlak, Rough Sets-Theoretical Aspects of Reasoning about Data, Kluwer, Dordrecht, The Netherlands, 1991. · Zbl 0758.68054 |

[3] | L. Polkowski and A. Skowron, Eds., Rough Sets in Knowledge Discovery 1: Methodology and Applications, Studies in Fuzziness and Soft Computing, vol. 18, Physical, Heidelberg, Germany, 1998. · Zbl 0910.00028 |

[4] | L. Polkowski and A. Skowron, Eds., Rough Sets in Knowledge Discovery 2: Applications. Studies in Fuzziness and Soft Computing, vol. 19, Physical, Heidelberg, Germany, 1998. |

[5] | Z. Pawlak and A. Skowron, “Rudiments of rough sets,” Information Sciences, vol. 177, no. 1, pp. 3-27, 2007. · Zbl 1142.68549 |

[6] | Z. Pawlak and A. Skowron, “Rough sets: some extensions,” Information Sciences, vol. 177, no. 1, pp. 28-40, 2007. · Zbl 1142.68550 |

[7] | Z. Pawlak and A. Skowron, “Rough sets and Boolean reasoning,” Information Sciences, vol. 177, no. 1, pp. 41-73, 2007. · Zbl 1142.68551 |

[8] | Z. Pawlak, S. Wong, and W. Ziarko, “Rough sets: probabilistic versus deterministic approach,” International Journal of Man-Machine Studies, vol. 29, no. 1, pp. 81-95, 1988. · Zbl 0663.68094 |

[9] | N. Morsi and M. Yakout, “Axiomatics for fuzzy rough sets,” Fuzzy Sets and Systems, vol. 100, no. 1-3, pp. 327-342, 1998. · Zbl 0938.03085 |

[10] | J. Mi and W. Zhang, “An axiomatic characterization of a fuzzy generalization of rough sets,” Information Sciences, vol. 160, no. 1-4, pp. 235-249, 2004. · Zbl 1041.03038 |

[11] | Y. Wang, “Mining stock price using fuzzy rough set system,” Expert Systems with Applications, vol. 24, no. 1, pp. 13-23, 2003. |

[12] | Y. Y. Yao, “Probabilistic rough set approximations,” International Journal of Approximate Reasoning, vol. 49, no. 2, pp. 255-271, 2008. · Zbl 1191.68702 |

[13] | W. Ziarko, “Variable precision rough set model,” Journal of Computer and System Sciences, vol. 46, no. 1, pp. 39-59, 1993. · Zbl 0764.68162 |

[14] | J. Wang and J. Zhou, “Research of reduct features in the variable precision rough set model,” Neurocomputing, vol. 72, no. 10-12, pp. 2643-2648, 2009. |

[15] | D. Slezak and W. Ziarko, “Bayesian rough set model,” in Proceedings of the International Workshop on Foundation of Data Mining and Discovery (FDM ’02), pp. 131-135, 2002. |

[16] | Q. Wu and Z. Liu, “Real formal concept analysis based on grey-rough set theory,” Knowledge-Based Systems, vol. 22, no. 1, pp. 38-45, 2009. |

[17] | Y. Y. Yao, S. K. M. Wong, and P. Lingras, “A decision-theoretic rough set model,” in Methodologies for Intelligent Systems 5, pp. 17-24, North-Holland, New York, NY, USA, 1990. |

[18] | Y. Y. Yao and S. K. M. Wong, “A decision theoretic framework for approximating concepts,” International Journal of Man-Machine Studies, vol. 37, pp. 793-809, 1992. |

[19] | Y.Y. Yao, “Probabilistic approaches to rough sets,” Expert Systems, vol. 20, pp. 287-297, 2003. |

[20] | Y.Y. Yao, “Information granulation and approximation in a decision-theoretical model of rough sets,” in Rough-Neural Computing: Techniques for Computing with Words, S. K. Pal, L. Polkowski, and A. Skowron, Eds., pp. 491-518, Springer, Berlin, Germany, 2003. |

[21] | Y. Y. Yao and Y. Zhao, “Attribute reduction in decision-theoretic rough set models,” Information Sciences, vol. 178, no. 17, pp. 3356-3373, 2008. · Zbl 1156.68589 |

[22] | J. P. Herbert and J. T. Yao, “Criteria for choosing a rough set model,” Computers & Mathmatics with Applications, vol. 57, no. 6, pp. 908-918, 2009. · Zbl 1186.91066 |

[23] | P. Lingras, M. Chen, and D. Q. Miao, “Rough cluster quality index based on decision theory,” IEEE Transactions on Knowledge and Data Engineering, vol. 21, no. 7, pp. 1014-1026, 2009. |

[24] | Y. Y. Yao, “Three-way decisions with probabilistic rough sets,” Information Sciences, vol. 180, no. 3, pp. 341-353, 2010. · Zbl 05663908 |

[25] | Y. Y. Yao, “Two semantic issues in a probabilistic rough set model,” Fundamenta Informaticae, vol. 108, no. 3-4, pp. 249-265, 2011. · Zbl 1242.68344 |

[26] | H. X. Li and X. Z. Zhou, “Risk decision making based on decision-theoretic rough set: a three-way view decision model,” International Journal of Computational Intelligence, vol. 4, no. 1, pp. 1-11, 2011. |

[27] | D. Liu, T. Li, and D. Ruan, “Probabilistic model criteria with decision-theoretic rough sets,” Information Sciences, vol. 181, no. 17, pp. 3709-3722, 2011. · Zbl 06055634 |

[28] | Y. Y. Yao, “Generalized rough set models,” in Rough Sets in Knowledge Discovery, 1, vol. 18, pp. 286-318, Physical, Heidelberg, Germany, 1998. · Zbl 0946.68137 |

[29] | Y. Y. Yao, “Relational interpretations of neighborhood operators and rough set approximation operators,” Information Sciences, vol. 111, no. 1-4, pp. 239-259, 1998. · Zbl 0949.68144 |

[30] | Y. Y. Yao and T. Y. Lin, “Generalization of rough sets using modal logic,” Intelligent Automation and Soft Computing, vol. 2, no. 103-120, 1996. |

[31] | Y. Y. Yao, “Constructive and algebraic methods of the theory of rough sets,” Information Sciences, vol. 109, no. 1-4, pp. 21-47, 1998. · Zbl 0934.03071 |

[32] | Z. Pawlak, “Rough classification,” International Journal of Man-Machine Studies, vol. 20, pp. 469-483, 1984. · Zbl 0541.68077 |

[33] | Y. Y. Yao, “Two views of the theory of rough sets in finite universes,” International Journal of Approximate Reasoning, vol. 15, no. 4, pp. 291-317, 1996. · Zbl 0935.03063 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.