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**A new measure of uncertainty based on knowledge granulation for rough sets.**
*(English)*
Zbl 1162.68666

Summary: In rough set theory, accuracy and roughness are used to characterize uncertainty of a set and approximation accuracy is employed to depict accuracy of a rough classification. Although these measures are effective, they have some limitations when the lower/upper approximation of a set under one knowledge is equal to that under another knowledge. To overcome these limitations, we address in this paper the issues of uncertainty of a set in an information system and approximation accuracy of a rough classification in a decision table. An axiomatic definition of knowledge granulation for an information system is given, under which these three measures are modified. Theoretical studies and experimental results show that the modified measures are effective and suitable for evaluating the roughness and accuracy of a set in an information system and the approximation accuracy of a rough classification in a decision table, respectively, and have a much simpler and more comprehensive form than the existing ones.

### MSC:

68T30 | Knowledge representation |

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

### Keywords:

rough set theory; knowledge granulation; roughness measure; accuracy measure; approximation accuracy### Software:

UCI-ml
Full Text:
DOI

### References:

[1] | Bazan, J.; Peters, J. F.; Skowron, A.; Nguyen, H. S.; Szczuka, M., Rough set approach to pattern extraction from classifiers, Electronic Notes in Theoretical Computer Science, 82, 4, 1-10 (2003) |

[2] | Beaubouef, T.; Petry, F. E.; Arora, G., Information-theoretic measures of uncertainty for rough sets and rough relational databases, Information Sciences, 109, 185-195 (1998) |

[4] | Liang, J. Y.; Qu, K. S., Information measures of roughness of knowledge and rough sets for information systems, Journal of Systems Science and Systems Engineering, 10, 1, 95-103 (2002) |

[5] | Liang, J. Y.; Li, D. Y., Uncertainty and Knowledge Acquisition in Information Systems (2005), Science Press: Science Press Beijing |

[6] | Liang, J. Y.; Chin, K. S.; Dang, C. Y.; YAM, C. M., A new method for measuring uncertainty and fuzziness in rough set theory, International Journal of General Systems, 31, 4, 331-342 (2002) · Zbl 1010.94004 |

[7] | Liang, J. Y.; Shi, Z. Z., The information entropy rough entropy knowledge granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 1, 37-46 (2004) · Zbl 1074.68072 |

[8] | Liang, J. Y.; Shi, Z. Z.; Li, D. Y., Information entropy, rough entropy and knowledge granulation in incomplete information systems, International Journal of General Systems, 35, 6, 641-654 (2006) · Zbl 1115.68130 |

[9] | Lin, T. Y., Granular computing on binary relations I: Data mining and neighborhood systems, II: Rough sets representations and belief functions, (Polkowski, L.; Skowron, A., Rough Sets in Knowledge Discovery 1 (1998), Physica-Verlag: Physica-Verlag Heidelberg), 107-140 · Zbl 0927.68090 |

[10] | Pal, S. K.; Pedrycz, W.; Skowron, A.; Swiniarski, R., Presenting the special issue on rough-neuro computing, Neurocomputing, 36, 1-3 (2001) |

[11] | Pawlak, Z., Rough sets, International Journal of Computer and Information Science, 11, 341-356 (1982) · Zbl 0501.68053 |

[12] | Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning about Data (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0758.68054 |

[13] | Pawlak, Z., Some remarks on conflict analysis, Europe Journal of Operational Research, 166, 3, 649-654 (2005) · Zbl 1097.91010 |

[14] | Pawlak, Z.; Skowron, A., Rudiments of rough sets, Information Sciences, 177, 3-27 (2007) · Zbl 1142.68549 |

[15] | Pawlak, Z.; Skowron, A., Rough sets: some extensions, Information Sciences, 177, 28-40 (2007) · Zbl 1142.68550 |

[16] | Pawlak, Z.; Skowron, A., Rough sets and boolean reasoning, Information Sciences, 177, 41-73 (2007) · Zbl 1142.68551 |

[17] | Pawlak, Z.; Wong, S. K.M.; Ziarko, W., Rough sets: probabilistic versus deterministic approach, International Journal of Man-Machine Studies, 29, 81-95 (1988) · Zbl 0663.68094 |

[19] | Qian, Y. H.; Liang, J. Y., Combination entropy and combination granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based systems, 16, 2, 179-193 (2008) · Zbl 1154.68520 |

[20] | Qian, Y. H.; Liang, J. Y.; Li, D. Y.; Zhang, H. Y.; Dang, C. Y., Measures for evaluating the decision performance of a decision table in rough set theory, Information Sciences, 178, 1, 181-202 (2008) · Zbl 1128.68102 |

[21] | Shannon, C. E., The mathematical theory of communication, The Bell System Technical Journal, 27, 3 and 4, 373-423 (1948), (see also 623-656) · Zbl 1154.94303 |

[22] | Shi, Z. Z., Knowledge Discovery (2002), Tsinghua University Press: Tsinghua University Press Beijing |

[23] | Wierman, M. J., Measuring uncertainty in rough set theory, International Journal of General Systems, 28, 283-297 (1999) · Zbl 0938.93034 |

[24] | Xu, B. W.; Zhou, Y. M.; Lu, H. M., An improved accuracy measure for rough sets, Journal of Computer and System Sciences, 71, 163-173 (2005) · Zbl 1076.68078 |

[26] | Zadeh, L. A., Fuzzy sets and information granularity, (Gupta, M.; Ragade, R.; Yager, R., Advances in Fuzzy Set Theory and Application (1979), North-Holland: North-Holland Amsterdam), 3-18 · Zbl 0377.04002 |

[27] | Zadeh, L. A., Fuzzy logic=computing with words, IEEE Transactions on Fuzzy Systems, 4, 1, 103-111 (1996) |

[28] | Zadeh, L. A., Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets and Systems, 90, 111-127 (1997) · Zbl 0988.03040 |

[29] | Zhang, L.; Zhang, B., Fuzzy reasoning model under quotient space structure, Information Sciences, 173, 4, 353-364 (2005) · Zbl 1088.68170 |

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