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Interval ordered information systems. (English) Zbl 1165.68513
Summary: Interval information systems are generalized models of single-valued information systems. By introducing a dominance relation to interval information systems, we propose a ranking approach for all objects based on dominance classes and establish a dominance-based rough set approach, which is mainly based on substitution of the indiscernibility relation by the dominance relation. Furthermore, we discuss interval ordered decision tables and dominance rules. To simplify knowledge representation and extract much simpler dominance rules, we propose attribute reductions of interval ordered information systems and decision tables that eliminate only the information that are not essential from the viewpoint of the ordering of objects or dominance rules. The approaches show how to simplify an interval ordered information system and find dominance rules directly from an interval ordered decision table. These results will be helpful for decision-making analysis in interval information systems.

68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence
03E72 Theory of fuzzy sets, etc.
Full Text: DOI
[1] Pawlak, Z., ()
[2] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Information sciences, 177, 3-27, (2007) · Zbl 1142.68549
[3] Dubois, D.; Prade, H., Rough fuzzy sets and fuuzy rough sets, International journal of general systems, 17, 191-209, (1990) · Zbl 0715.04006
[4] Düntsch, I.; Gediga, G., Uncertainty measures of rough set prediction, Artificial intelligence, 106, 109-137, (1998) · Zbl 0909.68040
[5] Gediga, G.; Düntsch, I., Rough approximation quality revisited, Artificial intelligence, 132, 219-234, (2001) · Zbl 0983.68194
[6] Jensen, R.; Shen, Q., Fuzzy-rough sets assisted attribute selection, IEEE transactions on fuzzy systems, 15, 1, 73-89, (2007)
[7] Liang, J.Y.; Dang, C.Y.; Chin, K.S.; Yam Richard, 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
[8] 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 science, 178, 181-202, (2008) · Zbl 1128.68102
[9] Xu, Z.B.; Liang, J.Y.; Dang, C.Y.; Chin, K.S., Inclusion degree: A perspective on measures for rough set data analysis, Informatin sciences, 141, 227-236, (2002) · Zbl 1008.68134
[10] Yao, Y.Y., Information granulation and rough set approximation, International journal of intelligent systems, 16, 87-104, (2001) · Zbl 0969.68079
[11] Guan, J.W.; Bell, D.A., Rough computational methods for information systems, Artificial intelligence, 105, 77-103, (1998) · Zbl 0909.68047
[12] Jeon, G.; Kim, D.; Jeong, J., Rough sets attributes reduction based expert system in interlaced video sequences, IEEE transactions on consumer electronics, 52, 4, 1348-1355, (2006)
[13] Kryszkiewicz, M., Rough set approach to incomplete information systems, Information sciences, 112, 39-49, (1998) · Zbl 0951.68548
[14] Leung, Y.; Wu, W.Z.; Zhang, W.X., Knowledge acquisition in incomplete information systems: A rough set approach, European journal operational research, 168, 164-180, (2006) · Zbl 1136.68528
[15] Liang, J.Y.; Li, D.Y., Uncertainty and knowledge acquisition in information systems, (2005), Science Press Beijing, China
[16] Liang, J.Y.; Qian, Y.H., Axiomatic approach of knowledge granulation in information systems, Lecture notes in artificial intelligence, 4304, 1074-1078, (2006)
[17] Qian, Y.H.; Liang, J.Y.; Dang, C.Y., Converse approximation and rule extraction from decision tables in rough set theory, Computers and mathmatics with applications, 55, 1754-1765, (2008) · Zbl 1147.68736
[18] Greco, S.; Matarazzo, B.; Slowinski, R., A new rough set approach to multicriteria and multiattribute classification, Lecture notes in artificial intelligence, 1424, 60-67, (1998)
[19] Greco, S.; Matarazzo, B.; Slowinski, R., Rough sets theory for multicriteria decision analysis, European journal of operational research, 129, 1-47, (2001) · Zbl 1008.91016
[20] Greco, S.; Matarazzo, B.; Slowinski, R., Rough sets methodology for sorting problems in presence of multiple attributes and criteria, European journal of operational research, 138, 247-259, (2002) · Zbl 1008.90509
[21] Greco, S.; Matarazzo, B.; Slowinski, R.; Stefanowski, J., An algorithm for induction of decision rules consistent with the dominance pronciple, Lecture notes in articial intelligence, 2005, 304-313, (2001) · Zbl 1014.68545
[22] Dembczynski, K.; Pindur, R.; Susmaga, R., Generation of exhaustive set of rules within dominance-based rough set approach, Electronic notes in theoretical computer science, 82, 4, (2003) · Zbl 1270.68313
[23] Dembczynski, K.; Pindur, R.; Susmaga, R., Dominance-based rough set classifier without induction of decision rules, Electronic notes in theoretical computer science, 82, 4, (2003) · Zbl 1270.68312
[24] Sai, Y.; Yao, Y.Y.; Zhong, N., Data analysis and mining in ordered information tables, (), 497-504
[25] Shao, M.W.; Zhang, W.X., Dominance relation and rules in an incomplete ordered information system, International journal of intelligent systems, 20, 13-27, (2005) · Zbl 1089.68128
[26] Bryson, N.; Mobolurin, A., An action learning evaluation procedure for multiple criteria decision making problems, European journal of operational research, 96, 379-386, (1996) · Zbl 0917.90005
[27] Facchinetti, G.; Ricci, R.G.; Muzzioli, S., Note on ranking fuzzy triangular numbers, International journal of intelligent systems, 13, 613-622, (1998)
[28] Iyer, N.S., A family of dominance rules for multiattribute decision making under uncertainty, IEEE transactions on systems, man, and cybernetics part A, 33, 441-450, (2003)
[29] Xu, Z.S., Uncertain multiple attribute decision making: methods and applications, (2004), TsingHua Press Beijing, China
[30] Z.S. Xu, H.F. Gu, An approach to uncertain multi-attribute decision making with preference information on alternatives, in: Proceedings of the 9th Bellman Continuum International Workshop on Uncertain Systems and Soft Computing, Beijing, China, 2002, pp. 89-95
[31] Xu, Z.S.; Da, Q.L., The uncertain OWA operator, International journal of intelligent systems, 17, 569-575, (2002) · Zbl 1016.68025
[32] Zhang, W.X.; Qiu, G.F., Uncertain decision making based on rough sets, (2005), Science Press Beijing, China
[33] Zhao, Y.; Luo, F.; Wong, S.K.M.; Yao, Y.Y., A general defintion of an attribute reduct, Lecutre notes in arfiticial intelligence, 4481, 101-108, (2007)
[34] Slezak, D., Approximate reducts in decision tables, (), 1159-1164
[35] Slezak, D., Searching for dynamic reducts in inconsistent decision tables, (), 1362-1369
[36] Tyebjee, T.T.; Bruno, A.V., A model of venture capitalist investment activity, Management science, 30, 9, 1051-1066, (1984)
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