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Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure. (English) Zbl 1360.68856
Summary: This paper investigates decision-theoretic rough set (DTRS) approach in the frameworks of fuzzy and interval-valued fuzzy (IVF) probabilistic approximation spaces, respectively. It takes fuzzy probability and IVF probability into consideration. Bayesian decision procedure is a basis of DTRS approach. By integrating fuzzy probability measure and IVF probability measure into Bayesian decision procedure, there come fuzzy decision-theoretic rough set (FDTRS) approach and interval-valued fuzzy decision-theoretic rough set (IVF-DTRS) approach. The new approaches have the ability to directly deal with real-valued and interval-valued data. This makes FDTRS and IVF-DTRS more applicable than DTRS. Two methods are presented to compare intervals while constructing the IVF-DTRS approach: one is compatible with DTRS and FDTRS approaches; the other is a total order based on which the decision procedure is much easier to operate. Cases of two different universes of discourse for FDTRS and IVF-DTRS are also taken into account.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
60A86 Fuzzy probability
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[1] van den Berg, J.; Kaymak, U.; Almeida, R. J., Conditional density estimation using probabilistic fuzzy systems, IEEE Trans. Fuzzy Syst., 21, 869-882, (2013)
[2] Burillo, P.; Bustince, H., Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets Syst., 78, 305-316, (1996) · Zbl 0872.94061
[3] Dembczyński, K.; Greco, S.; Kotłowski, W.; Słowiński, R., Statistical model for rough set approach to multicriteria classification, Lecture Notes Comput. Sci., 4702, 164-175, (2007)
[4] Deng, X.; Yao, Y., Decision-theoretic three-way approximations of fuzzy sets, Inform. Sci., 279, 702-715, (2014) · Zbl 1354.03073
[5] Duda, R. O.; Hart, P. E., Pattern classification and scene analysis, (1973), Wiely New York · Zbl 0277.68056
[6] Fodor, J. C.; Roubens, M., Structure of transitive valued binary relations, Math. Social Sci., 30, 71-94, (1995) · Zbl 0886.90004
[7] Hu, B. Q.; Wang, S., A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers, J. Indus. Manage. Optim., 2, 351-371, (2006) · Zbl 1115.65050
[8] Hu, B. Q., Three-way decisions space and three-way decisions, Inform. Sci., 281, 21-52, (2014) · Zbl 1355.68256
[9] Jia, X.; Liao, W.; Tang, Z.; Shang, L., Minimum cost attribute reduction in decision-theoretic rough set models, Inform. Sci., 219, 151-167, (2013) · Zbl 1293.91049
[10] Jia, X.; Tang, Z.; Liao, W.; Shang, L., On an optimization representation of decision-theoretic rough set model, Int. J. Approx. Reason., 55, 156-166, (2014) · Zbl 1316.68179
[11] Jia, X.; Zheng, K.; Li, W.; Liu, T.; Shang, L., Three-way decisions solution to filter spam email: an empirical study, Lecture Notes Comput. Sci., 7413, 287-296, (2012)
[12] Klir, G. J.; Yuan, B., Fuzzy sets and fuzzy logic, (1995), Prentice Hall New Jersey · Zbl 0915.03001
[13] Li, W.; Miao, D.; Wang, W.; Zhang, N., Hierarchical rough decision theoretic framework for text classification, (2010 9th IEEE International Conference on Cognitive Informatics (ICCI), (2010), IEEE), 484-489
[14] Li, T. J.; Yang, X. P., An axiomatic characterization of probabilistic rough sets, Int. J. Approx. Reason., 55, 130-141, (2014) · Zbl 1316.68182
[15] Li, F.; Ye, M.; Chen, X., An extension to rough c-means clustering based on decision-theoretic rough sets model, Int. J. Approx. Reason., 55, 116-129, (2014) · Zbl 1316.68115
[16] Li, Y.; Zhang, C.; Swan, J. R., An information filtering model on the web and its application in jobagent, Knowl.-Based Syst., 13, 285-296, (2000)
[17] Li, H.; Zhou, X., Risk decision making based on decision-theoretic rough set: a three-way view decision model, Int. J. Comput. Intell. Syst., 4, 1-11, (2011)
[18] Li, H.; Zhou, X.; Zhao, J.; Huang, B., Cost-sensitive classification based on decision-theoretic rough set model, Lecture Notes Comput. Sci., 7414, 379-388, (2012)
[19] Liang, D.; Liu, D., Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets, Inform. Sci., 276, 186-203, (2014)
[20] Liang, D.; Liu, D.; Pedrycz, W.; Hu, P., Triangular fuzzy decision-theoretic rough sets, Int. J. Approx. Reason., 54, 1087-1106, (2013) · Zbl 1316.68183
[21] Lingras, P.; Chen, M.; Miao, D., Rough multi-category decision theoretic framework, Lecture Notes Comput. Sci., 5009, 676-683, (2008)
[22] Lingras, P.; Chen, M.; Miao, D., Rough cluster quality index based on decision theory, IEEE Trans. Knowl. Data Eng., 21, 1014-1026, (2009)
[23] Liu, D.; Li, T.; Liang, D., Three-way government decision analysis with decision-theoretic rough sets, Int. J. Uncert. Fuzziness Knowl. -Based Syst., 20, 119-132, (2012)
[24] Liu, D.; Li, T.; Ruan, D., Probabilistic model criteria with decision-theoretic rough sets, Inform. Sci., 181, 3709-3722, (2011)
[25] Liu, D.; Yao, Y. Y.; Li, T., Three-way investment decisions with decision-theoretic rough sets, Int. J. Comput. Intell. Syst., 4, 66-74, (2011)
[26] Ma, W.; Sun, B., Probabilistic rough set over two universes and rough entropy, Int. J. Approx. Reason., 53, 608-619, (2012) · Zbl 1246.68234
[27] Moore, R. E., Interval analysis, (1966), Prentice-Hall Englewood Cliffs · Zbl 0176.13301
[28] Ovchinnikov, S., Numerical representation of transitive fuzzy relations, Fuzzy Sets Syst., 126, 225-232, (2002) · Zbl 0996.03510
[29] Pawlak, Z., Rough set, Int. J. Comput. Inform. Sci., 11, 341-356, (1982) · Zbl 0501.68053
[30] Pawlak, Z., Rough set: theoretical aspects of reasoning about data, (1991), Kluwer Academic Publisher Boston · Zbl 0758.68054
[31] Pedrycz, W., Granular computing: analysis and design of intelligent systems, (2013), CRC Press/Francis Taylor Boca Raton
[32] Qian, Y.; Zhang, H.; Sang, Y.; Liang, J., Multigranulation decision-theoretic rough sets, Int. J. Approx. Reason., 55, 225-237, (2014) · Zbl 1316.68190
[33] Śle¸zak, D.; Ziarko, W., The investigation of the Bayesian rough set model, Int. J. Approx. Reason., 40, 81-91, (2005) · Zbl 1099.68089
[34] Sun, B.; Ma, W.; Zhao, H., Decision-theoretic rough fuzzy set model and application, Inform. Sci., 283, 180-196, (2014) · Zbl 1355.68260
[35] Turksen, I. B., Interval valued fuzzy sets based on normal forms, Fuzzy Sets Syst., 20, 191-210, (1986) · Zbl 0618.94020
[36] Valverde, L.; Ovchinnikov, S., Representations of T-similarity relations, Fuzzy Sets Syst., 159, 2211-2220, (2008) · Zbl 1175.03034
[37] Xu, Z. S.; Da, Q. L., The uncertain OWA operator, Int. J. Intell. Syst., 17, 569-575, (2002) · Zbl 1016.68025
[38] Yang, H. L.; Liao, X.; Wang, S.; Wang, J., Fuzzy probabilistic rough set model on two universes and its applications, Int. J. Approx. Reason., 54, 1410-1420, (2013) · Zbl 1316.03035
[39] Yao, Y. Y., Decision-theoretic rough set models, Lecture Notes Comput. Sci., 4481, 1-12, (2007)
[40] Yao, Y. Y., Probabilistic rough set approximations, Int. J. Approx. Reason., 49, 255-271, (2008) · Zbl 1191.68702
[41] Yao, Y. Y., Three-way decision: an interpretation of rules in rough set theory, Lecture Notes Comput. Sci., 5589, 642-649, (2009)
[42] Yao, Y. Y., Three-way decisions with probabilistic rough sets, Inform. Sci., 180, 341-353, (2010)
[43] Yao, Y. Y., The superiority of three-way decisions in probabilistic rough set models, Inform. Sci., 181, 1080-1096, (2011) · Zbl 1211.68442
[44] Yao, J.; Herbert, J. P., Web-based support systems with rough set analysis, Lecture Notes Comput. Sci., 4585, 360-370, (2007)
[45] Yao, Y. Y.; Wong, S. K.W.; Lingras, P., A decision-theoretic rough set model, (Ras, Z. W.; Zemankova, M.; Emrich, M. L., Methodologies for Intelligent System, (1990), North-Holland New York), 17-24
[46] Yao, Y. Y.; Wong, S. K.W., A decision theoretic framework for approximating concepts, Int. J. Man-Machine Stud., 37, 793-809, (1992)
[47] Yao, Y. Y.; Zhao, Y., Attribute reduction in decision-theoretic rough set models, Inform. Sci., 178, 3356-3373, (2008) · Zbl 1156.68589
[48] Yao, Y. Y.; Zhou, B., Naive Bayesian rough sets, Lecture Notes Comput. Sci., 6401, 719-726, (2010)
[49] Yu, H.; Liu, Z.; Wang, G., Automatically determining the number of clusters using decision-theoretic rough set, Lecture Notes Comput. Sci., 6954, 504-513, (2011)
[50] Zadeh, L. A., Fuzzy sets, Inform. Control, 8, 338-358, (1965) · Zbl 0139.24606
[51] Zadeh, L. A., Probability measures of fuzzy events, J. Math. Anal. Appl., 23, 421-427, (1968) · Zbl 0174.49002
[52] Zhao, Y.; Wong, S. K.M.; Yao, Y. Y., A note on attribute reduction in the decision-theoretic rough set model, Lecture Notes Comput. Sci., 6499, 260-275, (2011) · Zbl 1316.68202
[53] Zhou, B.; Yao, Y. Y.; Luo, J., A three-way decision approach to email spam filtering, Lecture Notes Comput. Sci., 6085, 28-39, (2010)
[54] Zhou, B., Multi-class decision-theoretic rough sets, Int. J. Approx. Reason., 55, 211-224, (2014) · Zbl 1316.68203
[55] Ziarko, W., Variable precision rough set model, J. Comput. Syst. Sci., 46, 39-59, (1993) · Zbl 0764.68162
[56] Ziarko, W., Probabilistic approach to rough sets, Int. J. Approx. Reason., 49, 272-284, (2008) · Zbl 1191.68705
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