×

zbMATH — the first resource for mathematics

Generalized three-way decision models based on subset evaluation. (English) Zbl 1404.68168
Summary: The notion of three-way decisions was originally introduced based on the need to explain the three regions of probabilistic rough sets. In a three-way decision model, every object can be evaluated by a function and according to the evaluation value, the object can be arranged in one of the three regions (i.e., positive, negative, and boundary regions). In this study, we generalize Yao’s three-way decision models to a case where every subset in the universe can be evaluated by the evaluation function, and we then propose generalized three-way models. The properties and examples of these new models are presented, as well as extensions of these models. We also give some remarks regarding Hu’s three-way decision spaces. Three-way matroids are introduced based on Hu’s axiomatic approach and our generalized three-way models. Furthermore, three-way matroids are generalized to three fuzzy matroids as an application of our new model. Finally, we suggest future research related to our new models and three-way fuzzy matroids.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
05B35 Combinatorial aspects of matroids and geometric lattices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] K.T. Atanassov, Intuitionistic fuzzy sets, in: VII ITKR’s Session, Sofia, June 1983 (Deposited in the Central Science-Technical Library of Library of Bulgarian Academy of Science, 1697/84) (in Bulgarian).
[2] Atanassov, K. T., On intuitionistic fuzzy sets theory, (2012), Springer-Verlag Berlin · Zbl 0939.03057
[3] Cabitza, F.; Ciuccia, D.; Locoro, A., Exploiting collective knowledge with three-way decision theory: cases from the questionnaire-based research, Int. J. Approx. Reason., (2016)
[4] Davey, B. A.; Priestley, H. A., Introduction to lattices and order, (1990), Cambridge University Press Cambridge · Zbl 0701.06001
[5] Deng, X. F.; Yao, Y. Y., Decision-theoretic three-way approximations of fuzzy sets, Inf. Sci., 279, 702-715, (2014) · Zbl 1354.03073
[6] Goetschel, R.; Voxman, W., Fuzzy matroids, Fuzzy Sets Syst., 32, 291-302, (1988) · Zbl 0651.05024
[7] Hu, B. Q., Three-way decision spaces and three-way decisions, Inf. Sci., 281, 21-52, (2014) · Zbl 1355.68256
[8] Hu, B. Q., Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets, Knowl.-Based Syst., 91, 16-31, (2016)
[9] Hu, B. Q.; Wong, H.; Yiu, K. F.C., The aggregation of multiple three-way decision spaces, Knowl.-Based Syst., 98, 126-142, (2016)
[10] Li, H. X.; Zhou, X. Z., Risk decision making based on decision-theoretic rough sets, Int. J. Comput. Intell. Syst., 4, 1-11, (2011)
[11] Liu, D.; Li, H. X.; Zhou, X. Z., Two Decades’s research on decision-theoretic rough sets, (Proceedings of 9th IEEE International Conference on Cognitive Informatics, (2010)), 968-973
[12] Liu, D.; Yao, Y. Y.; Li, T. R., Three-way investment decisions with decision-theoretic rough sets, Int. J. Comput. Intell. Syst., 4, 66-74, (2011)
[13] Liu, D.; Li, T. R.; Ruan, D., Probabilistic model criteria with decision-theoretic rough sets, Inf. Sci., 181, 3709-3722, (2011)
[14] Liu, D.; Li, T. R.; Liang, D. C., Incorporating logistic regression to decision-theoretic rough sets for classifications, Int. J. Approx. Reason., 55, 197-210, (2014) · Zbl 1316.68185
[15] Liu, D.; Liang, D. C.; Wang, C. C., A novel three-way decision model based on incomplete information system, Knowl.-Based Syst., 91, 32-45, (2016)
[16] Li, X. N.; Liu, S. Y.; Li, S. G., Connectedness of refined GV-fuzzy matroids, Fuzzy Sets Syst., 161, 2709-2723, (2010) · Zbl 1205.05042
[17] Li, X. N.; Liu, S. Y., Matroidal approaches to rough sets via closure operators, Int. J. Approx. Reason., 53, 513-527, (2012) · Zbl 1246.68233
[18] Li, X. N.; Yi, H. J.; Liu, S. Y., Rough sets and matroids from a lattice-theoretic viewpoint, Inf. Sci., 342, 37-52, (2016) · Zbl 1403.06018
[19] Li, X. N.; Yi, H. J., Fuzzy bases of fuzzy independent set systems, Fuzzy Sets Syst., 311, 99-111, (2017) · Zbl 1368.05018
[20] Liang, D. C.; Liu, D., Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets, Inf. Sci., 300, 28-48, (2015) · Zbl 1360.68841
[21] Liang, D. C.; Pedrycz, W.; Liu, D.; Hu, P., Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making, Appl. Soft Comput., 29, 256-269, (2015)
[22] Liang, D. C.; Liu, D., A novel risk decision-making based on decision-theoretic rough sets under hesitant fuzzy information, IEEE Trans. Fuzzy Syst., 23, 237-247, (2015)
[23] Liu, G. L., Generalized rough sets over fuzzy lattices, Inf. Sci., 178, 1651-1662, (2008) · Zbl 1136.03328
[24] de Luca, A.; Termini, S., A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Inf. Control, 20, 301-312, (1972) · Zbl 0239.94028
[25] Min, F.; He, H. P.; Qian, Y. H.; Zhu, W., Test-cost-sensitive attribute reduction, Inf. Sci., 181, 4928-4942, (2011)
[26] Oxley, J. G., Matroid theory, (1992), Oxford University Press New York · Zbl 0784.05002
[27] Pawlak, Z., Rough sets, Int. J. Comput. Inf. Sci., 11, 341-356, (1982) · Zbl 0501.68053
[28] Pawlak, Z., Rough sets: theoretical aspects of reasoning about data, System Theory, Knowledge Engineering and Problem Solving, vol. 9, (1991), Kluwer Academic Publishers Dordrecht, Netherlands · Zbl 0758.68054
[29] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Inf. Sci., 177, 1, 3-27, (2007) · Zbl 1142.68549
[30] Pawlak, Z.; Skowron, A., Rough sets: some extensions, Inf. Sci., 177, 1, 28-40, (2007) · Zbl 1142.68550
[31] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Inf. Sci., 177, 1, 41-73, (2007) · Zbl 1142.68551
[32] Peters, J. F.; Ramanna, S., Proximal three-way decisions: theory and applications in social networks, Knowl.-Based Syst., 91, 4-15, (2016)
[33] Sun, B. Z.; Ma, W. M.; Xiao, X., Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes, Int. J. Approx. Reason., 81, 87-102, (2017) · Zbl 1401.68330
[34] Yang, X. P.; Yao, J. T., Modelling multi-agent three-way decisions with decision-theoretic rough sets, Fundam. Inform., 115, 157-171, (2012) · Zbl 1248.68505
[35] Yao, Y. Y.; Wong, S. K.M., A decision theoretic framework for approximating concepts, Int. J. Man-Mach. Stud., 37, 793-809, (1992)
[36] Yao, Y. Y., Probabilistic approaches to rough sets, Expert Syst., 20, 287-297, (2003)
[37] Yao, Y. Y., Probabilistic rough set approximations, Int. J. Approx. Reason., 49, 255-271, (2008) · Zbl 1191.68702
[38] Yao, Y. Y., Three-way decisions with probabilistic rough sets, Inf. Sci., 180, 341-353, (2010)
[39] Yao, Y. Y., The superiority of three-way decisions in probabilistic rough set models, Inf. Sci., 180, 1080-1096, (2011) · Zbl 1211.68442
[40] Yao, Y. Y., An outline of a theory of three-way decisions, (Yao, J. T.; etal., RSCTC 2012, LNAI, vol. 7413, (2012), Springer Heidelberg), 1-17
[41] Yao, Y. Y., Rough sets and three-way decisions, (Ciucci, D.; etal., RSKT 2015, lNAI 9436, (2015), Springer Berlin), 62-73
[42] Yu, H.; Wang, G. Y.; Hu, B. Q., Methods and practices of three-way decisions for complex problem solving, (Ciucci, D.; etal., RSKT 2015, lNAI 9436, (2015), Springer Berlin), 255-265
[43] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, (Memorandum EUL-M, Berkeley, (October 1973)) · Zbl 0404.68075
[44] Zhang, W. X.; Xu, Z. B.; Liang, Y.; Liang, K. S., Inclusion degree theory, Fuzzy Syst. Math., 10, 4, 1-9, (1996), (in Chinese) · Zbl 1332.68210
[45] Zhao, X. R.; Hu, B. Q., Fuzzy probabilistic rough sets and their corresponding three-way decisions, Knowl.-Based Syst., 91, 126-142, (2016)
[46] Zimmermann, H. J., Fuzzy set theory and its applications, (2001), Kluwer Academic Publishers Dordrecht
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.