A Theory of Three-way Decisions
Three-way decisions are thinking in threes. In contrast to dichotomous thinking in terms of two options, three-way decisions introduce a third option. We move from true/false, black/white, yes/no etc. into true/unsure/false, black/grey/white, yes/maybe/no etc. The third option provides the necessary flexibility and universality of thinking in threes.
A theory of three-way decisions (3WD) may be
interpreted within a trisecting-and-acting framework.
With respect to trisecting, we divide a
whole into three parts. With respect to acting, we
design most effective strategies for processing the three parts.
In a set-theoretic model of three-way decisions,
we divide a universal set into three pair-wise disjoint
regions known as a trisection or a weak tri-partition.
We design most effective strategies for processing the
three regions. The identification and explicit investigation
of different strategies for different regions are
a distinguishing feature of three-way decisions.
A specific model of three-way decisions may be formulated based on the
notions of acceptance, rejection and noncommitment. It is an extension
of the commonly used binary-decision model with an added third option.
Three-way decisions play a key role in everyday decision-making and have
been widely used in many fields and disciplines.
The notion of three-way decisions was originally introduced
by the needs to explain the three regions of probabilistic rough sets.
One can construct rules for acceptance from the positive region and rules for
rejection from the negative region. When neither a decision of an acceptance
nor a decision of rejection can be made, a third option of noncommitment
is chosen. Recent studies show that rough set theory is only one of possible ways
to construct three regions. A more general theory of three-way decisions
has been proposed, embracing ideas from rough sets, interval sets, shadowed
sets, three-way approximations of fuzzy sets, orthopairs, square
of oppositions, and others.
Most Recent Papers
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姚一豫 ,
三支决ç–: 三分而治的æ€ç»´æ–¹å¼å’Œæ–¹æ³•
,
(Yao, Y.Y., Three-Way Decisions: Thinking through Trisecting and Acting,
in:
å¼ ç‡•å¹³,‎ 姚一豫,‎ 苗夺谦,‎ 王国胤, æ¢å‰ä¸šï¼ŒæŽå¤©ç‘žï¼Œå´ä¼Ÿå¿—, èµµå§, 《粒计算ã€å•†ç©ºé—´åŠä¸‰æ”¯å†³ç–的回顾与å‘展》, 科å¦å‡ºç‰ˆç¤¾, 北京, pp. 146-161, 2017.
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Yao, Y.Y.,
Three-way decisions and cognitive computing,
Cognitive Computations 8, 543-554, 2016.
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Yao, Y.Y.,
Rough sets and three-way decisions,
in: Ciucci, D., Wang, G.Y., Mitra, S., Wu, W.Z. (eds.) RSKT 2015. LNCS
(LNAI), vol. 9436, pp. 62-73, 2015.
Basic Theory of Three-way Decisions
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Yao, Y.Y.,
An outline of a theory of three-way decisions.
In: Yao, J., Yang, Y., Slowinski, R., Greco, S., Li, H., Mitra, S.,
Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1-17. Springer,
Heidelberg (2012).
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Deng, X.F. and Yao, Y.Y.,
A multifaceted analysis of probabilistic three-way decisions,
Fundamenta Informaticae 132 (3), 291-313, 2014.
Sequential Three-way Decisions
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Yao, Y.Y.,
Granular computing and sequential three-way decisions.
In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S.,
Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171,
pp. 16-27. Springer, Heidelberg (2013).
Statistical Three-way Decisions
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Yao, Y.Y., and Gao, C.,
Statistical interpretations of three-way decisions,
in: Ciucci, D., Wang, G.Y., Mitra, S., Wu, W.Z. (eds.) RSKT 2015. LNCS
(LNAI), vol. 9436, pp. 309-320, 2015.
Three-Way Decisions with Decision-theoretic Rough Set Model (DTRSM)
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Yao, Y.Y.
The superiority of three-way decisions in probabilistic rough set models,
Information Sciences 181 (2011) 1080-1096.
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Yao, Y.Y.
Three-way decisions with probabilistic rough sets,
Information Sciences 180 (2010) 341-353.
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Yao, Y.Y.
Three-way decision: an interpretation of rules in rough set theory,
Rough Sets and Knowledge Technology, Fourth International Conference, RSKT 2009,
LNAI 5589, pp. 642-649, 2009.
Three-way Approximations of Fuzzy Sets
Three-way Cluster Analysis
Applications of Three-way Decisions
ä¸æ–‡è®ºæ–‡ (Chinese Papers)
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姚一豫, 于 洪,
三支决ç–概述,
in: 于洪,
王国胤,
æŽå¤©ç‘ž,
æ¢å‰ä¸š,
苗夺谦,
姚一豫,
(ç¼–è‘—)
《三支决ç–：å¤æ‚问题求解方法与实践》
科å¦å‡ºç‰ˆç¤¾,
北京,
pp. 1-19, 2015.
(Yao, Y.Y. and Yu, H., Introduction to three-way decisions,
in: Yu, H., Wang, G.Y., Li, T.R., Liang, J.Y., Miao, D.Q., and Yao, Y.Y. (Eds.),
Three-Way Decisions: Methods and Practices of Complex Problem Solving,
Sience Press, Beijing, pp. 1-19, 2015.
)
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姚一豫,
三支决ç–ç ”ç©¶çš„è‹¥å¹²é—®é¢˜
,
刘盾，æŽå¤©ç‘žï¼Œè‹—夺谦，王国胤，粱å‰ä¸š （编著). 《三支决ç–与粒计算》，科å¦å‡ºç‰ˆç¤¾ï¼Œ
北京，1-13, 2013.
(Yao, Y.Y., Several issues in studies on three-way decisions (in Chinese), in: Dun, L., Li, T.R., Miao, D.Q., Wang, G.Y., Liang, J.Y. (Eds.),
Three-way Decisions and Granular Computing, Science Press, Beijing, China, pp. 1-13, 2013.)
(
Scanned version)
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姚一豫,
三支决ç–
,
姚一豫, 三支决ç–, 贾修一, 商ç³, 周献ä¸, æ¢å‰ä¸š, 苗夺谦, 王国胤, æŽå¤©ç‘ž, å¼ ç‡•å¹³ （编著）. 《三支决ç–ç†è®ºä¸Žåº”用》, å—京大å¦å‡ºç‰ˆç¤¾, å—京, 1-16, 2012.
(Yao, Y.Y., Three-way decisions (in Chinese), in: Jia, X.Y., Shang, L., Zhou, X.Z., Liang, J.Y., Miao, D.Q., Wang, G.Y., Li, T.R., Zhang, Y.P. (Eds.), Theory of Three-way Decisions and Application, Nanjing University Press, Nanjing, China, pp. 1-16, 2012.)
(
Scanned copy)
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