A Theory of Threeway Decisions
Threeway decisions are thinking in threes. In contrast to dichotomous thinking in terms of two options, threeway 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 threeway decisions (3WD) may be
interpreted within a trisectingandacting 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 settheoretic model of threeway decisions,
we divide a universal set into three pairwise disjoint
regions known as a trisection or a weak tripartition.
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 threeway decisions.
A specific model of threeway decisions may be formulated based on the
notions of acceptance, rejection and noncommitment. It is an extension
of the commonly used binarydecision model with an added third option.
Threeway decisions play a key role in everyday decisionmaking and have
been widely used in many fields and disciplines.
The notion of threeway 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 threeway decisions
has been proposed, embracing ideas from rough sets, interval sets, shadowed
sets, threeway approximations of fuzzy sets, orthopairs, square
of oppositions, and others.
Most Recent Papers

姚一豫 ,
三支决策: 三分而治的思维方式和方法
,
(Yao, Y.Y., ThreeWay Decisions: Thinking through TrisectingandActing,
Working Paper, 2017.

Yao, Y.Y.,
Threeway decisions and cognitive computing,
Cognitive Computations 8, 543554, 2016.

Yao, Y.Y.,
Rough sets and threeway decisions,
in: Ciucci, D., Wang, G.Y., Mitra, S., Wu, W.Z. (eds.) RSKT 2015. LNCS
(LNAI), vol. 9436, pp. 6273, 2015.
Basic Theory of Threeway Decisions

Yao, Y.Y.,
An outline of a theory of threeway decisions.
In: Yao, J., Yang, Y., Slowinski, R., Greco, S., Li, H., Mitra, S.,
Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 117. Springer,
Heidelberg (2012).

Deng, X.F. and Yao, Y.Y.,
A multifaceted analysis of probabilistic threeway decisions,
Fundamenta Informaticae 132 (3), 291313, 2014.
Sequential Threeway Decisions

Yao, Y.Y.,
Granular computing and sequential threeway decisions.
In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S.,
Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171,
pp. 1627. Springer, Heidelberg (2013).
Statistical Threeway Decisions

Yao, Y.Y., and Gao, C.,
Statistical interpretations of threeway decisions,
in: Ciucci, D., Wang, G.Y., Mitra, S., Wu, W.Z. (eds.) RSKT 2015. LNCS
(LNAI), vol. 9436, pp. 309320, 2015.
ThreeWay Decisions with Decisiontheoretic Rough Set Model (DTRSM)

Yao, Y.Y.
The superiority of threeway decisions in probabilistic rough set models,
Information Sciences 181 (2011) 10801096.

Yao, Y.Y.
Threeway decisions with probabilistic rough sets,
Information Sciences 180 (2010) 341353.

Yao, Y.Y.
Threeway decision: an interpretation of rules in rough set theory,
Rough Sets and Knowledge Technology, Fourth International Conference, RSKT 2009,
LNAI 5589, pp. 642649, 2009.
Threeway Approximations of Fuzzy Sets
Threeway Cluster Analysis
Applications of Threeway Decisions
中文论文 (Chinese Papers)

姚一豫, 于 洪,
三支决策概述,
in: 于洪,
王国胤,
李天瑞,
梁吉业,
苗夺谦,
姚一豫,
(编著)
《三支决策：复杂问题求解方法与实践》
科学出版社,
北京,
pp. 119, 2015.
(Yao, Y.Y. and Yu, H., Introduction to threeway decisions,
in: Yu, H., Wang, G.Y., Li, T.R., Liang, J.Y., Miao, D.Q., and Yao, Y.Y. (Eds.),
ThreeWay Decisions: Methods and Practices of Complex Problem Solving,
Sience Press, Beijing, pp. 119, 2015.
)

姚一豫,
三支决策研究的若干问题
,
刘盾，李天瑞，苗夺谦，王国胤，粱吉业 （编著). 《三支决策与粒计算》，科学出版社，
北京，113, 2013.
(Yao, Y.Y., Several issues in studies on threeway decisions (in Chinese), in: Dun, L., Li, T.R., Miao, D.Q., Wang, G.Y., Liang, J.Y. (Eds.),
Threeway Decisions and Granular Computing, Science Press, Beijing, China, pp. 113, 2013.)
(
Scanned version)

姚一豫,
三支决策
,
姚一豫, 三支决策, 贾修一, 商琳, 周献中, 梁吉业, 苗夺谦, 王国胤, 李天瑞, 张燕平 （编著）. 《三支决策理论与应用》, 南京大学出版社, 南京, 116, 2012.
(Yao, Y.Y., Threeway 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 Threeway Decisions and Application, Nanjing University Press, Nanjing, China, pp. 116, 2012.)
(
Scanned copy)
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