Papers on A Theory of Three-way Decisions

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

姚一豫 , 三支决策: 三分而治的思维方式和方法 , (Yao, Y.Y., Three-Way Decisions: Thinking through Trisecting and Acting, in: 张燕平,‎ 姚一豫,‎ 苗夺谦,‎ 王国胤, 梁吉业，李天瑞，吴伟志, 赵姝, 《粒计算、商空间及三支决策的回顾与发展》, 科学出版社, 北京, pp. 146-161, 2017.

Yao, Y.Y., Three-way decisions and cognitive computing, Cognitive Computations 8, 543-554, 2016.
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

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).
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

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

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)

Yao, Y.Y. The superiority of three-way decisions in probabilistic rough set models, Information Sciences 181 (2011) 1080-1096.
Yao, Y.Y. Three-way decisions with probabilistic rough sets, Information Sciences 180 (2010) 341-353.
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

Deng, X.F., and Yao, Y.Y., Decision-theoretic three-way approximations of fuzzy sets, Information Sciences 279: 702-715, 2014.

Three-way Cluster Analysis

Yu, Y., Jiao, P., Yao, Y.Y., Wang, G.Y., Detecting and refining overlapping regions in complex networks with three-way decisions, Information Sciences 373 (2016) 21-41.

Applications of Three-way Decisions

Zhou, B., Yao, Y.Y. and Luo, J.G., Cost-sensitive three-way email spam filtering, Journal of Intelligent Information Systems 42(1): 19-45, 2014.

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. 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. )
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，北京，1-13, 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)
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, 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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