Skip to main content
SpringerLink
Log in

Three-Way Decisions and Cognitive Computing

  • Published:
Cognitive Computation Aims and scope Submit manuscript

Abstract

A trisecting-and-acting model explains three-way decisions (3WD) in terms of two basic tasks. One task is to divide a universal set into three pair-wise disjoint regions called a trisection or a tri-partition of the universal set. The other task is to act upon objects in one or more regions by developing appropriate strategies. 3WD are a class of effective ways and heuristics commonly used in human problem solving and information processing. We argue that 3WD are built on solid cognitive foundations and offer cognitive advantages and benefits. We demonstrate the flexibility and general applicability of 3WD by using examples from across many fields and disciplines.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Arnauld A, Nicole P. Logic or the art of thinking (translated by Jill Vance Buroker). Cambridge: Cambridge University Press; 1996.

    Book  Google Scholar 

  2. Bobelli R. The art of thinking clearly (translated by Nicky Griffin). New York: Harper; 2013.

    Google Scholar 

  3. Chen J, Zhang YP, Zhao S. Multi-granular mining for boundary regions in three-way decision theory. Knowl Based Syst. 2016;91:287–92.

    Article  Google Scholar 

  4. Ciucci D. Orthopairs in the 1960s: historical remarks and new ideas. In: RSCTC 2014, LNCS (LNAI) 8536, Berlin: Springer; 2014. p. 1–12.

  5. Ciucci D, Dubois D, Lawry J. Borderline vs. unknown: comparing three-valued representations of imperfect information. Int J Approx Reason. 2014;55:1866–89.

    Article  Google Scholar 

  6. Ciucci D, Dubois D, Prade H. Oppositions in rough set theory. In: RSKT 2012, LNCS (LNAI) 7414, Berlin: Springer; 2012. p. 504–13.

  7. Clayton M. Brilliant influence: what the most influential people know, do and say. New York: Prentice Hall; 2011.

    Google Scholar 

  8. Clermont KM. Procedure’s magical number three: psychological bases for standards of decision. Cornell Law Rev. 1987;72:1115–56.

    Google Scholar 

  9. Cowan N. The magical number 4 in short-term memory: a reconsideration of mental storage capacity. Behav Brain Sci. 2000;24:87–185.

    Article  Google Scholar 

  10. Davidson SM. Response to “causal reasoning: the ‘magical number’ three”. EMBO Rep. 2009;10:938.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Deng XF, Yao YY. Decision-theoretic three-way approximations of fuzzy sets. Inf Sci. 2014;279:702–15.

    Article  Google Scholar 

  12. Dubois D, Prade H. From Blanché hexagonal organization of concepts to formal concept analysis and possibility theory. Log Univers. 2012;6:149–69.

    Article  Google Scholar 

  13. Dundes A. The number three in American culture. In: Dundes A, editor. Every man his way: readings in cultural anthropology. Englewood Cliffs: Prentice-Hall; 1968. p. 401–24.

    Google Scholar 

  14. Fujita H, Li TR, Yao YY. Advances in three-way decisions and granular computing. Knowl Based Syst. 2016;91:1–3.

    Article  Google Scholar 

  15. Gladwell M. David and Goliath: underdogs, misfits, and the art of battling giants. New York: Back Bay Books; 2015.

    Google Scholar 

  16. Hartshorne C. Wisdom as moderation: a philosophy of the middle way. Albany: State University of New York Press; 1987.

    Google Scholar 

  17. Hu BQ. Three-way decisions space and three-way decisions. Inf Sci. 2014;281:21–52.

    Article  Google Scholar 

  18. Hurwitz J, Kaufman M, Bowles A. Cognitive computing and big data analytics. Indianapolis: Wiley; 2015.

    Google Scholar 

  19. Hussain A. Cognitive computation: an introduction. Cogn Comput. 2009;1:1–3.

    Article  Google Scholar 

  20. Jia XY, Shang L, Zhou XZ, Liang JY, Miao DQ, Wang GY, Li TR, Zhang YP, editors. Theory of three-way decisions and applications (in Chinese). Nanjing: Nanjing University Press; 2012.

    Google Scholar 

  21. Kahneman D. Thinking, fast and slow. Anchor Canada; 2013.

  22. Kelly, JE. Computing, cognition, and the future of knowing. 2015. http://www.research.ibm.com/software/IBMResearch/multimedia/Computing_Cognition_WhitePaper. Accessed 8 Jan 2016.

  23. Kelly K. Old world and new: early medical care, 1700–1840. New York: Facts On File, Inc.; 2010.

    Google Scholar 

  24. Kováč L. Causal reasoning: the ‘magical number’ three. EMBO Rep. 2009;10:418.

    PubMed  PubMed Central  Google Scholar 

  25. Lachowicz M. Microscopic, mesoscopic and macroscopic descriptions of complex systems. Probab Eng Mech. 2011;26:54–60.

    Article  Google Scholar 

  26. Lease EB. The number three, mysterious, mystic, magic. Class Philol. 1919;14:56–73.

    Article  Google Scholar 

  27. Li HX, Zhang LB, Huang B, Zhou XZ. Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl Based Syst. 2016;91:241–51.

    Article  Google Scholar 

  28. Li MZ, Wang GY. Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts. Knowl Based Syst. 2016;91:165–78.

    Article  Google Scholar 

  29. Li WW, Huang ZQ, Li Q. Three-way decisions based software defect prediction. Knowl Based Syst. 2016;91:263–74.

    Article  Google Scholar 

  30. Li Y, Zhang ZH, Chen WB, Min F. TDUP: an approach to incremental mining of frequent itemsets with three-way-decision pattern updating. Int J Mach Learn Cybern. doi:10.1007/s13042-015-0337-6

  31. Liang DC, Liu D. Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets. Inf Sci. 2015;300:28–48.

    Article  Google Scholar 

  32. Licklider JCR. Man-computer symbiosis. IRE Trans Hum Factors Electron. 1960; HFE-1: 4–11.

  33. Lidwell W, Holden K, Butler J. Universal principles of design. Gloucester: Rockport Publishers; 2003.

    Google Scholar 

  34. Liu D, Li TR, Miao DQ, Wang GY, Liang JY, editors. Three-way decisions and granular computing (in Chinese). Beijing: Science Press; 2013.

    Google Scholar 

  35. Liu D, Liang DC, Wang CC. A novel three-way decision model based on incomplete information system. Knowl Based Syst. 2016;91:32–45.

    Article  Google Scholar 

  36. Luhn HP. The automatic creation of literature abstracts. IBM J Res Dev. 1958;2:159–65.

    Article  Google Scholar 

  37. Marinoff L. The middle way, finding happiness in a world of extremes. New York: Sterling; 2007.

    Google Scholar 

  38. Marr D. Vision, a computational investigation into human representation and processing of visual information. San Francisco: W.H. Freeman and Company; 1982.

    Google Scholar 

  39. McCutchen D. The magical number three, plus or minus two: working memory in writing. In: Butterfield EC, editor. Advances in cognition and educational practice, volume 2, children’s writing: toward a process theory of the development of skilled writing. Greenwich: JAI Press Inc.; 1994. p. 1–30.

    Google Scholar 

  40. Miller GA. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychol Rev. 1956;63:81–97.

    Article  CAS  PubMed  Google Scholar 

  41. Minsky M. The emotion machine: commonsense thinking, artificial intelligence, and the future of the human mind. New York: Simon & Schuster Paperbacks; 2007.

    Google Scholar 

  42. Modha DS, Ananthanarayanan R, Esser SK, Ndirango A, Sherbondy AJ, Singh R. Cognitive computing. Commun ACM. 2011;54:62–71.

    Article  Google Scholar 

  43. Pauker SG, Kassirer JP. The threshold approach to clinical decision making. New Engl J Med. 1980;302:1109–17.

    Article  CAS  PubMed  Google Scholar 

  44. Pawlak Z. Rough sets, theoretical aspects of reasoning about data. Dordrecht: Kluwer; 1991.

    Google Scholar 

  45. Pedrycz W. Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern. 1998;28:103–9.

    Article  CAS  Google Scholar 

  46. Peters JF, Ramanna S. Proximal three-way decisions: theory and applications in social networks. Knowl Based Syst. 2016;91:4–15.

    Article  Google Scholar 

  47. Pinker S. How the mind works. New York: W. W. Norton & Company; 1997.

    Google Scholar 

  48. Qi JJ, Qian T, Wei L. The connections between three-way and classical concept lattices. Knowl Based Syst. 2016;91:143–51.

    Article  Google Scholar 

  49. Rourke JT. International politics on the world stage (3rd edition). Sluice Dock: The Dushkin Publishing Group, Inc.; 1991.

    Google Scholar 

  50. Salton G, McGill MH. Introduction to modern information retrieval. New York: McGraw-Hill; 1983.

    Google Scholar 

  51. Shakiba A, Hooshmandasl MR. S-approximation spaces: a three-way decision approach. Fundam Informaticae. 2015;39:307–28.

    Article  Google Scholar 

  52. Sherif M, Hovland CI. Social judgment: assimilation and contrast effects in communication and attitude change. New Haven: Yale University Press; 1961.

    Google Scholar 

  53. Shu SB, Carlson KA. When three charms but four alarms: identifying the optimal number of claims in persuasion settings. J. Mark. 2014;78:127–39.

    Article  Google Scholar 

  54. Smith T. Pricing strategy: setting price levels, managing price discounts, and establishing price structure. Mason: South-Western Cengage Learning; 2012.

    Google Scholar 

  55. Squartini S, Schuller B, Hussain A. Cognitive and emotional information processing for human-machine interaction. Cogn Comput. 2012;4:383–5.

    Article  Google Scholar 

  56. Tavenner E. Three as a magic number in latin literature. In: Transactions and proceedings of the American Philological Association, vol. 47. 1916; p. 117–43.

  57. The National Scientific Council on the Developing Child. Toxic stress. http://developingchild.harvard.edu/science/key-concepts/toxic-stress/. Accessed Jan 18 2016.

  58. van Rijsbergen CJ. Information retrieval. London: Butterworth; 1979.

    Google Scholar 

  59. Wald A. Sequential tests of statistical hypotheses. Ann Math Stat. 1945;16:117–86.

    Article  Google Scholar 

  60. Warfield JN. The magical number three-plus or minus zero. Cybern Syst. 1988;19:339–58.

    Article  Google Scholar 

  61. Weller AC. Editorial peer review: its strengths and weaknesses. Medford: Information Today, Inc.; 2001.

    Google Scholar 

  62. Yang B, Liu JM, Liu DY. Characterizing and extracting multiplex patterns in complex networks. IEEE Trans Syst Man Cybern Part B Cybern. 2012;42:469–81.

    Article  Google Scholar 

  63. Yang YR. Modern principles of economic mechanics vol. 1: qualitative initiatives toward integrating economics, cognitive science, and theoretical physics. Xlibris Corporation; 2012.

  64. Yao JT, Azam N. Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets. IEEE Trans Fuzzy Syst. 2015;23:3–15.

    Article  Google Scholar 

  65. Yao YY. Interval-set algebra for qualitative knowledge representation. In: Proceedings of the 5th international conference on computing and information, 1993. p. 370–74.

  66. Yao YY. Three-way decision: an interpretation of rules in rough set theory. In: RSKT 2009, LNCS (LNAI) 5589, Berlin: Springer; 2009; p. 642–49.

  67. Yao YY. Three-way decisions with probabilistic rough sets. Inf Sci. 2010;180:341–53.

    Article  Google Scholar 

  68. Yao YY. The superiority of three-way decisions in probabilistic rough set models. Inf Sci. 2011;181:1080–96.

    Article  Google Scholar 

  69. Yao YY. An outline of a theory of three-way decisions. In: RSCTC 2012, LNCS (LNAI) 7413, Springer; 2012; pp. 1–17.

  70. Yao YY. Granular computing and sequential three-way decisions. In: RSKT 2013, LNCS (LNAI) 8171, Berlin: Springer; 2013. p. 16–27.

  71. Yao YY. Duality in rough set theory based on the square of opposition. Fundam Inform. 2013;127:49–64.

    Google Scholar 

  72. Yao YY. Rough sets and three-way decisions. In: RSKT 2015, LNCS (LNAI) 9436, Springer; 2015. p. 62–73.

  73. Yao YY, Gao C. Statistical interpretations of three-way decisions. In: RSKT 2015, LNCS (LNAI) vol. 9436, Berlin: Springer; 2015. p. 309–20.

  74. Yao YY, Yu H. An introduction to three-way decisions. In: Yu H, Wang GY, Li TR, Liang JY, Miao DQ, Yao YY, editors. Three-way decisions: methods and practices for complex problem solving (in Chinese). Beijing: Science Press; 2015. p. 1–19.

    Google Scholar 

  75. Yu H, Wang GY, Li TR, Liang JY, Miao DQ, Yao YY, editors. Three-way decisions: methods and practices for complex problem solving (in Chinese). Beijing: Science Press; 2015.

    Google Scholar 

  76. Yu H, Zhang C, Wang GY. A tree-based incremental overlapping clustering method using the three-way decision theory. Knowl Based Syst. 2016;91:189–203.

    Article  Google Scholar 

  77. Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–53.

    Article  Google Scholar 

  78. Zhang HR, Min F. Three-way recommender systems based on random forests. Knowl Based Syst. 2016;91:275–86.

    Article  Google Scholar 

  79. Zhang HY, Yang SY, Ma JM. Ranking interval sets based on inclusion measures and applications to three-way decisions. Knowl Based Syst. 2016;91:62–70.

    Article  Google Scholar 

  80. Zhao XR, Hu BQ. Fuzzy probabilistic rough sets and their corresponding three-way decisions. Knowl Based Syst. 2016;91:126–42.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported in part by a Discovery Grant from NSERC, Canada. The author thanks Professor Amir Hussain for his encouragement during the preparation of this paper. The author thanks Ling Wei, Jingyu Chen, Shunling Wang, Jianjun Qi, Mengjun Hu and Ruisi Ren for their constructive comments.

Funding

This study was funded by NSERC, Canada.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2, Canada

    Yiyu Yao

Authors
  1. Yiyu Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yiyu Yao.

Ethics declarations

Conflicts of interest

Yiyu Yao declares no conflict of interest.

Informed Consent

All procedures followed were in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, as revised in 2008 (5). Additional informed consent was obtained from all patients for which identifying information is included in this article.

Human and Animal Rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, Y. Three-Way Decisions and Cognitive Computing. Cogn Comput 8, 543–554 (2016). https://doi.org/10.1007/s12559-016-9397-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12559-016-9397-5

Keywords

Search

Navigation