Welcome to visit Journal of Shaanxi Normal University(Natural Science Edition)!

Triadic thinking: the theory and practice of three-way decision

  • SUO Langwangqing ,
  • YANG Hailong ,
  • YAO Yiyu
Expand
  • 1 School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, Shaanxi, China;
    2 Department of Computer Science, University of Regina, Regina S4S 0A2, Canada

Received date: 2021-04-02

  Online published: 2022-05-10

Abstract

The concept of triadic thinking is given. From the perspective of triadic thinking, the basic ideas ofthree-way decision is introduced, that is, to explain and deal with an whole system through three independent and relevant parts, reasonably divide the whole system into three parts, and take effective strategies to deal with each part, so as to obtain the required results. Then, several related models and specific applications of three-way decision are summarized. Finally, the research status of three-way decision is analyzed and the future research direction is prospected from two aspects of model and application.

Cite this article

SUO Langwangqing , YANG Hailong , YAO Yiyu . Triadic thinking: the theory and practice of three-way decision[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2022 , 50(3) : 7 -16 . DOI: 10.15983/j.cnki.jsnu.2022102

References

[1] YAO Y Y. Three-way decisions with probabilistic rough sets[J].Information Sciences, 2010, 180(3): 341-353.
[2] YAO Y Y. The superiority of three-way decisions in probabilistic rough set models[J].Information Sciences, 2011, 181(6): 1080-1096.
[3] YAO Y Y. Tri-level thinking: models of three-way decision[J].International Journal of Machine Learning and Cybernetics, 2020, 11(5): 947-959.
[4] YAO Y Y. The geometry of three-way decision[J].Applied Intelligence, 2021, 51(9): 6298-6325.
[5] YAO Y Y. Three-way decisions and cognitive computing[J].Cognitive Computation, 2016, 8(4): 543-554.
[6] YAO Y Y. Three-way decision and granular computing[J].International Journal of Approximate Reasoning, 2018, 103: 107-123.
[7] YAO Y Y. Set-theoretic models of three-way decision[J].Granular Computing, 2021, 6(1): 133-148.
[8] YAO Y Y. An outline of a theory of three-way decisions[C]//International Conference on Rough Sets and Current Trends in Computing.Berlin:Springer,2012:1-17.
[9] LI X N, SUN Q Q, CHEN H M, et al. Three-way decision on two universes[J].Information Sciences, 2020, 515: 263-279.
[10] LI X N, WANG X, SUN B Z, et al. Three-way decision on information tables[J].Information Sciences, 2021, 545: 25-43.
[11] LIU D, LIANG D C, WANG C C. A novel three-way decision model based on incomplete information system[J].Knowledge-Based Systems, 2016, 91: 32-45.
[12] LUO C, LI T R, HUANG Y Y, et al. Updating three-way decisions in incomplete multi-scale information systems[J].Information Sciences, 2019, 476: 274-289.
[13] HUANG Q Q, LI T R, HUANG Y Y, et al. Incremental three-way neighborhood approach for dynamic incomplete hybrid data[J].Information Sciences, 2020, 541: 98-122.
[14] LUO J F, FUJITA H, YAO Y Y, et al. On modeling similarity and three-way decision under incomplete information in rough set theory[J].Knowledge-Based Systems, 2020, 191: 105251.
[15] LUO J F, HU M J, QIN K Y. Three-way decision with incomplete information based on similarity and satisfiability[J].International Journal of Approximate Reasoning, 2020, 120: 151-183.
[16] HU B Q. Three-way decisions space and three-way decisions[J].Information Sciences, 2014, 281: 21-52.
[17] HU B Q.Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets[J].Knowledge-Based Systems, 2016, 91: 16-31.
[18] HU B Q, KWONG C K. On type-2 fuzzy sets and their t-norm operations[J].Information Sciences, 2014, 255: 58-81.
[19] HU B Q, WONG H, YIU K C. On two novel types of three-way decisions in three-way decision spaces[J].International Journal of Approximate Reasoning, 2017, 82: 285-306.
[20] HU B Q. Three-way decisions based on semi-three-way decision spaces[J].Information Sciences, 2017, 382: 415-440.
[21] ZHAO X R, HU B Q. Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure[J].Information Sciences, 2015, 298: 534-554.
[22] ZHAO X R, HU B Q. Fuzzy probabilistic rough sets and their corresponding three-way decisions[J].Knowledge-Based Systems, 2016, 91: 126-142.
[23] WILLE R. Restructuring lattice theory: an approach based on hierarchies of concepts[J].Ordered Sets D Reidel, 1982, 83: 314-339.
[24] QI J J, WEI L, YAO Y Y. Three-way formal concept analysis[C]//International Conference on Rough Sets and Knowledge Technology. Cham: Springer, 2014:732-741.
[25] QI J J, QIAN T, WEI L. The connections between three-way and classical concept lattices[J].Knowledge-Based Systems, 2016, 91: 143-151.
[26] REN R S, WEI L. The attribute reductions of three-way concept lattices[J].Knowledge-Based Systems, 2016, 99: 92-102.
[27] LI J H, HUANG C C, QI J J, et al. Three-way cognitive concept learning via multi-granularity[J].Information Sciences, 2017, 378: 244-263.
[28] HUANG C C, LI J H, MEI C L, et al. Three-way concept learning based on cognitive operators: an information fusion viewpoint[J].International Journal of Approximate Reasoning, 2017, 83: 218-242.
[29] SINGH P K. Three-way fuzzy concept lattice representation using neutrosophic set[J].International Journal of Machine Learning and Cybernetics, 2017, 8(1): 69-79.
[30] YAO Y Y. Interval sets and three-way concept analysis in incomplete contexts[J].International Journal of Machine Learning and Cybernetics, 2017, 8(1): 3-20.
[31] LI M Z, WANG G Y. Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts[J].Knowledge-Based Systems, 2016, 91: 165-178.
[32] LONG B H, XU W H, ZHANG X Y, et al. The dynamic update method of attribute-induced three-way granular concept in formal contexts[J].International Journal of Approximate Reasoning, 2020, 126: 228-248.
[33] YU H, LIU Z G, WANG G Y. An automatic method to determine the number of clusters using decision-theoretic rough set[J].International Journal of Approximate Reasoning, 2014, 55(1): 101-115.
[34] YU H, ZHANG C, WANG G Y. A tree-based incremental overlapping clustering method using the three-way decision theory[J].Knowledge-Based Systems, 2016, 91: 189-203.
[35] AFRIDI M K, AZAM N, YAO J T, et al. A three-way clustering approach for handling missing data using GTRS[J].International Journal of Approximate Reasoning, 2018, 98: 11-24.
[36] WANG P X, YAO Y Y.CE3: a three-way clustering method based on mathematical morphology[J].Knowledge-Based Systems, 2018, 155: 54-65.
[37] YU H, WANG X C, WANG G Y, et al. An active three-way clustering method via low-rank matrices for multi-view data[J].Information Sciences, 2020, 507: 823-839.
[38] PAWLAK Z. An inquiry into anatomy of conflicts[J].Information Sciences, 1998, 109(1/2/3/4): 65-78.
[39] PAWLAK Z. Some remarks on conflict analysis[J].European Journal of Operational Research, 2005, 166(3): 649-654.
[40] YAO Y Y. Three-way conflict analysis: reformulations and extensions of the Pawlak model[J].Knowledge-Based Systems, 2019, 180: 26-37.
[41] LANG G M, MIAO D Q, CAI M J. Three-way decision approaches to conflict analysis using decision-theoretic rough set theory[J].Information Sciences, 2017, 406: 185-207.
[42] LANG G M, MIAO D Q, FUJITA H. Three-way group conflict analysis based on Pythagorean fuzzy set theory[J].IEEE Transactions on Fuzzy Systems, 2020, 28(3): 447-461.
[43] LI X N, WANG X, LANG G M, et al. Conflict analysis based on three-way decision for triangular fuzzy information systems[J].International Journal of Approximate Reasoning, 2021, 132: 88-106.
[44] LANG G M, LUO J F, YAO Y Y. Three-way conflict analysis: a unification of models based on rough sets and formal concept analysis[J].Knowledge-Based Systems, 2020, 194: 105556.
[45] LANG G M. A general conflict analysis model based on three-way decision[J].International Journal of Machine Learning and Cybernetics, 2020, 11(5): 1083-1094.
[46] SUN B Z, MA W M, ZHAO H Y. Rough set-based conflict analysis model and method over two universes[J].Information Sciences, 2016, 372: 111-125.
[47] SUN B Z, CHEN X T, ZHANG L Y, et al. Three-way decision making approach to conflict analysis and resolution using probabilistic rough set over two universes[J].Information Sciences, 2020, 507: 809-822.
[48] LI X N, YI H J, SHE Y H, et al. Generalized three-way decision models based on subset evaluation[J].International Journal of Approximate Reasoning, 2017, 83: 142-159.
[49] LI X N, SUN B Z, SHE Y H. Generalized matroids based on three-way decision models[J].International Journal of Approximate Reasoning, 2017, 90: 192-207.
[50] LI X N. Three-way fuzzy matroids and granular computing[J].International Journal of Approximate Reasoning, 2019, 114: 44-50.
[51] ZHANG S Y, LI S G, YANG H L. Three-way convex systems and three-way fuzzy convex systems[J].Information Sciences, 2020, 510: 89-98.
[52] ZHANG H R, MIN F. Three-way recommender systems based on random forests[J].Knowledge-Based Systems, 2016, 91: 275-286.
[53] ZHANG H R, MIN F, SHI B. Regression-based three-way recommendation[J].Information Sciences, 2017, 378: 444-461.
[54] YANG X P, YAO J T. Modelling multi-agent three-way decisions with decision-theoretic rough sets[J].Fundamenta Informaticae, 2012, 115(2/3): 157-171.
[55] LIANG D C, LIU D. Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets[J].Information Sciences, 2014, 276: 186-203.
[56] YANG D D, DENG T Q, FUJITA H. Partial-overall dominance three-way decision models in interval-valued decision systems[J].International Journal of Approximate Reasoning, 2020, 126: 308-325.
[57] GAO C, ZHOU J, MIAO D Q, et al. Three-way decision with co-training for partially labeled data[J].Information Sciences, 2021, 544: 500-518.
[58] YAO J T, AZAM N. Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets[J].IEEE Transactions on Fuzzy Systems, 2014, 23(1): 3-15.
[59] LI H X, ZHOU X Z. Risk decision making based on decision-theoretic rough set: a three-way view decision model[J].International Journal of Computational Intelligence Systems, 2011, 4(1): 1-11.
[60] SUN B Z, MA W M, XIAO X. Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes[J].International Journal of Approximate Reasoning, 2017, 81: 87-102.
[61] LIANG D C, XU Z S, LIU D. Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information[J].Information Sciences, 2017, 396: 127-143.
[62] LIU D, LI T R, LI H X. A multiple-category classification approach with decision-theoretic rough sets[J].Fundamenta Informaticae, 2012, 115(2/3): 173-188.
[63] ZHOU B. Multi-class decision-theoretic rough sets[J].International Journal of Approximate Reasoning, 2014, 55(1): 211-224.
[64] LIU D, LI T R, RUAN D. Probabilistic model criteria with decision-theoretic rough sets[J].Information Sciences, 2011, 181(17): 3709-3722.
[65] LIU D, YAO Y Y, LI T R. Three-way investment decisions with decision-theoretic rough sets[J].International Journal of Computational Intelligence Systems, 2011, 4(1): 66-74.
[66] LIU D, LI T R, LIANG D C. Three-way government decision analysis with decision-theoretic rough sets[J].International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2012, 20: 119-132.
[67] LIANG D C, LIU D. A novel risk decision making based on decision-theoretic rough sets under hesitant fuzzy information[J].IEEE Transactions on Fuzzy Systems, 2014, 23(2): 237-247.
[68] LIANG D C, LIU D. Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets[J].Information Sciences, 2015, 300: 28-48.
[69] LIANG D C, XU Z S, LIU D. Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators[J].Information Sciences, 2017, 375: 183-201.
[70] LIANG D C, XU Z S, LIU D, et al. Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information[J].Information Sciences, 2018, 435: 282-295.
[71] LIANG D C, WANG M W, XU Z S, et al. Risk appetite dual hesitant fuzzy three-way decisions with TODIM[J].Information Sciences, 2020, 507: 585-605.
[72] LIANG D C, PEDRYCZ W, LIU D, et al. Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making[J].Applied Soft Computing, 2015, 29: 256-269.
[73] YE J, ZHAN J M, XU Z S. A novel decision-making approach based on three-way decisions in fuzzy information systems[J].Information Sciences, 2020, 541: 362-390.
[74] LI H X, ZHANG L B, HUANG B, et al. Sequential three-way decision and granulation for cost-sensitive face recognition[J].Knowledge-Based Systems, 2016, 91: 241-251.
[75] LI H X, ZHANG L B, ZHOU X Z, et al. Cost-sensitive sequential three-way decision modeling using a deep neural network[J].International Journal of Approximate Reasoning, 2017, 85: 68-78.
[76] LI H X, ZHANG L B, HUANG B, et al. Cost-sensitive dual-bidirectional linear discriminant analysis[J].Information Sciences, 2020, 510: 283-303.
[77] ZHANG L B, LI H X, ZHOU X Z, et al. Sequential three-way decision based on multi-granular autoencoder features[J].Information Sciences, 2020, 507: 630-643.
[78] ZHOU B, YAO Y Y, LOU J G. Cost-sensitive three-way email spam filtering[J].Journal of Intelligent Information Systems, 2014, 42(1): 19-45.
[79] LIANG D C, LIU D, KOBINA A. Three-way group decisions with decision-theoretic rough sets[J].Information Sciences, 2016, 345: 46-64.
[80] SUN B Z, MA W M, LI B J, et al. Three-way decisions approach to multiple attribute group decision making with linguistic information-based decision-theoretic rough fuzzy set[J].International Journal of Approximate Reasoning, 2018, 93: 424-442.
[81] JIAO L, YANG H L, LI S G. Three-way decision based on decision-theoretic rough sets with single-valued neutrosophic information[J].International Journal of Machine Learning and Cybernetics, 2020, 11(3): 657-665.
[82] ZHANG C, LI D Y, LIANG J Y. Multi-granularity three-way decisions with adjustable hesitant fuzzy linguistic multigranulation decision-theoretic rough sets over two universes[J].Information Sciences, 2020, 507: 665-683.
[83] LIU D, LI T R, LIANG D C. Incorporating logistic regression to decision-theoretic rough sets for classifications[J].International Journal of Approximate Reasoning, 2014, 55(1): 197-210.
[84] LI W W, HUANG Z Q, JIA X Y, et al. Neighborhood based decision-theoretic rough set models[J].International Journal of Approximate Reasoning, 2016, 69: 1-17.
[85] YANG X, LI T R, FUJITA H, et al. A unified model of sequential three-way decisions and multilevel incremental processing[J].Knowledge-Based Systems, 2017, 134: 172-188.
[86] YANG X, LI T R, LIU D, et al. A unified framework of dynamic three-way probabilistic rough sets[J].Information Sciences, 2017, 420: 126-147.
[87] YANG X, LI T R, FUJITA H, et al. A sequential three-way approach to multi-class decision[J].International Journal of Approximate Reasoning, 2019, 104: 108-125.
[88] HAO C, LI J H, FAN M, et al. Optimal scale selection in dynamic multi-scale decision tables based on sequential three-way decisions[J].Information Sciences, 2017, 415: 213-232.
Outlines

/