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Effectiveness measure in change-based three-way decision


The trisecting–acting–outcome model of a three-way decision is a practical approach to solving complex problems, consisting of three components: trisecting, acting, and outcome. Trisecting means dividing a complex problem into three parts based on an evaluation function, and acting means designing the corresponding action to apply to these three parts. The outcome denotes evaluation effectiveness based on the first two steps. Measuring this outcome is a challenging and moving question after trisecting-and-acting (T &A). This paper proposes a method to measure outcome based on object changes before and after T &A based on top-down and bottom-up perspectives, depending on the decision needs. First, evaluation functions are constructed that extend the traditional evaluation functions to measure changes. Then, based on the introduced evaluation functions, qualitative and quantitative of three-way changes are introduced and analyzed. Furthermore, we present the processes that determine the optimal strategy with the quantitative analysis. The analysis of several examples shows the effectiveness and practicality of our proposed method.

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  • Fan B, Tsang E, Xu W, Chen D, Li W (2019) Attribute-oriented cognitive concept learning strategy: a multi-level method. Int J Mach Learn Cybern 10(9):2421–2437

    Article  Google Scholar 

  • Ganter B, Wille R (1999) Formal concept analysis: mathematical foundations. Springer, Berlin

    Book  MATH  Google Scholar 

  • Hu J, Yang Y, Chen X (2018) A novel TODIM method-based three-way decision model for medical treatment selection. Int J Fuzzy Syst 20(4):1240–1255

    Article  MathSciNet  Google Scholar 

  • Jia X, Shang L (2014) Three-way decisions versus two-way decisions on filtering spam email. LNCS Trans Rough Sets XVII I:69–91

    Article  Google Scholar 

  • Jia X, Deng Z, Min F, Liu D (2019) Three-way decisions based feature fusion for Chinese irony detection. Int J Approx Reason 113:324–335

    Article  Google Scholar 

  • Jiang C, Yao Y (2018) Effectiveness measures in movement-based three-way decisions. Knowl Based Syst 160:136–143

    Article  Google Scholar 

  • Jiang C, Zhao S (2020) Action strategy analysis in probabilistic preference movement-based three-way decision. Math Probl Eng.

  • Jiang C, Wu J, Li Z (2019a) Adaptive thresholds determination for saving cloud energy using three-way decisions. Cluster Comput 22(4):8475–8482

  • Jiang C, Duan Y, Yao J (2019b) Resource-utilization-aware task scheduling in cloud platform using three-way clustering. J Intell Fuzzy Syst 37:1–9

  • Jiang C, Guo D, Duan Y, Liu Y (2020) Strategy selection under entropy measures in movement-based three-way decision. Int J Approx Reason 119:280–291

    Article  MathSciNet  MATH  Google Scholar 

  • Jiang C, Guo D, Xu R (2021a) Measuring the outcome of movement-based three-way decision using proportional utility functions. Appl Intell 51(12):8598–8612

    Article  Google Scholar 

  • Jiang C, Guo D, Sun L (2021b) Effectiveness measure for TAO model of three-way decisions with interval set. J Intell Fuzzy Syst 40(6):11071–11084

  • Jiang C, Guo D, Duan Y (2022) Measure effectiveness of change-based three-way decision using utility theory. Cognit Comput 14(3):1009–1018

  • Ma X, Wang G, Yu H, Li T (2014) Decision region distribution preservation reduction in decision-theoretic rough set model. Inf Sci 278:614–640

    Article  MathSciNet  MATH  Google Scholar 

  • Qian F, Min Q, Zhao S, Chen J, Wang X, Zhang Y (2019a) Three-way decision collaborative recommendation algorithm based on user reputation. In: Proceedings of the 2019 international joint conference on rough sets, pp 424–438

  • Qian T, Wei L, Qi J (2019b) A theoretical study on the object (property) oriented concept lattices based on three-way decisions. Soft Comput 23(19):9477–9489

    Article  MATH  Google Scholar 

  • Xu W, Li W (2014) Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans Cybern 46(2):366–379

    Article  Google Scholar 

  • Xu Y, Zhang H, Min F (2017) A three-way recommender system for popularity-based costs, lecture notes in artificial intelligence, vol 10314. Springer International Publishing Ag, Cham, pp 278–289

  • Xu W, Yuan K, Li W (2022) Dynamic updating approximations of local generalized multigranulation neighborhood rough set. Appl Intell 52(8):9148–9173

  • Yao Y (2004) Information granulation and approximation in a decision-theoretical model of rough sets. In: Pal S, Polkowshi L, Skowron A (eds) Rough-neural computing: techniques for computing with words. Springer, Berlin, pp 491–516

  • Yao Y (2008) Probabilistic rough set approximations. Int J Approx Reason 49(2):255–271

    Article  MATH  Google Scholar 

  • Yao Y (2009) Three-way decision: an interpretation of rules in rough set theory. In: Proceedings of 4th international conference on rough sets and knowledge technology, pp 642–649

  • Yao Y (2012) An outline of a theory of three-way decisions. In: Proceedings of 8th international conference on rough sets and current trends in computing, pp 1–17

  • Yao Y (2020a) Tri-level thinking: models of three-way decision. Int J Mach Learn Cybern 11(5):947–959

    Article  Google Scholar 

  • Yao Y (2020b) Three-way granular computing, rough sets, and formal concept analysis. Int J Approx Reason 116:106–125

    Article  MathSciNet  MATH  Google Scholar 

  • Yao Y (2021) Set-theoretic models of three-way decision. Granul Comput 6(1):133–148

    Article  Google Scholar 

  • Yu H, Chu S, Yang D (2010) Autonomous knowledge-oriented clustering using decision-theoretic rough set theory. In: Proceedings of 5th international conference on rough set and knowledge technology, pp 687–694

  • Yu H, Wang X, Wang G, Zeng X (2020) An active three-way clustering method via low-rank matrices for multi-view data. Inf Sci 507:823–839

    Article  Google Scholar 

  • Yuan K, Xu W, Li W, Ding W (2022) An incremental learning mechanism for object classification based on progressive fuzzy three-way concept. Inf Sci 584:127–147

    Article  Google Scholar 

  • Zhang Y, Yao J (2020) Game theoretic approach to shadowed sets: a three-way tradeoff perspective. Inf Sci 507:540–552

    Article  MATH  Google Scholar 

  • Zhi H, Qi J, Qian T, Wei L (2019) Three-way dual concept analysis. Int J Approx Reason 114:151–165

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou B, Yao Y, Luo J (2010) A three-way decision approach to email spam filtering. In: Proceedings of 23th Canadian conference on artificial intelligence, pp 514–522

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This work was supported in part by the Natural Science Foundation of Heilongjiang Province (LH2020F031).


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Correspondence to Chunmao Jiang.

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Chunmao Jiang declares that he has no conflict of interest. Ying Duan declares that she has no conflict of interest. Doudou Guo declares that he has no conflict of interest.

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Jiang, C., Duan, Y. & Guo, D. Effectiveness measure in change-based three-way decision. Soft Comput 27, 2783–2793 (2023).

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  • Three-way decision
  • Outcome measure
  • Trisecting-acting-outcome
  • Three-way change