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An Overview of Function Based Three-Way Decisions

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Rough Sets and Knowledge Technology (RSKT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8818))

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Abstract

By considering the various of studies on loss functions with three-way decisions, a function based three-way decisions is proposed to generalize the existing models. A “four-level” approach with granular perspective is built, and the existing models can be categorized to a “four-level” framework through different decision criteria. Our work provides a novel “granularity” viewpoint on the current three-way decision researches.

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References

  1. Azam, N., Yao, J.T.: Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets. International Journal of Approximate Reasoning 55, 142–155 (2014)

    Article  MathSciNet  Google Scholar 

  2. Abd El-Monsef, M.M.E., Kilany, N.M.: Decision analysis via granulation based on general binary relation. International Journal of Mathematics and Mathematical Sciences, article ID 12714 (2007), doi:10.1155/2007/12714

    Google Scholar 

  3. Chebrolu, S., Sanjeevi, S.G.: Attribute reduction in decision-theoretic rough set models using genetic algorithm. In: Panigrahi, B.K., Suganthan, P.N., Das, S., Satapathy, S.C. (eds.) SEMCCO 2011, Part I. LNCS, vol. 7076, pp. 307–314. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  4. Deng, X., Yao, Y.: An information-theoretic interpretation of thresholds in probabilistic rough sets. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 369–378. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Deng, X.F., Yao, Y.Y.: Mean-value-based decision-theoretic shadowed sets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp. 1381–1387 (2013)

    Google Scholar 

  6. Duda, R.O., Hart, P.E.: Pattern classification and scene analysis. Wiley Press, New York (1973)

    MATH  Google Scholar 

  7. Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundamenta Informaticae 108, 267–286 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Jia, X.Y., Liao, W.H., Tang, Z.M., Shang, L.: Minimum cost attribute reduction in decision-theoretic rough set models. Information Sciences 219, 151–167 (2012)

    Article  MathSciNet  Google Scholar 

  9. Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: A three-way view decision model. International Journal of Computational Intelligence Systems 4, 1–11 (2011)

    Article  Google Scholar 

  10. Li, H.X., Zhou, X.Z., Zhao, J.B., Liu, D.: Non-monotonic attribute reduction in decision-theoretic rough sets. Fundamenta Informaticae 126, 415–432 (2013)

    MathSciNet  MATH  Google Scholar 

  11. Li, H., Zhou, X., Huang, B., Liu, D.: Cost-sensitive three-way decision: A sequential strategy. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS, vol. 8171, pp. 325–337. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Liang, D.C., Liu, D., Pedrycz, W., Hu, P.: Triangular fuzzy decision-theoretic rough sets. International Journal of Approximate Reasoning 54, 1087–1106 (2013)

    Article  Google Scholar 

  13. Liang, D.C., Liu, D.: A novel risk decision-making based on decision-theoretic rough sets under hesitant fuzzy information. IEEE Transactions on Fuzzy Systems (2014), doi:10.1109/TFUZZ.2014.2310495

    Google Scholar 

  14. Liang, D.C., Liu, D.: Systematic studies on three-way decisions with interval-valued decision-theoretic rough sets. Information Sciences 276, 186–203 (2014)

    Article  Google Scholar 

  15. Liang, D.C., Liu, D.: Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets. Information Sciences (manuscript)

    Google Scholar 

  16. Lingras, P., Chen, M., Miao, D.Q.: Rough cluster quality index based on decision theory. IEEE Transaction on Knowledge and Data Engineering 21, 1014–1026 (2009)

    Article  Google Scholar 

  17. Liu, D., Li, H.X., Zhou, X.Z.: Two decades’ research on decision-theoretic rough sets. In: Proceeding of 9th IEEE International Conference on Cognitive Informatics, pp. 968–973 (2010)

    Google Scholar 

  18. Liu, D., Yao, Y.Y., Li, T.R.: Three-way investment decisions with decision-theoretic rough sets. International Journal of Computational Intelligence Systems 4, 66–74 (2011)

    Article  Google Scholar 

  19. Liu, D., Li, T.R., Ruan, D.: Probabilistic model criteria with decision-theoretic rough sets. Information Sciences 181, 3709–3722 (2011)

    Article  MathSciNet  Google Scholar 

  20. Liu, D., Li, T.R., Li, H.X.: A multiple-category classification approach with decision-theoretic rough sets. Fundamenta Informaticae 115, 173–188 (2012)

    MathSciNet  MATH  Google Scholar 

  21. Liu, D., Li, T., Liang, D.: Decision-theoretic rough sets with probabilistic distribution. In: Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J., Janicki, R., Hassanien, A.E., Yu, H. (eds.) RSKT 2012. LNCS, vol. 7414, pp. 389–398. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Liu, D., Li, T.R., Liang, D.C.: Three-way government decision analysis with decision-theoretic rough sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 20, 119–132 (2012)

    Article  Google Scholar 

  23. Liu, D., Li, T.R., Li, H.X.: Interval-valued decision-theoretic rough sets. Computer Science 39(7), 178–181 (2012) (in chinese)

    Google Scholar 

  24. Liu, D., Li, T.R., Liang, D.C.: Fuzzy decision-theoretic rough sets. Computer Science 39(12), 25–29 (2012) (in chinese)

    Google Scholar 

  25. Liu, D., Li, T.R., Liang, D.C.: Incorporating logistic regression to decision-theoretic rough sets for classifications. International Journal of Approximate Reasoning 55, 197–210 (2014)

    Article  MathSciNet  Google Scholar 

  26. Liu, D., Li, T.R., Liang, D.C.: Rough Set Theory: A three-way decisions perspective. Journal of Nanjing University: Nat. Sci. Ed. 49(5), 574–581 (2013) (in chinese)

    Google Scholar 

  27. Liu, D., Li, T.R., Liang, D.C.: Fuzzy interval decision-theoretic rough sets. In: Proc. of 2013 IFSA World Congress NAFIPS Annual Meeting, pp. 1315–1320 (2013)

    Google Scholar 

  28. Liu, D., Li, T., Liang, D.: Three-way decisions in dynamic decision-theoretic rough sets. In: Lingras, P., Wolski, M., Cornelis, C., Mitra, S., Wasilewski, P. (eds.) RSKT 2013. LNCS (LNAI), vol. 8171, pp. 291–301. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  29. Ma, W.M., Sun, B.Z.: On relationship between probabilistic rough set and Bayesian risk decision over two universes. International Journal of General Systems 41, 225–245 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. Min, F., He, H.P., Qian, Y.H., Zhu, W.: Test-cost-sensitive attribute reduction. Information Sciences 181, 4928–4942 (2011)

    Article  Google Scholar 

  31. Pawlak, Z.: Rough sets. International Journal of Computer and Information Science 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ślęzak, D., Ziarko, W.: The investigation of the bayesian. International Journal of Approximate Reasoning 40, 81–91 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  33. Yang, X.P., Yao, J.T.: Modelling multi-agent three-way decisions with decision-theoretic rough sets. Fundamenta Informaticae 115, 157–171 (2012)

    MathSciNet  MATH  Google Scholar 

  34. Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-Machine Studies 37, 793–809 (1992)

    Article  Google Scholar 

  35. Yao, Y.: Decision-theoretic rough set models. In: Yao, J., Lingras, P., Wu, W.-Z., Szczuka, M.S., Cercone, N.J., Ślęzak, D. (eds.) RSKT 2007. LNCS (LNAI), vol. 4481, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  36. Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)

    Article  MATH  Google Scholar 

  37. Yao, Y.Y., Zhao, Y.: Attribute reduction in decision-theoretic rough set models. Information Sciences 178, 3356–3373 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  38. Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Information Sciences 180, 341–353 (2010)

    Article  MathSciNet  Google Scholar 

  39. Yao, Y.Y.: The superiority of three-way decision in probabilistic rough set models. Information Sciences 181, 1080–1096 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Yao, Y.Y.: Two semantic issues in a probabilistic rough set model. Fundamenta Informaticae 108, 249–265 (2011)

    MathSciNet  MATH  Google Scholar 

  41. Yao, Y.Y., Deng, X.F.: Sequential three-way decisions with probabilistic rough sets. In: Proc. 10th IEEE International Conference on Cognitive Informatics and Cognitive Computing, pp. 120–125 (2011)

    Google Scholar 

  42. Yao, Y.Y.: Three-way decisions using rough sets. In: Peters, G., et al. (eds.) Rough Sets: Selected Methods and Applications in Management and Engineering, Advanced Information and Knowledge Processing, pp. 79–93 (2012)

    Google Scholar 

  43. Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  44. Yu, H., Liu, Z.G., Wang, G.Y.: An automatic method to determine the number of clusters using decision-theoretic rough set. International Journal of Approximate Reasoning 55, 101–115 (2014)

    Article  MathSciNet  Google Scholar 

  45. Zhao, Y., Wong, S.K.M., Yao, Y.: A note on attribute reduction in the decision-theoretic rough set model. In: Peters, J.F., Skowron, A., Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) Transactions on Rough Sets XIII. LNCS, vol. 6499, pp. 260–275. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  46. Zhou, B.: A new formulation of multi-category decision-theoretic rough sets. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS (LNAI), vol. 6954, pp. 514–522. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  47. Zhou, B.: Multi-class decision-theoretic rough sets. International Journal of Approximate Reasoning, 211–224 (2014)

    Google Scholar 

  48. Ziarko, W.: Probabilistic approach to rough set. International Journal of Approximate Reasoning 49, 272–284 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Economics and Management, Southwest Jiaotong University, Chengdu, 610031, P.R. China

    Dun Liu

  2. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 610054, P.R. China

    Decui Liang

Authors
  1. Dun Liu
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  2. Decui Liang
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Corresponding author

Correspondence to Dun Liu .

Editor information

Editors and Affiliations

  1. Tongji University, Shanghai, China

    Duoqian Miao

  2. Department of Electrical and Computer En, University of Alberta, Edmonton, Alberta, Canada

    Witold Pedrycz

  3. University of Warsaw, Warsaw, Poland

    Dominik Ślȩzak

  4. University of Applied Sciences, München, Germany

    Georg Peters

  5. Tianjin University, Tianjin, China

    Qinghua Hu

  6. Tongji University, Shanghai, China

    Ruizhi Wang

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Liu, D., Liang, D. (2014). An Overview of Function Based Three-Way Decisions. In: Miao, D., Pedrycz, W., Ślȩzak, D., Peters, G., Hu, Q., Wang, R. (eds) Rough Sets and Knowledge Technology. RSKT 2014. Lecture Notes in Computer Science(), vol 8818. Springer, Cham. https://doi.org/10.1007/978-3-319-11740-9_74

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  • DOI: https://doi.org/10.1007/978-3-319-11740-9_74

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11739-3

  • Online ISBN: 978-3-319-11740-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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