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Probabilistic Estimation for Generalized Rough Modus Ponens and Rough Modus Tollens

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Book cover Rough Sets (IJCRS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9920))

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Abstract

We review concepts and principles of Modus Ponens and Modus Tollens in the areas of rough set theory and probabilistic inference. Based on the upper and the lower approximation of a set as well as the existing probabilistic results, we establish a generalized version of rough Modus Ponens and rough Modus Tollens with a new fact different from the premise (or the conclusion) of “if ...then ...” rule, and address the problem of computing the conditional probability of the conclusion given the new fact (or of the premise given the new fact) from the probability of the new fact and the certainty factor of the rule. The solutions come down to the corresponding interval for the conditional probabilities, which are more appropriate than the exact values in the environment full of uncertainty due to errors and inconsistency existed in measurement, judgement, management, etc., plus illustration analysis.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. Bareinboim, E., Pearl, J.: Causal inference from big data: theoretical foundations and the data-fusion problem. UCLA Cognitive Systems Laboratory, Technical Report (R-450) (2015). Proceedings of the National Academy of Sciences (2016)

    Google Scholar 

  3. Greco, S., Pawlak, Z., Słowiński, R.: Generalized decision algorithms, rough inference rules, and flow graphs. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 93–104. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Inuiguchi, M., Greco, S., Słowiński, R.: Fuzzy-rough modus ponens and modus tollens as a basis for approximate reasoning. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 84–94. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Johnson-Laird, P.N., Khemlani, S.S., Goodwin, G.P.: Logic, probability, and human reasoning. Trends Cogn. Sci. 19(4), 201–214 (2015)

    Article  Google Scholar 

  6. Jue, W., Yiyu, Y., Feiyue, W.: ‘Rule plus Exception’ learning based on reduct. Chin. J. Comput. (11), 1778–1789 (2005)

    Google Scholar 

  7. Pawlak, Z.: Rough probability. Bull. Polish Acad. Sci. Tech. 33(9–10), 499–504 (1985)

    MathSciNet  MATH  Google Scholar 

  8. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    Book  MATH  Google Scholar 

  9. Pawlak, Z., Skowron, A.: Rough membership functions: a tool for reasoning with uncertainty. In: Algebraic Methods in Logic and in Computer Science, Banach Center Publications, vol. 28, pp. 135–150 (1993)

    Google Scholar 

  10. Pawlak, Z.: Rough Modus Ponens. In: Traitement d’information et gestion d’incertitudes dans les systèmesà base de connaissances. Conférence Internationale, pp. 1162–1166 (1998)

    Google Scholar 

  11. Pawlak, Z.: Rough sets, decision algorithms and Bayes’ theorem. Eur. J. Oper. Res. 136(1), 181–189 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wagner, C.G.: Modus tollens probabilized. British J. Philos. Sci. 55(4), 747–753 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Pfeifer, N., Kleiter, G.D.: Inference in conditional probability logic. Kybernetika 42(4), 391–404 (2006)

    MathSciNet  MATH  Google Scholar 

  14. Ślȩzak, D., Ziarko, W.: The investigation of the bayesian rough set model. Int. J. Approximate Reason. 40(40), 81–91 (2005)

    MathSciNet  MATH  Google Scholar 

  15. Sobel, J.H.: Modus Ponens and Modus Tollens for conditional probabilities, and updating on uncertain evidence. Theor. Decis. 66(2), 103–148 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough sets models. Inf. Sci. 181(6), 1080–1096 (2011)

    Article  MATH  Google Scholar 

  17. Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 3, 28–44 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang, H.Y., Zhou, J., Miao, D.Q., Gao, C.: Bayesian rough set model: a further investigation. Int. J. Approximate Reason. 53(4), 541–557 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhang, X.Y., Miao, D.Q., Liu, C.H., Le, M.L.: Constructive methods of rough approximation operators and multigranulation rough sets. Knowl. Based Syst. 91, 114–125 (2016)

    Article  Google Scholar 

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Acknowledgments

The authors would like to thank the reviewers for their comments that help improve the manuscript. This research was supported in parts by the National Natural Science Foundation of China (No. 61273304, 61202170, 61573255, 61573259), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130072130004), and the program of Further Accelerating the Development of Chinese Medicine Three Year Action of Shanghai (2014–2016) (No. ZY3-CCCX-3-6002).

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Authors and Affiliations

  1. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, China

    Ning Yao, Duoqian Miao, Zhifei Zhang & Guangming Lang

  2. The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai, 201804, China

    Ning Yao, Duoqian Miao, Zhifei Zhang & Guangming Lang

Authors
  1. Ning Yao
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  2. Duoqian Miao
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  3. Zhifei Zhang
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  4. Guangming Lang
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Corresponding author

Correspondence to Duoqian Miao .

Editor information

Editors and Affiliations

  1. Universidad Católica del Norte, Antofagasta, Chile

    Víctor Flores

  2. University of Campinas, Campinas, SP, Brazil

    Fernando Gomide

  3. University of Warsaw, Warsaw, Poland

    Andrzej Janusz

  4. Universidad del Católica del Norte, Antofagasta, Chile

    Claudio Meneses

  5. Tongji University, Shanghai, China

    Duoqian Miao

  6. University of Applied Sciences, Munich, Germany

    Georg Peters

  7. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  8. Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

  9. Universidad de Chile, Santiago, Chile

    Richard Weber

  10. University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

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Yao, N., Miao, D., Zhang, Z., Lang, G. (2016). Probabilistic Estimation for Generalized Rough Modus Ponens and Rough Modus Tollens. In: Flores, V., et al. Rough Sets. IJCRS 2016. Lecture Notes in Computer Science(), vol 9920. Springer, Cham. https://doi.org/10.1007/978-3-319-47160-0_15

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  • DOI: https://doi.org/10.1007/978-3-319-47160-0_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47159-4

  • Online ISBN: 978-3-319-47160-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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