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The Use of Intuitionistic Fuzzy Values in Rule-Base Evidential Reasoning

  • Ludmila Dymova
  • Pavel Sevastjanov
  • Kamil Tkacz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7894)

Abstract

A new approach to the rule-base evidential reasoning based on the synthesis of fuzzy logic, Atannasov’s intuitionistic fuzzy sets theory and the Dempster-Shafer theory of evidence is proposed. It is shown that the use of intuitionistic fuzzy values and the classical operations on them directly may provide counter-intuitive results. Therefore, an interpretation of intuitionistic fuzzy values in the framework of Dempster-Shafer theory is proposed and used in the evidential reasoning. Using the real-world example, it is shown that such an approach provides reasonable and intuitively obvious results when the classical method of rule-base evidential reasoning cannot produce any reasonable results.

Keywords

Rule-base evidential reasoning Atannasov’s intuitionistic fuzzy sets Dempster-Shafer Theory 

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References

  1. 1.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Atanassov, K.: New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems 61, 137–142 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Springer Physica-Verlag, Berlin (1999)zbMATHCrossRefGoogle Scholar
  4. 4.
    Binaghi, E., Madella, P.: Fuzzy Dempster-Shafer reasoning for rule-based classifiers. Intelligent Syst. 14, 559–583 (1999)zbMATHCrossRefGoogle Scholar
  5. 5.
    Binaghi, E., Gallo, I., Madella, P.: A neural model for fuzzy Dempster-Shafer classifiers. International Journal of Approximate Reasoning 25, 89–121 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Chen, S.M., Tan, J.M.: Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 67, 163–172 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Dey, S.K., Biswas, R., Roy, A.R.: Some operations on intuitionistic fuzzy sets. Fuzzy Sets and Systems 114, 477–484 (2000)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Dempster, A.P.: Upper and lower probabilities induced by a muilti-valued mapping. Ann. Math. Stat. 38, 325–339 (1967)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., Prade, H.: Terminological difficulties in fuzzy set theory-The case of “Intuitionistic Fuzzy Sets”. Fuzzy Sets and Systems 156, 485–491 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Dymova, L., Sevastjanov, P.: An interpretation of intuitionistic fuzzy sets in terms of evidence theory: Decision making aspect. Knowledge-Based Systems 23, 772–782 (2010)CrossRefGoogle Scholar
  11. 11.
    Dymova, L., Sevastianov, P., Bartosiewicz, P.: A new approach to the rule-base evidential reasoning: Stock trading expert system application. Expert Systems with Applications 37, 5564–5576 (2010)CrossRefGoogle Scholar
  12. 12.
    Dymova, L., Sevastjanov, P.: The operations on intuitionistic fuzzy values in the framework of Dempster-Shafer theory. Knowledge-Based Systems 35, 132–143 (2012)CrossRefGoogle Scholar
  13. 13.
    Dymova, L., Sevastianov, P., Kaczmarek, K.: A stock trading expert system based on the rule-base evidential reasoning using Level 2 Quotes. Expert Systems with Applications 39, 7150–7157 (2012)CrossRefGoogle Scholar
  14. 14.
    Hong, D.H., Choi, C.-H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114, 103–113 (2000)zbMATHCrossRefGoogle Scholar
  15. 15.
    Ishizuka, M., Fu, K.S., Yao, J.T.P.: Inference procedure and uncertainty for the problem reduction method. Inform. Sci. 28, 179–206 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Khatibi, V., Montazer, G.A.: A fuzzy-evidential hybrid inference engine for coronary heart disease risk assessment. Expert Systems with Applications 37, 8536–8542 (2010)CrossRefGoogle Scholar
  17. 17.
    Sevastianov, P., Dymova, L., Bartosiewicz, P.: A framework for rule-base evidential reasoning in the interval setting applied to diagnosing type 2 diabetes. Expert Systems with Applications 39, 4190–4200 (2012)CrossRefGoogle Scholar
  18. 18.
    Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  19. 19.
    Straszecka, E.: Combining uncertainty and imprecision in models of medical diagnosis. Information Sciences 176, 3026–3059 (2006)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Xu, Z.: Intuitionistic preference relations and their application in group decision making. Information Sciences 177, 2363–2379 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Xu, D.-L., Liu, J., Yang, J.-B., Liu, G.-P., Wang, J., Jenkinson, I., Ren, J.: Inference and learning methodology of belief-rule-based expert system for pipeline leak detection. Expert Systems with Applications 32, 103–113 (2007)CrossRefGoogle Scholar
  22. 22.
    Yager, R.R.: Generalized probabilities of fuzzy events from belief structures. Information Sciences 28, 45–62 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Yang, J.B.: Rule and utility based evidential reasoning approach for multi-attribute decision analysis under uncertainties. European Journal of Operational Research 131, 31–61 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Yang, J.B., Liu, J., Wang, J., Sii, H.S., Wang, H.: Belief rule-base inference methodology using the evidential reasoning approach - RIMER. IEEE Transactions on Systems Man and Cybernetics. Part A-Systems and Humans 36(2), 266–285 (2006)CrossRefGoogle Scholar
  25. 25.
    Yang, J.B., Liu, J., Xu, D.L., Wang, J., Wang, H.: Optimization Models for Training Belief-Rule-Based Systems. IEEE Transactions on Systems Man and Cybernetics, Part A-Systems and Humans 37(4), 569–585 (2007)CrossRefGoogle Scholar
  26. 26.
    Yen, J.: Generalizing the Dempster-Shafer theory to fuzzy sets. IEEE Transactions on Systems Man and Cybernetics 20, 559–570 (1990)zbMATHCrossRefGoogle Scholar
  27. 27.
    Zadeh, L.: A simple view of the Dempster-Shafer theory of evidence and its application for the rule of combination. AI Magazine 7, 85–90 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ludmila Dymova
    • 1
  • Pavel Sevastjanov
    • 1
  • Kamil Tkacz
    • 1
  1. 1.Institute of Comp.& Information Sci.Czestochowa University of TechnologyCzestochowaPoland

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