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An Interpretation of Intuitionistic Fuzzy Sets in the Framework of the Dempster-Shafer Theory

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Book cover Artificial Intelligence and Soft Computing (ICAISC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6113))

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Abstract

A new interpretation of Intuitionistic Fuzzy Sets in the framework of the Dempster-Shafer Theory is proposed. Such interpretation allows us to reduce all mathematical operations on the Intuitionistic Fuzzy values to the operations on belief intervals. The proposed approach is used for the solution of Multiple Criteria Decision Making (MCDM) problem in the Intuitionistic Fuzzy setting.

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References

  1. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Atanassov, K.T.: New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems 61, 137–142 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Beynon, M., Curry, B., Morgan, P.: The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modeling. Omega 28, 37–50 (2000)

    Article  Google Scholar 

  4. 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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dempster, A.P.: Upper and lower probabilities induced by a muilti-valued mapping. Ann. Math. Stat. 38, 325–339 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dempster, A.P.: A generalization of Bayesian inference (with discussion). J. Roy. Stat. Soc., Series B 30, 208–247 (1968)

    MathSciNet  Google Scholar 

  7. Denoeux, T.: Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artificial Intelligence 172, 234–264 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  8. Deschrijver, G., Kerre, E.E.: On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. Information Sciences 177, 1860–1866 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4, 244–264 (1998)

    Article  Google Scholar 

  10. Hong, D.H., Choi, C.-H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114, 103–113 (2000)

    Article  MATH  Google Scholar 

  11. Hua, Z., Gong, B., Xu, X.: A DS-AHP approach for multi-attribute decision making problem with incomplete information. Expert Systems with Applications 34, 2221–2227 (2008)

    Article  Google Scholar 

  12. Li, D.-F.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences 70, 73–85 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Murphy, C.K.: Combining belief functions when evidence coflicts. Decision Support Systems 29, 1–9 (2000)

    Article  Google Scholar 

  14. Sevastjanov, P.: Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster-Shafer theory. Information Sciences 177 (2007)

    Google Scholar 

  15. Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)

    MATH  Google Scholar 

  16. Smets, P.: The combination of evidence in the transferable belief model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 447–458 (1990)

    Article  Google Scholar 

  17. Xu, Z.: Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems 15, 1179–1187 (2007)

    Article  Google Scholar 

  18. Xu, Z., Yager, R.R.: Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning 48, 246–262 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  19. Yager, R.R.: On the Dempster-Shafer framework and new combitanion rules. Information Sciences 41, 93–138 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  20. 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 

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Author information

Authors and Affiliations

  1. Institute of Comp.& Information Sci., Czestochowa University of Technology, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Ludmila Dymova & Pavel Sevastjanov

Authors
  1. Ludmila Dymova
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  2. Pavel Sevastjanov
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Editor information

Editors and Affiliations

  1. Department of Artificial Intelligence, Academy of Humanities and Economics, Poland

    Leszek Rutkowski

  2. Academy of Humanities and Economics in Łódź,, ul. Rewolucji 1905 nr 64, Łódź, Poland

    Rafał Scherer

  3. Institute of Automatics,, AGH University of Science and Technology, Al. Mickiewicza 30, PL-30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  4. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Initiative in Soft Computing (BISC), 94720-1776, Berkeley, CA,  

    Lotfi A. Zadeh

  5. Computational Intelligence Laboratory Department of Electrical and Computer Engineering, University of Louisville, 40292, Louisville, KY

    Jacek M. Zurada

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© 2010 Springer-Verlag Berlin Heidelberg

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Dymova, L., Sevastjanov, P. (2010). An Interpretation of Intuitionistic Fuzzy Sets in the Framework of the Dempster-Shafer Theory. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2010. Lecture Notes in Computer Science(), vol 6113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13208-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-13208-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13207-0

  • Online ISBN: 978-3-642-13208-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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