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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)
Atanassov, K.T.: New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems 61, 137–142 (1994)
Beynon, M., Curry, B., Morgan, P.: The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modeling. Omega 28, 37–50 (2000)
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)
Dempster, A.P.: Upper and lower probabilities induced by a muilti-valued mapping. Ann. Math. Stat. 38, 325–339 (1967)
Dempster, A.P.: A generalization of Bayesian inference (with discussion). J. Roy. Stat. Soc., Series B 30, 208–247 (1968)
Denoeux, T.: Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artificial Intelligence 172, 234–264 (2008)
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)
Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4, 244–264 (1998)
Hong, D.H., Choi, C.-H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114, 103–113 (2000)
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)
Li, D.-F.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences 70, 73–85 (2005)
Murphy, C.K.: Combining belief functions when evidence coflicts. Decision Support Systems 29, 1–9 (2000)
Sevastjanov, P.: Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster-Shafer theory. Information Sciences 177 (2007)
Shafer, G.: A mathematical theory of evidence. Princeton University Press, Princeton (1976)
Smets, P.: The combination of evidence in the transferable belief model. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 447–458 (1990)
Xu, Z.: Intuitionistic fuzzy aggregation operators. IEEE Transactions on Fuzzy Systems 15, 1179–1187 (2007)
Xu, Z., Yager, R.R.: Dynamic intuitionistic fuzzy multi-attribute decision making. International Journal of Approximate Reasoning 48, 246–262 (2008)
Yager, R.R.: On the Dempster-Shafer framework and new combitanion rules. Information Sciences 41, 93–138 (1987)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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)