Abstract
In this paper, we review some existing entropies of interval-valued fuzzy set, and propose some new formulas to calculate the entropy of interval-valued fuzzy set. Finally, we give one comparison with some existing entropies to illustrate our proposed entropies reasonable.
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References
Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg (1999)
Bustince, H., Burillo, P.: Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems 78, 305–316 (1996)
De Luca, A., Termini, S.: A definition of non-probabilistic entropy in the setting of fuzzy sets theory. Inform. and Control 20, 301–312 (1972)
Deschrijver, G., Kerre, E.E.: On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems 133, 227–235 (2003)
Deschrijver, G.: Arithmetic operators in interval-valued fuzzy set theory. Information Sciences 177, 2906–2924 (2007)
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)
Grzegorzewski, P.: Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets and Systems 148, 319–328 (2004)
Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets-Fundamental Theoretical Elements, vol. 1. Academic Press, New York (1975)
Wang, G.J., He, Y.Y.: Intuitionistic fuzzy sets and L-fuzzy sets. Fuzzy Sets and Systems 110, 271–274 (2000)
Wang, G.J., Li, X.P.: On the IV-fuzzy degree and the IV-similarity degree of IVFS and their integral representation. J. Engineering Mathematics 21, 195–201 (2004)
Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S.: On the combination and normalization of interval-valued belief structures. Information Sciences 177, 1230–1247 (2007)
Yager, R.R.: On the measure of fuzziness and negation, Part I: Membership in the unit interval. Internat. J. General Systems 5, 189–200 (1979)
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning (I). Inform. Sci. 8, 199–249 (1975)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning (II). Inform. Sci. 8, 301–357 (1975)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning (III). Inform. Sci. 9, 43–80 (1975)
Zeng, W.Y., Li, H.X.: Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets and Systems 157, 1477–1484 (2006)
Zeng, W.Y., Li, H.X.: Inclusion measure, similarity measure and the fuzziness of fuzzy sets and their relations. International J. Intelli. Systems 21, 639–653 (2006)
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Zeng, W., Li, H., Feng, S. (2011). Some New Entropies on the Interval-Valued Fuzzy Set. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_22
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DOI: https://doi.org/10.1007/978-3-642-22833-9_22
Publisher Name: Springer, Berlin, Heidelberg
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