Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29284


Select areas to restrict search in scientific publication database:
16791
A Family of Entropies on Interval-valued Intuitionistic Fuzzy Sets and Their Applications in Multiple Attribute Decision Making
Abstract:
The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFS. Firstly, we propose a family of entropies on IvIFS with a parameter λ ∈ [0, 1], which generalize two entropy measures defined independently by Zhang and Wei, for IvIFS, and then we prove that the new entropy is an increasing function with respect to the parameter λ. Furthermore, a new multiple attribute decision making (MADM) method using entropy-based attribute weights is proposed to deal with the decision making situations where the alternatives on attributes are expressed by IvIFS and the attribute weights information is unknown. Finally, a numerical example is given to illustrate the applications of the proposed method.
Digital Object Identifier (DOI):

References:


[1] Zadeh L.A., Fuzzy Sets. Information and Control, 1965, 8: 338-353.
[2] Atanassov K., Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986, 20: 87-96.
[3] Atanassov K., Gargov G., Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1989, 31(3): 343-349.
[4] DeLuca A., Termini S., A deTnition of nonprobabilistic entropy in the setting of fuzzy sets theory. Information and Control, 1972, 20: 301-312.
[5] Kaufmann A., Introduction to the theory of fuzzy sets: Fundamental Theoretical Elements, Vol.1, Academic Press, New York, 1975.
[6] Yager R.R., On themeasure of fuzziness and negation. Part 1: Membership in the unit interval, Internat. J. General System, 1979, 5: 221-229.
[7] Szmidt E., Kacprzyk J., Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 2001, 118: 467-477.
[8] Bustince H., Burillo P., Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Systems, 1996, 79: 403-405.
[9] Hung W., A note on entropy of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2003, 11(5): 627-633.
[10] Zhang H., Zhang W., Mei C., Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowledge- Based Systems, 2009, 22(6): 449-454.
[11] Vlachos I., Sergiadis G., Intuitionistic fuzzy information- Applications to pattern recognition. Pattern Recognition Letters, 2007, 28(2): 197-206.
[12] Zeng, W., Yu F., Yu X., Chen H. and Wu S., Entropy of intuitionistic fuzzy set based on similarity measure. International Journal of Innovative Computing, Information and Control, 2009, 5(12): 4737-4744.
[13] Zhang Y.J., Ma P.J., Su X.H., Zhang C.P., Entropy on Interval-valued Intuitionistic Fuzzy Sets and Its Application in Multi-attribute Decision Making. 2011 Proceedings of the 14th International Conference on Information Fusion (FUSION), 2011, 1-7.
[14] Ye J., Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Applied Mathematical Modelling, 2010, 34(12): 3864-3870.
[15] Zhang Q.S., Jiang S.Y., Jia B.G. and Luo S.H., Some information measures for interval-valued intuitionistic fuzzy sets. Information Sciences, 2010, 180: 5130-5145.
[16] Wei C.P, Wang P., Zhang Y.Z., Entropy, similarity measure of intervalvalued intuitionistic fuzzy sets and their applications. Information Sciences, 2011, 181: 4273-4286.
[17] Wei C.P., Gao Z.H., An intuitionistic fuzzy entropy measure based on the trigonometric function. Control and Decision(Accepted).
[18] Qi X.W., Liang C.Y., Zhang E.Q., Ding Y., Approach to intervalvalued intuitionistic fuzzy multiple attributes group decision making based on maximum entropy. Systems Engineering-Theory and Practice, 2011, 31(10): 1940-1948.
[19] Xu Z.S., Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision, 2007, 22(2): 215-219.
[20] Wei G.W., Zhao X.F., Lin R., Wang H.J., Generalized triangular fuzzy correlated averaging operator and their application to multiple attribute decision making. Applied Mathematical Modelling, 2011, doi:10.1016/j.apm.2011.09.062.
[21] Ye J., Multiple Attribute Group Decision-Making Methods with Completely UnknownWeights in Intuitionistic Fuzzy Setting and Interval- Valued Intuitionistic Fuzzy Setting. Group Decis. Negot., 2011, DOI 10.1007/s10726-011-9255-5.

Vol:13 No:02 2019Vol:13 No:01 2019
Vol:12 No:12 2018Vol:12 No:11 2018Vol:12 No:10 2018Vol:12 No:09 2018Vol:12 No:08 2018Vol:12 No:07 2018Vol:12 No:06 2018Vol:12 No:05 2018Vol:12 No:04 2018Vol:12 No:03 2018Vol:12 No:02 2018Vol:12 No:01 2018
Vol:11 No:12 2017Vol:11 No:11 2017Vol:11 No:10 2017Vol:11 No:09 2017Vol:11 No:08 2017Vol:11 No:07 2017Vol:11 No:06 2017Vol:11 No:05 2017Vol:11 No:04 2017Vol:11 No:03 2017Vol:11 No:02 2017Vol:11 No:01 2017
Vol:10 No:12 2016Vol:10 No:11 2016Vol:10 No:10 2016Vol:10 No:09 2016Vol:10 No:08 2016Vol:10 No:07 2016Vol:10 No:06 2016Vol:10 No:05 2016Vol:10 No:04 2016Vol:10 No:03 2016Vol:10 No:02 2016Vol:10 No:01 2016
Vol:9 No:12 2015Vol:9 No:11 2015Vol:9 No:10 2015Vol:9 No:09 2015Vol:9 No:08 2015Vol:9 No:07 2015Vol:9 No:06 2015Vol:9 No:05 2015Vol:9 No:04 2015Vol:9 No:03 2015Vol:9 No:02 2015Vol:9 No:01 2015
Vol:8 No:12 2014Vol:8 No:11 2014Vol:8 No:10 2014Vol:8 No:09 2014Vol:8 No:08 2014Vol:8 No:07 2014Vol:8 No:06 2014Vol:8 No:05 2014Vol:8 No:04 2014Vol:8 No:03 2014Vol:8 No:02 2014Vol:8 No:01 2014
Vol:7 No:12 2013Vol:7 No:11 2013Vol:7 No:10 2013Vol:7 No:09 2013Vol:7 No:08 2013Vol:7 No:07 2013Vol:7 No:06 2013Vol:7 No:05 2013Vol:7 No:04 2013Vol:7 No:03 2013Vol:7 No:02 2013Vol:7 No:01 2013
Vol:6 No:12 2012Vol:6 No:11 2012Vol:6 No:10 2012Vol:6 No:09 2012Vol:6 No:08 2012Vol:6 No:07 2012Vol:6 No:06 2012Vol:6 No:05 2012Vol:6 No:04 2012Vol:6 No:03 2012Vol:6 No:02 2012Vol:6 No:01 2012
Vol:5 No:12 2011Vol:5 No:11 2011Vol:5 No:10 2011Vol:5 No:09 2011Vol:5 No:08 2011Vol:5 No:07 2011Vol:5 No:06 2011Vol:5 No:05 2011Vol:5 No:04 2011Vol:5 No:03 2011Vol:5 No:02 2011Vol:5 No:01 2011
Vol:4 No:12 2010Vol:4 No:11 2010Vol:4 No:10 2010Vol:4 No:09 2010Vol:4 No:08 2010Vol:4 No:07 2010Vol:4 No:06 2010Vol:4 No:05 2010Vol:4 No:04 2010Vol:4 No:03 2010Vol:4 No:02 2010Vol:4 No:01 2010
Vol:3 No:12 2009Vol:3 No:11 2009Vol:3 No:10 2009Vol:3 No:09 2009Vol:3 No:08 2009Vol:3 No:07 2009Vol:3 No:06 2009Vol:3 No:05 2009Vol:3 No:04 2009Vol:3 No:03 2009Vol:3 No:02 2009Vol:3 No:01 2009
Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007