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A novel entropy of intuitionistic fuzzy sets based on similarity and its application in finance

Published: 01 January 2022 Publication History

Abstract

In this paper, we propose a new formula for the entropy based on similarity measures of intuitionistic fuzzy sets (IFS). The contribution of this work is the proof that the new formula satisfies all the conditions of entropy. The experimentation on some examples shows that the new entropy is useful. Besides, we use the new entropy and similarity measures to design an algorithm for ranking assets in stock markets. The numerical results on 5 benchmark data sets were reported. It points out that the entropy and the similarity measures of IFS may provide an alternative tool for solving portfolio selection problems.

References

[1]
Shen F., Xu J. and Xu Z., An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets, Information Sciences 334 (2016), 338–353.
[2]
Zadeh L.A., Fuzzy sets, Information and Control 8(3) (1965), 338–353. Available from: https://www.sciencedirect.com/science/article/pii/S001999586590241X.
[3]
Atanassov K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87–96. Available from: https://www.sciencedirect.com/science/article/pii/S0165011486800343.
[4]
Huang J., Jin X., Lee S.J., Huang S. and Jiang Q., An effective similarity/distance measure between intuitionistic fuzzy sets based on the areas of transformed isosceles right triangle and its applications, Journal of Intelligent & Fuzzy Systems (Preprint) (2021), 1–21.
[5]
Jiang Q., Jin X., Lee S.J. and Yao S., A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition, Expert Systems with Applications 116 (2019), 439–453.
[6]
Thao N.X. and Duong T.T.T., Selecting target market by similar measures in interval intuitionistic fuzzy set, Technological and Economic Development of Economy 25(5) (2019), 934–950.
[7]
Kumari R. and Mishra A.R., Multi-criteria COPRAS method based on parametric measures for intuitionistic fuzzy sets: application of green supplier selection, Iranian Journal of Science and Technology, Transactions of Electrical Engineering 44(4) (2020), 1645–1662.
[8]
Meng F. and Chen X., Entropy and similarity measure of Atanassov’s intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures, Pattern Analysis and Applications 19(1) (2016), 11–20.
[9]
Joshi R. and Kumar S., A novel fuzzy decision-making method using entropy weights-based correlation coefficients under intuitionistic fuzzy environment, International Journal of Fuzzy Systems 21(1) (2019), 232–242.
[10]
Singh S. and Sharma S., On a generalized entropy and dissimilarity measure in intuitionistic fuzzy environment with applications, Soft Computing 25(11) (2021), 7493–7514.
[11]
Gohain B., Dutta P., Gogoi S. and Chutia R., Construction and generation of distance and similarity measures for intuitionistic fuzzy sets and various applications, International Journal of Intelligent Systems (2021).
[12]
De Luca A. and Termini S., A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Information and Control 20(4) (1972), 301–312.
[13]
Batyrshin I., On fuzzinesstic measures of entropy on Kleene algebras, Fuzzy Sets and Systems 34(1) (1990), 47–60.
[14]
Wang J.Q., Peng J.J., Zhang H.Y. and Chen X.H., Outranking approach for multi-criteria decision-making problems with hesitant interval-valued fuzzy sets, Soft Computing 23(2) (2019), 419–430.
[15]
Burillo P. and Bustince H., Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78(3) (1996), 305–316.
[16]
Szmidt E. and Kacprzyk J., Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems 118(3) (2001), 467–477.
[17]
Hung W.L. and Yang M.S., Fuzzy entropy on intuitionistic fuzzy sets, International Journal of Intelligent Systems 21(4) (2006), 443–451.
[18]
Zhu Y.J. and Li D.F., A new definition and formula of entropy for intuitionistic fuzzy sets, Journal of Intelligent & Fuzzy Systems 30(6) (2016), 3057–3066.
[19]
Joshi R. and Kumar S., A new parametric intuitionistic fuzzy entropy and its applications in multiple attribute decision making, International Journal of Applied and Computational Mathematics 4(1) (2018), 1–23.
[20]
Ye J., Two effective measures of intuitionistic fuzzy entropy, Computing 87(1) (2010), 55–62.
[21]
Thao N.X. and Chou S.Y., Novel similarity measures, entropy of intuitionistic fuzzy sets and their application in software quality evaluation, Soft Computing 2021, 1–12.
[22]
Ansari M.D., Mishra A.R. and Ansari F.T., New divergence and entropy measures for intuitionistic fuzzy sets on edge detection, International Journal of Fuzzy Systems 20(2) (2018), 474–487.
[23]
Markowitz H., Portfolio Selection, The Journal of Finance 7(1) (1952), 77–91. Available from: http://www.jstor.org/stable/2975974.
[24]
Campbell R., Huisman R. and Koedijk K., Optimal portfolio selection in a Value-at-Risk framework, Journal of Banking & Finance 25(9) (2001), 1789–1804.
[25]
Yao H., Li Z., Li X. and Zeng Y., Optimal Sharpe ratio in continuous-time markets with and without a risk-free asset, Journal of Industrial & Management Optimization 13(3) (2017), 1273.
[26]
Le Thi H.A. and Tran D.Q., Solving continuous min max problem for single period portfolio selection with discrete constraints by DCA, Optimization 61(8) (2012), 1025–1038.
[27]
Jimbo H.C., Ngongo I.S., Andjiga N.G., Suzuki T. and Onana C.A., Portfolio optimization under cardinality constraints: A comparative study, Open Journal of Statistics 7(4) (2017), 731–742.
[28]
Chou S., Duong T.T. and Xuan N., Thao, Renewable energy selection based on a new entropy and dissimilarity measure on an interval-valued neutrosophic set, Journal of Intelligent & Fuzzy Systems (Preprint) 1–18.
[29]
Song Y., Wang X., Quan W. and Huang W., A new approach to construct similarity measure for intuitionistic fuzzy sets, Soft Computing 23(6) (2019), 1985–1998.
[30]
Quynh T.D., Thao N.X., Thuan N.Q. and Van Dinh N., A new similarity measure of IFSs and its applications, In: 2020 12th International Conference on Knowledge and Systems Engineering (KSE). IEEE (2020), 242–246.
[31]
Cesarone F., Scozzari A. and Tardella F., Efficient algorithms for mean-variance portfolio optimization with hard real-world constraints, Citeseer (2009).

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              cover image Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
              Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology  Volume 43, Issue 4
              2022
              1429 pages

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              IOS Press

              Netherlands

              Publication History

              Published: 01 January 2022

              Author Tags

              1. Intuitionistic fuzzy set
              2. similarity measures
              3. stock markets
              4. assets ranking
              5. entropy

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