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Triangular entropy of uncertain variables with application to portfolio selection

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Abstract

Entropy is used as a measure to characterize the uncertainty. So far, entropy for uncertain variables in the forms of logarithm function and triangular function has been proposed. This paper mainly studies the concept of triangular entropy, and verifies its properties such as translation invariance and positive linearity. As an application, this paper also considers a mean-variance portfolio selection problem with triangular entropy as a constraint.

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References

  • Bezdek JC (1973) Fuzzy mathematics in pattern classification, Ph.D. Dissertation, Cornell University

  • Chen XW, Dai W (2011) Maximum entropy principle for uncertain variables. Int J Fuzzy Syst 13(3):232–236

    MathSciNet  Google Scholar 

  • Chen XW, Kar S, Ralescu DA (2012) Cross-entropy measure of uncertain variables. Inform Sci 201:53–60

    Article  MathSciNet  MATH  Google Scholar 

  • Dai W (2014) Quadratic entropy of uncertain variables. Inform Int Interdiscip J (to be published)

  • Dai W, Chen XW (2012) Entropy of function of uncertain variables. Math Comput Model 55(3–4):754–760

    Article  MathSciNet  MATH  Google Scholar 

  • Gao X (2009) Some properties of continuous uncertain measure. Int J Uncertain Fuzziness Knowl Based Syst 17(3):419–426

    Article  MATH  Google Scholar 

  • Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106(4):620–630

    Article  MathSciNet  Google Scholar 

  • Jiao DY, Yao K (2014) An interest rate model in uncertain environment. Soft Comput. doi:10.1007/s00500-014-1301-1

  • Kapur J, Kesavan H (1992) Entropy optimization principles with applications. Academic Press, New York

    Book  MATH  Google Scholar 

  • Li X, Liu BD (2007) Maximum entropy principle for fuzzy variables. Int J Uncertain Fuzziness Knowl Based Syst 15(2):43–52

    Article  Google Scholar 

  • Li PK, Liu BD (2008) Entropy of credibility distributions for fuzzy variables. IEEE Trans Fuzzy Syst 16(1):123–129

    Article  Google Scholar 

  • Liu BD (2013) Toward uncertain finance theory. J Uncertainty Anal Appl 1. Article 1

  • Liu BD (2004) Uncertainty theory: an introduction to its axiomatic foundation. Springer, Berlin

    Book  Google Scholar 

  • Liu BD (2007) Uncertainty theory, 2nd edn. Springer, Berlin

    Google Scholar 

  • Liu BD (2009) Some research problems in uncertainty theory. J Uncertain Syst 3(1):3–10

    Google Scholar 

  • Liu BD (2010) Uncertain risk analysis and uncertain reliability analysis. J Uncertain Syst 4(3):163–170

    Google Scholar 

  • Liu BD (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin

    Book  Google Scholar 

  • Liu BD (2010) Uncertain set theory and uncertain inference rule with application to uncertain control. J Uncertain Syst 4(2):83–98

    Google Scholar 

  • Liu YH, Ha MH (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(3):181–186

    Google Scholar 

  • Liu BD (2011) Uncertain logic for modeling human language. J Uncertain Syst 5(1):3–20

    Google Scholar 

  • De Luca A, Termini S (1972) A definition of nonprobabilitistic entropy in the setting of fuzzy sets theory. Inform Control 20:301–312

    Article  MATH  Google Scholar 

  • Pal NR, Pal SK (1992) Higher order fuzzy entropy and hybrid entropy of a set. Inform Sci 61:211–231

    Article  MathSciNet  MATH  Google Scholar 

  • Peng ZX, Chen XW (2014) Uncertain systems are universal approximators. J Uncertain Anal Appl 2. Article 13

  • Peng ZX, Iwamura K (2010) A sufficient and necessary condition of uncertainty distribution. J Interdiscip Math 13(3):277–285

  • Shannon C (1949) The mathematical theory of communication. The University of Illinois Press, Urbana

  • Tang WP, Gao WN (2013) Triangular entropy of uncertain variables. Inform Int Interdiscip J 16(2(A)):1279–1282

    MathSciNet  Google Scholar 

  • Vaida I (1968) Bounds of the minimal error probability on checking a finite or countable number of hypothesis. Inform Transm Probl 4:9–19

    MathSciNet  MATH  Google Scholar 

  • Wang XS, Peng ZX (2014) Method of moments for estimating uncertainty distributions. J Uncertain Anal Appl 2. Article 5

  • Yager RR (2000) On the entropy of fuzzy measures. IEEE Trans Fuzzy Syst 8(4):453–461

    Article  Google Scholar 

  • Yao K (2012) No-arbitrage determinant theorems on mean-reverting stock model in uncertain market. Knowl Based Syst 35:259–263

    Article  Google Scholar 

  • Yao K, Gao JW, Dai W (2013) Sine entropy for uncertain variable. Int J Uncertain Fuzziness Knowl Based Syst 21(5):743–753

    Article  MathSciNet  Google Scholar 

  • Yao K, Ralescu DA (2013) Age replacement policy in uncertain environment. Iran J Fuzzy Syst 10(2):29–39

    MathSciNet  Google Scholar 

  • Yao K, Ji XY (2014) Uncertain decision making and its application to portfolio selection problem. Int J Uncertain Fuzziness Knowl Based Syst 22(1):113–123

    Article  MathSciNet  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1968) Probability measures of fuzzy events. J Math Anal Appl 23:421–427

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant No. 71001080 and Grant No. 71371141).

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Authors and Affiliations

  1. School of Information Engineering, Shandong Youth University of Political Science, Jinan, 250014, China

    Yufu Ning

  2. School of Economics and Management, Tongji University, Shanghai, 200092, China

    Hua Ke

  3. School of Information, Renmin University of China, Beijing, 100872, China

    Zongfei Fu

Authors
  1. Yufu Ning
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  2. Hua Ke
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  3. Zongfei Fu
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Corresponding author

Correspondence to Zongfei Fu.

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Communicated by V. Loia.

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Ning, Y., Ke, H. & Fu, Z. Triangular entropy of uncertain variables with application to portfolio selection. Soft Comput 19, 2203–2209 (2015). https://doi.org/10.1007/s00500-014-1402-x

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