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The mean chance conditional value at risk under interval type-2 intuitionistic fuzzy random environment

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Abstract

The interval type-2 intuitionistic fuzzy random variable is an extension of the intuitionistic fuzzy random variable such that it can be a effective tool to determine some high-uncertainty phenomena. In this paper, the interval type-2 intuitionistic fuzzy random variable is introduced for the first time, and then, a scalar expected value operator of interval type-2 intuitionistic fuzzy random variable is proposed. Moreover, the new concepts of mean chance value at risk and mean chance conditional value at risk are discussed for the interval type-2 intuitionistic fuzzy random variables which have application in uncertain optimization, like fuzzy inverse location problems. Finally, it is proven that mean chance value at risk and mean chance conditional value at risk fulfill the convex risk metric properties.

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References

  • Acerbi C, Tasche D (2002) On the coherence of expected shortfall. J Bank Finance 26:1487–1503

    Article  Google Scholar 

  • Atanassov KT (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg, New York

    Book  MATH  Google Scholar 

  • Bai XJ (2016) Two-stage multiobjective optimization for emergency supplies allocation problem under integrated uncertainty. Math Probl Eng 2016:1–13

    MathSciNet  MATH  Google Scholar 

  • Coung BC, Anh TH, Hai BD (2012) Some operations on type-2 intuitionistic fuzzy sets. J Comput Sci Cybern 28:274–283

    Google Scholar 

  • Dubois D, Prade H (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum, New York

    Book  MATH  Google Scholar 

  • Duffie D, Pan J (1997) An overview of value at risk. J Deriv 4(3):7–49

    Article  Google Scholar 

  • Garg H, Singh S (2018) A novel triangular interval type-2 intuitionistic fuzzy sets and their aggregation operators. Iran J Fuzzy Syst 15:69–93

    MathSciNet  MATH  Google Scholar 

  • Gao R, Yao K (2016) Importance index of components in uncertain random systems. Knowl-Based Syst 109:208–217

    Article  Google Scholar 

  • Gotoh JY, Takano Y (2007) Newsvendor solutions via conditional value-at-risk minimization. Eur J Oper Res 179:80–96

    Article  MATH  Google Scholar 

  • Huang T, Zhao RQ, Tang WS (2009) Risk model with fuzzy random individual claim amount. Eur J Oper Res 192:879–890

    Article  MathSciNet  MATH  Google Scholar 

  • Jana DK (2016) Novel arithmetic operations on type-2 intuitionistic fuzzy and its application to transportation problem. Pac Sci Rev A Nat Sci Eng 18:178–189

    Google Scholar 

  • Kruse R, Meyer KD (1987) Statistics with vague data. D. Reidel Publishing Company, Dordrecht

    Book  MATH  Google Scholar 

  • Kwakernaak H (1978) Fuzzy random variables: definitions and theorems. Inf Sci 15:1–29

    Article  MathSciNet  MATH  Google Scholar 

  • Li C, Jin J (2018) A scalar expected value of intuitionistic fuzzy random individuals and its application to risk evaluation in insurance companies. Math Probl Eng 2018:1–18

    MathSciNet  Google Scholar 

  • Liu B (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  • Liu B (2012) Why is there a need for uncertainty theory. J Uncertain Syst 6:3–10

    Google Scholar 

  • Liu B (2015) Uncertainty theory, 4th edn. Springer, Berlin

    MATH  Google Scholar 

  • Liu YH (2013) Uncertain random variable programming with applications. Fuzzy Optim Decis Mak 12(2):153–169

    Article  MathSciNet  MATH  Google Scholar 

  • Liu YH, Ralescu DA (2014) Risk index in uncertain random risk analysis. Int J Uncertain Fuzziness Knowl-Based Syst 22:491–504

    Article  MathSciNet  MATH  Google Scholar 

  • Liu BD, Liu YK (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450

    Article  Google Scholar 

  • Liu YK, Liu BD (2003) Expected value operator of random fuzzy variable and random fuzzy expected value models. Int J Uncertain Fuzziness Knowl-Based Syst 11:195–215

    Article  MathSciNet  MATH  Google Scholar 

  • Liu YK, Liu BD (2003) Fuzzy random variables: a scalar expected value operator. Fuzzy Optim Decis Mak 2:143–160

    Article  MathSciNet  MATH  Google Scholar 

  • Liu YK, Liu BD (2005) On minimum-risk problems in fuzzy random decision systems. Comput Oper Res 32:257–283

    Article  MathSciNet  MATH  Google Scholar 

  • Liu ZQ, Liu YK (2010) Type-2 fuzzy variables and their arithmetic. Soft Comput 14:729–747

    Article  MATH  Google Scholar 

  • Loève M (1963) Probability theory, 3rd edn. Van Nostrand, Princeton

    MATH  Google Scholar 

  • Mendel JM, John RB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10:117–127

    Article  Google Scholar 

  • Mendel JM, John RI, Liu F (2006) Interval type-2 fuzzy logic systems made simple. IEEE Trans Fuzzy Syst 14:808–821

    Article  Google Scholar 

  • Nahmias S (1978) Fuzzy variable. Fuzzy Sets Syst 1:97–101

    Article  MathSciNet  MATH  Google Scholar 

  • Negoita CV, Ralescu D (1987) Simulation, knowledge-based computing and fuzzy statistics. Van Nostrand Reinhold Company, New York

    MATH  Google Scholar 

  • Pei Z (2015) Intuitionistic fuzzy variables: concepts and applications in decision making. Expert Syst Appl 42(22):9033–9045

    Article  Google Scholar 

  • Peng J (2009) Average value at risk in fuzzy risk analysis. Fuzzy Inf Eng 2:1303–1313

    MATH  Google Scholar 

  • Peng J (2011) Credibilistic value and average value at risk in fuzzy risk analysis. Fuzzy Inf Eng 3:69–79

    Article  MathSciNet  MATH  Google Scholar 

  • Puri ML, Ralescu DA (1985) The concept of normality for fuzzy random variables. Ann Probab 13:1371–1379

    Article  MathSciNet  MATH  Google Scholar 

  • Puri ML, Ralescu DA (1986) Fuzzy random variables. J Math Anal Appl 114:409–422

    Article  MathSciNet  MATH  Google Scholar 

  • Qin R, Liu YK, Liu ZQ (2011) Methods of critical value reduction for type-2 fuzzy variables and their applications. J Comput Appl Math 235:1454–1481

    Article  MathSciNet  MATH  Google Scholar 

  • Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21–41

    Article  Google Scholar 

  • Rockafeller RT, Uryasev S (2001) Conditional value at risk for general loss distributions. J Bank Finance 26:1443–1471

    Article  Google Scholar 

  • Shen Q, Zhao RQ (2010) Risk assessment of serious crime with fuzzy random theory. Inf Sci 180:4401–4411

    Article  Google Scholar 

  • Singh S, Garg H (2017) Distance measures between type-2 intuitionistic fuzzy sets and their application to multicriteria decision-making process. Appl Intell 46:788–799

    Article  Google Scholar 

  • Stambaugh F (1996) Risk and value at risk. Eur Manag J 114:612–621

    Article  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-III. Inf Sci 9:43–80

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao T, Xiao J (2012) Type-2 intuitionistic fuzzy sets. Control Theory Appl 29:1215–1222

    Google Scholar 

  • Zhang M, Lu S, Li B (2014) A fuzzy reliability model of blades to avoid resonance and its convergence analysis. Math Probl Eng 2014:1–10

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

    Sepideh Taghikhani, Fahimeh Baroughi & Behrooz Alizadeh

Authors
  1. Sepideh Taghikhani
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  2. Fahimeh Baroughi
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  3. Behrooz Alizadeh
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Correspondence to Fahimeh Baroughi.

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Communicated by A. Di Nola.

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Taghikhani, S., Baroughi, F. & Alizadeh, B. The mean chance conditional value at risk under interval type-2 intuitionistic fuzzy random environment. Soft Comput 24, 9361–9373 (2020). https://doi.org/10.1007/s00500-020-04975-9

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