Skip to main content
SpringerLink
Log in

Fuzzy record values

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

A new approach in developing crisp record values of fuzzy random variables is proposed. In this approach, the \(\alpha \)-pessimistic notion of fuzzy random variables is used to extend the crisp record values and their fuzzy cumulative distribution and density functions. Parametric and nonparametric examples are also given to clarify the concepts and methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Ahmadi J, Arghami NR (2001) Some univariate stochastic orders on record values. Commun Stat Theor Method 30:69–74

    Article  MathSciNet  MATH  Google Scholar 

  • Akbari MG, Rezaei A (2009) Order statistics using fuzzy random variables. Stat Probab Lett 79:1031–1037

    Article  MathSciNet  MATH  Google Scholar 

  • Akbari MG, Rezaei A (2012) Record statistics using fuzzy random variables. Pak J Stat 28:315–330

    MathSciNet  Google Scholar 

  • Arefi M, Taheri SM (2011) Testing fuzzy hypotheses using fuzzy data based on fuzzy test statistic. J Uncertain Syst 5:45–61

    MATH  Google Scholar 

  • Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York

    Book  MATH  Google Scholar 

  • Bertoluzza C, Gil MA, Ralescu DA (eds) (2002) Statistical modeling, analysis and management of fuzzy data. Physica-Verlag, Heidelberg

  • Brown M, Proschan F (1983) Imperfect repair. J Appl Probab 20:851–859

    Article  MathSciNet  MATH  Google Scholar 

  • Chachi J, Taheri SM (2011) Fuzzy confidence intervals for mean of Gaussian fuzzy random variables. Expert Syst Appl 38:5240–5244

    Article  Google Scholar 

  • Chandler KN (1952) The distribution and frequency of record values. J R Stat Soc Ser B 14:220–228

    MathSciNet  MATH  Google Scholar 

  • Colubi A, Coppi R, D’urso P, Gil MA (2007) Statistics with fuzzy random variables. Metron Int J Stat LXV:277–303

    MATH  Google Scholar 

  • Hesamian G, Chachi J (2015) Two-sample Kolmogorov-Smirnov fuzzy test for fuzzy random variables. Stat Papers 56:61–82

    Article  MathSciNet  MATH  Google Scholar 

  • Kurse R, Meyer KD (1987) Statistics with vague data. Reidel publishing company, Dordrecht

    Book  Google Scholar 

  • Kwakernaak H (1978) Fuzzy random variables. Part I: definitions and theorems. Inf Sci 19:1–15

    Article  MATH  Google Scholar 

  • Kwakernaak H (1979) Fuzzy random variables. Part II: algorithms and examples for the discrete case. Inf Sci 17:253–278

    Article  MATH  Google Scholar 

  • Lee K (2005) First course on fuzzy theory and applications. Springer, Berlin

    MATH  Google Scholar 

  • Liu B (2013) Uncertainty theory, 4th edn. Springer, Berlin

    Google Scholar 

  • Nevzorov V (2001) Records: mathematical theory. In: Translation of Mathematical Monographs, vol 194. American Mathematical Society, Providence, RI

  • Peng J, Liu B (2004) Some properties of optimistic and pessimistic values of fuzzy. IEEE Int Conf Fuzzy Syst 2:745–750

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Resnick SI (1973) Record values and Maxima. Ann Probab 1:650–662

    Article  MathSciNet  MATH  Google Scholar 

  • Shaked M, Shanthikumar JG (1994) Stochastic orders and their applications. Academic Press Inc, New York

    MATH  Google Scholar 

  • Shorrock RW (1973) Record values and inter-record times. J Appl Probab 10:543–555

    Article  MathSciNet  MATH  Google Scholar 

  • Viertl R (2011) Statistical methods for fuzzy data. Wiley, Chichester

    Book  MATH  Google Scholar 

  • Wasserman L (2006) All of nonparametric statistics. Springer, New York

    MATH  Google Scholar 

  • Wu HC (1999) The central limit theorems for fuzzy random variables. Inf Sci 120:239–256

    Article  MathSciNet  MATH  Google Scholar 

  • Wu HC (2003) The fuzzy estimators of fuzzy parameters based on fuzzy random variables. Eur J Oper Res 146:101–114

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Zimmermann HJ (2010) Fuzzy set theory. Wiley Interdiscip Rev Comput Stat 2:317–332

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Birjand, Birjand, Iran

    M. G. H. Akbari & M. Chahkandi

Authors
  1. M. G. H. Akbari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Chahkandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Chahkandi.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akbari, M.G.H., Chahkandi, M. Fuzzy record values. Soft Comput 21, 1013–1020 (2017). https://doi.org/10.1007/s00500-015-1836-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-015-1836-9

Keywords

Search

Navigation