Skip to main content
SpringerLink
Log in

Interval-Valued Finite Markov Chains

  • Published:
Reliable Computing

Abstract

The requirement that precise state and transition probabilities be available is often not realistic because of cost, technical difficulties or the uniqueness of the situation under study. Expert judgements, generic data, heterogeneous and partial information on the occurrences of events may be sources of the probability assessments. All this source information cannot produce precise probabilities of interest without having to introduce drastic assumptions often of quite an arbitrary nature. in this paper the theory of interval-valued coherent previsions is employed to generalise discrete Markov chains to interval-valued probabilities. A general procedure of interval-valued probability elicitation is analysed as well. In addition, examples are provided.

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

Similar content being viewed by others

References

  1. Kemeny, J. G. and Snell, J. L.: Finite Markov Chains, Van Nostrand Reinhold Company, New York, 1960.

    Google Scholar 

  2. Kuznetsov, V. P.: Interval Statistical Models, Radio and Communication, Moscow, 1991 (in Russian).

    Google Scholar 

  3. Walley, P.: Measures of Uncertainty in Expert Systems, Artificial Intelligence 83 (1996), pp.1–58.

    Google Scholar 

  4. Walley, P.: Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, London, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Systems Analysis Department, Risø National Laboratory, P.O. Box 49, 4000, Roskilde, Denmark

    Igor O. Kozine

  2. Department of Computer Science, Forest Technical Academy, Institutski per. 5, St.Petersburg, 194021, Russia

    Lev V. Utkin

Authors
  1. Igor O. Kozine
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lev V. Utkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozine, I.O., Utkin, L.V. Interval-Valued Finite Markov Chains. Reliable Computing 8, 97–113 (2002). https://doi.org/10.1023/A:1014745904458

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014745904458

Keywords

Search

Navigation