Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Monte Carlo integration for Choquet integral

Published: 23 April 2019 Publication History

Abstract

In this paper, a numerical Monte Carlo integration for Choquet integrals is proposed by using a generalized version of mean value theorem based on Choquet integral. In special cases, this generalization can help us to have the classical Monte Carlo integration and the mean value theorem over some unbounded regions.

References

References

[1]
Gubernatis JE. The Monte Carlo method in the physical sciences. In: AIP Conference Proceedings, Vol. 690. Melville, NY: AIP; 2003.
[2]
Newman M, Barkema GT. Monte Carlo Methods in Statistical Physics. Oxford, UK: Oxford University Press; 1999.
[3]
Krauth W. Statistical Mechanics: Algorithms and Computations. Oxford, UK: Oxford University Press; 2006.
[4]
Gubernatis J, Kawashima N, Werner P. Quantum Monte Carlo Methods. Cambridge, UK: Cambridge University Press; 2016.
[5]
Foulkes WMC, Mitas L, Needs RJ, Rajagopal G. Quantum Monte Carlo simulations of solids. Rev Mod Phys. 2001;73:33.
[6]
Bortz AB, Kalos MH, Lebowitz JL. A new algorithm for Monte Carlo simulation of Ising spin systems. J Comput Phys. 1975;17:10‐18.
[7]
Carlson J, Gandolfi S, Pederiva F, et al. Quantum Monte Carlo methods for nuclear physics. Rev Mod Phys. 2015;87:1067.
[8]
Fodor Z, Hoelbling C. Light hadron masses from lattice QCD. Rev Mod Phys. 2012;84:449.
[9]
Manly BF. Randomization, Bootstrap and Monte Carlo Methods in Biology. Vol. 70. Boca Raton, FL: CRC Press; 2006.
[10]
Mode CJ. Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science. Rijeka, Croatia: InTech; 2011.
[11]
Glasserman P. Monte Carlo Methods in Financial Engineering. Vol. 53. Berlin: Springer; 2003.
[12]
Barabesi L, Marcheselli M. Some large‐sample results on a modified Monte Carlo integration method. J Stat Plann Infer. 2005;135(2):420‐432.
[13]
Tan Z. Monte Carlo integration with Markov chain. J Stat Plann Infer. 2008;138:1967‐1980.
[14]
Liang F. On the use of stochastic approximation Monte Carlo for Monte Carlo integration. Stat Probab Lett. 2009;79(5):581‐587.
[15]
Flett TM. A mean value theorem. Math Gaz. 1958;42:38‐39.
[16]
Choquet G. Theory of capacities. Ann Inst Fourier. 1954;5:131‐295.
[17]
Sugeno M. A note on derivatives of functions with respect to fuzzy measures. Fuzzy Sets Syst. 2013;222:1‐17.
[18]
Sugeno M. A way to Choquet calculus. IEEE Trans Fuzzy Syst. 2015;23:1439‐1457.
[19]
Torra V, Narukawa Y. Numerical integration for the Choquet integral. Inf Fusion. 2016;31:137‐145.
[20]
Torra V, Narukawa Y, Sugeno M, Carlson M Hellinger distance for fuzzy measures. In: Proceedings of the EUSFLAT Conference; 2013.
[21]
Mesiar R, Li J, Pap E. The Choquet integral as Lebesgue integral and related inequalities. Kybernetika. 2010;46:1098‐1107.
[22]
Ridaoui M, Grabisch M. Choquet integral calculus on a continuous support and its applications. Oper Res Decis. 2016;1:73‐93.
[23]
Torra V, Narukawa Y, Sugeno M. On the f‐divergence for monotone measures. Fuzzy Sets Syst. 2016;292:364‐379.
[24]
Torra V. Entropy for non‐additive measures in continuous domains. Fuzzy Sets Syst. 2017;324:49‐59.
[25]
Torra V, Guillen M, Santolino M. Continuous m‐dimensional distorted probabilities. Inf Fusion. 2018;44:97‐102.
[26]
Denneberg D. Non‐additive and Integral. Dordrecht: Kluwer Academic Publishers; 1994.
[27]
Pap E. Null‐additive Set Functions. Vol. 24. Dordrecht: Kluwer Academic Publishers; 1995.

Cited By

View all
  • (2023)New horizon in fuzzy distributions: statistical distributions in continuous domains generated by Choquet integralSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-08529-727:15(10447-10456)Online publication date: 1-Aug-2023

Recommendations

Comments

Information & Contributors

Information

Published In

cover image International Journal of Intelligent Systems
International Journal of Intelligent Systems  Volume 34, Issue 6
June 2019
298 pages
ISSN:0884-8173
DOI:10.1002/int.2019.34.issue-6
Issue’s Table of Contents

Publisher

John Wiley and Sons Ltd.

United Kingdom

Publication History

Published: 23 April 2019

Author Tags

  1. Choquet integral
  2. mean value theorem
  3. Monte Carlo integration
  4. simulation

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 10 Nov 2024

Other Metrics

Citations

Cited By

View all
  • (2023)New horizon in fuzzy distributions: statistical distributions in continuous domains generated by Choquet integralSoft Computing - A Fusion of Foundations, Methodologies and Applications10.1007/s00500-023-08529-727:15(10447-10456)Online publication date: 1-Aug-2023

View Options

View options

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media