Skip to main content
SpringerLink
Log in

Solution to Convex Variational Problems with Fuzzy Initial Condition Using Zadeh’s Extension

  • Conference paper
  • First Online:
Fuzzy Information Processing (NAFIPS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 831))

Included in the following conference series:

Abstract

This paper investigates conditions to solve a fuzzy variational problem using Zadeh’s extension. The fuzzy problem is obtained by extending a classical one in the initial condition. The solution to the problem is a fuzzy bunch of functions (fuzzy set of functions) obtained by extending the classical solution in the initial condition. For convex functionals the resulting functional value is a fuzzy number that is proved to be the smallest element in a partial order.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Barros, L.C., Bassanezi, R.C., Lodwick, W.A.: A First Course in Fuzzy Logic, Fuzzy Dynamical Systems, and Biomathematics. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53324-6

    Book  MATH  Google Scholar 

  2. Chang, S.S.L., Zadeh, L.A.: On fuzzy mapping and control. IEEE Trans. Syst. Man Cybern. 2, 30–34 (1972)

    Article  MathSciNet  Google Scholar 

  3. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic Press Inc., Orlando (1980)

    MATH  Google Scholar 

  4. Farhadinia, B.: Necessary optimality conditions for fuzzy variational problems. Inf. Sci. 181, 1348–1357 (2012)

    Article  MathSciNet  Google Scholar 

  5. Gomes, L.T., Barros, L.C., Bede, B.: Fuzzy Differential Equations in Various Approaches. Springer, Berlin (2015). https://doi.org/10.1007/978-3-319-22575-3

    Book  MATH  Google Scholar 

  6. Nguyen, H.T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64, 369–380 (1978)

    Article  MathSciNet  Google Scholar 

  7. Troutman, J.L.: Variational Calculus and Optimal Control: Optimization with Elementary Convexity. Springer, New York (2012). https://doi.org/10.1007/978-1-4612-0737-5

    Book  MATH  Google Scholar 

  8. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto Federal de São Paulo, São José dos Campos, SP, Brazil

    Michael M. Diniz

  2. Departamento de Física, Química e Matemática, Universidade Federal de São Carlos, Sorocaba, SP, Brazil

    Luciana T. Gomes

  3. IMECC, Universidade Estadual de Campinas, Campinas, SP, Brazil

    Rodney C. Bassanezi

Authors
  1. Michael M. Diniz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luciana T. Gomes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rodney C. Bassanezi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael M. Diniz .

Editor information

Editors and Affiliations

  1. Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Guilherme A. Barreto

  2. Department of Statistics & Applied Mathematics, Federal University of Ceará, Fortaleza, Ceará, Brazil

    Ricardo Coelho

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Diniz, M.M., Gomes, L.T., Bassanezi, R.C. (2018). Solution to Convex Variational Problems with Fuzzy Initial Condition Using Zadeh’s Extension. In: Barreto, G., Coelho, R. (eds) Fuzzy Information Processing. NAFIPS 2018. Communications in Computer and Information Science, vol 831. Springer, Cham. https://doi.org/10.1007/978-3-319-95312-0_37

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-95312-0_37

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95311-3

  • Online ISBN: 978-3-319-95312-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation