Skip to main content
SpringerLink
Log in

Uncertain Linear Systems of Equations: Strong Solvability and Strong Feasibility

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The authors consider strong solvability and strong feasibility of uncertain linear systems of equations in five grades (exact, quasi-exact, semi-exact, quasi-fuzzy, and fuzzy).

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. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning,” Information Sciences, 8, 199–249 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  2. L. A. Zadeh, “Fuzzy sets and their application to pattern recognition and clustering analysis,” in: Classification and a Clustering, New York–San Francisco–London (1977), pp. 251–299.

  3. A. Kaufman, Introduction to Theory of Fuzzy Subsets, Academic, New York (1975).

    Google Scholar 

  4. A. Kaufman and H. Hil Aluha, Introducci_n de la Teoria de los Subconjuntos Borrosos a la Gestion de las Empresas [in Spanish] (Introduction to Theory of Fuzzy Sets in Business Management), Milladoiro, Santiago de Compostela (1986).

  5. I. V. Sergienko and M. F. Kaspshitskaya, “Using concepts of fuzzy mathematics for formalization and solution of combinatorial optimization problems,” Cybern. Syst. Analysis, 31, No. 2, 293–296 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  6. I. V. Sergienko, I. N. Parasyuk, and M. F. Kaspshitskaya, “A fuzzy problem of multiparametric choice of optimal solutions,” Cybern. Syst. Analysis, 39, No. 2, 163–173 (2003).

    Article  MathSciNet  MATH  Google Scholar 

  7. I. N. Parasyuk and S. V. Ershov, “Transformations of fuzzy graphs specified by FD-grammars,” Cybern. Syst. Analysis, 43, No. 2, 266–280 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  8. D. A. Pospelov (ed.), Fuzzy Sets in Models of Control and Artificial Intelligence [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  9. O. O. Iemets and O. O. Yemets’, Solving Combinatorial Optimization Problems on Fuzzy Sets: A Monograph [in Ukrainian], PUET, Poltava (2011).

  10. O. O. Iemets and O. O. Yemets’, “Fuzzy numbers manipulations and relations,” Naukovi Visti NTUU “KPI,” No. 5, 39–46 (2008).

  11. O. O. Iemets and O. O. Yemets’, “Constructing the mathematical model of one combinatorial problem of packing rectangles with fuzzy dimensions,” Naukovi Visti NTUU “KPI,” No. 6, 25–33 (2008).

  12. G. A. Donets and O. O. Yemets, “The statement and solution of the knapsack problem with fuzzy data,” J. Autom. Inform. Sci., 41, No. 9, 1–13 (2009).

    Article  Google Scholar 

  13. T. A. Parfonova and O. A. Yemets, “Operaions on fuzzy numbers with bearer of the cardinality of continuum for modeling in combinatorial optimization,” J. Autom. Inform. Sci., 42, No. 4, 19–36 (2010).

    Article  Google Scholar 

  14. O. A. Iemets, A. O. Yemets, and T. A. Parfonova, “Branch and bound method for optimization problems on fuzzy sets,” J. Autom. Inform. Sci., 45, No. 4, 23–29 (2013).

    Article  Google Scholar 

  15. Yu. P. Zaichenko, Operations Research. Fuzzy Optimization: A Handbook [in Russian], Vyshcha Shkola, Kyiv (1991).

  16. L. G. Raskin and O. V. Seraya, Fuzzy Mathematics. Fundamentals of the Theory. Applications [in Russian], Parus, Kharkiv (2008).

  17. I. V. Sergienko, O. O. Iemets, and O. O. Yemets, “Systems of linear equations with fuzzy set data: Weak solvability and weak admissibility,” Cybern. Syst. Analysis, 50, No. 2, 191–200 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  18. O. A. Iemets and A. O. Yemets, “Strong solvability and strong feasibility of fuzzy linear systems of inequalities,” J. Autom. Inform. Sci., 46, No. 12, 36–47 (2014).

    Article  Google Scholar 

  19. O. O. Iemets and O. O. Yemets’, “About the problem of growing of a discrete fuzzy number carrier during algebraic operations,” in: Proc. 20th Intern. Conf. “Problems of Decision Making under Uncertainties” (PDMU–2012), September 17–21, 2012, Kyiv (2012), p. 47.

  20. T. L Saaty, “Decision making with the analytic hierarchy process,” Int. J. Services, 1, No. 1 (2008).

  21. M. Fiedler, J. Nedoma, J. Ramik, I. Rohn, and K. Zimmermann, Linear Optimization Problems with Inexact Data, Springer-Verlag, New York, (2006).

    MATH  Google Scholar 

  22. J. Rohn, “Solvability of systems of linear interval equations,” SIAM J. on Matrix Analysis and Applications, 25, 237–245 (2003).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Poltava University of Economics and Trade, Poltava, Ukraine

    O. O. Iemets & O. O. Yemets’

Authors
  1. O. O. Iemets
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. O. Yemets’
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. O. Iemets.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2016, pp. 73–83.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iemets, O.O., Yemets’, O.O. Uncertain Linear Systems of Equations: Strong Solvability and Strong Feasibility. Cybern Syst Anal 52, 896–904 (2016). https://doi.org/10.1007/s10559-016-9891-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-016-9891-5

Keywords

Search

Navigation