Ural Mathematical Journal
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Ural Math. J.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Ural Math. J., 2020, Volume 6, Issue 2, Pages 3–14 (Mi umj121)  

Min-max solutions for parametric continuous static game under roughness (parameters in the cost function and feasible region is a rough set)

Yousria A. Aboelnagaa, Mai F. Zidanb

a Higher Technological Institute, Tenth of Ramadan City, 44629, Egypt
b Tanta University

Abstract: Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the 1$^{st}$ kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.

Keywords: continuous static game, rough programming, non-linear programming, rough set theory, parametric linear programming, parametric non-linear programming.

DOI: https://doi.org/10.15826/umj.2020.2.001

Full text: PDF file (162 kB)
Full text: https:/.../263
References: PDF file   HTML file

Bibliographic databases:

Language:

Citation: Yousria A. Aboelnaga, Mai F. Zidan, “Min-max solutions for parametric continuous static game under roughness (parameters in the cost function and feasible region is a rough set)”, Ural Math. J., 6:2 (2020), 3–14

Citation in format AMSBIB
\Bibitem{AboZid20}
\by Yousria~A.~Aboelnaga, Mai~F.~Zidan
\paper Min-max solutions for parametric continuous static game under roughness (parameters in the cost function and feasible region is a rough set)
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 2
\pages 3--14
\mathnet{http://mi.mathnet.ru/umj121}
\crossref{https://doi.org/10.15826/umj.2020.2.001}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR4194009}
\elib{https://elibrary.ru/item.asp?id=44611145}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85099607154}


Linking options:
  • http://mi.mathnet.ru/eng/umj121
  • http://mi.mathnet.ru/eng/umj/v6/i2/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Ural Mathematical Journal
    Number of views:
    This page:31
    Full text:11
    References:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021