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Tolerance-localized and control-localized solutions of interval linear equations system and their application to course assignment problem

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  • Leela-apiradee, Worrawate
  • Gorka, Artur
  • Burimas, Kanokwan
  • Thipwiwatpotjana, Phantipa

Abstract

There are many approaches to solving a system of interval linear equations. Each of them has different semantics based on the context of the system. We define here two other types of solutions called ‘tolerance-localized’ and ‘control-localized’ solutions. A tolerance-localized solution means that it provides either tolerance, L-localized, or R-localized behavior in each equation of the system. The similar argument serves for a control-localized solution. Theorems are proved to obtain the characterizations of the new solutions. Both sets of tolerance-localized and control-localized solutions could be represented by a system of integer linear equations. An example of application to the course assignment problem is presented, where the teaching workload restriction has been considered as tolerance-localized or control-localized constraints.

Suggested Citation

  • Leela-apiradee, Worrawate & Gorka, Artur & Burimas, Kanokwan & Thipwiwatpotjana, Phantipa, 2022. "Tolerance-localized and control-localized solutions of interval linear equations system and their application to course assignment problem," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000169
    DOI: 10.1016/j.amc.2022.126930
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    References listed on IDEAS

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    1. Popova, Evgenija D., 2017. "Parameterized outer estimation of AE-solution sets to parametric interval linear systems," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 353-360.
    2. Shary, Sergey P., 1995. "Solving the linear interval tolerance problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(1), pages 53-85.
    3. Artur Gorka & Phantipa Thipwiwatpotjana, 2015. "The Importance of Fuzzy Preference in Course Assignment Problem," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-8, October.
    4. Shary, Sergey P., 2015. "New characterizations for the solution set to interval linear systems of equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 570-573.
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