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AE solutions to two-sided interval linear systems over max-plus algebra.

Lihua Wang1, Wei Li1, Haohao Li2

  • 11Institute of Operational Research & Cybernetics, Hangzhou Dianzi University, Hangzhou, China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces AE solutions for two-sided interval max-plus linear systems, unifying various existing solution concepts. An efficient method for finding the AE solution set is demonstrated with an example.

Keywords:
AE solutionsMax-plus algebraTwo-sided interval linear systems

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Area of Science:

  • Max-plus algebra
  • Interval analysis
  • Linear systems

Background:

  • Existing solution concepts for interval systems lack generality.
  • Two-sided interval max-plus linear systems require a unified solution framework.

Purpose of the Study:

  • Introduce and characterize AE solutions for two-sided interval max-plus linear systems.
  • Demonstrate the general applicability of AE solutions, encompassing prior concepts.
  • Provide an efficient method for determining the AE solution set.

Main Methods:

  • Development of the AE solution concept for max-plus algebra.
  • Formulation of characterizations for AE solutions in both inequalities and equations.
  • Illustrative example for practical application of the proposed method.

Main Results:

  • AE solutions offer a generalized framework for interval max-plus linear systems.
  • Full characterizations of AE solutions are established.
  • An efficient algorithm for finding AE solutions is presented.

Conclusions:

  • AE solutions provide a comprehensive approach to interval max-plus linear systems.
  • The proposed method simplifies the determination of solution sets.
  • This work unifies and extends existing solution concepts in the field.