Approximation of symmetrically reciprocal matrices using mutations in Max Algebra

Document Type : Research Paper

Authors

Department of Mathematics, Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran

Abstract

The objective of this paper is to propose a method for constructing a transitive matrix by maximizing the mutation of a symmetrically reciprocal matrix $A$, such that the resulting matrix is closest to $A$ in terms of a relative error measure. By employing this approach, the need for calculating the maximum eigenvector is eliminated, leading to faster results. Additionally, we investigate the impact of mutations on two cases of change, specifically when a single measurement is corrected or when a new alternative is added, and analyse their effectiveness in ranking.

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References

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History

  • Receive Date: 08 February 2024
  • Revise Date: 05 July 2024
  • Accept Date: 20 July 2024
  • Publish Date: 19 April 2025

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