# The Analysis of the Fuzzy Solution to Fully Fuzzy Linear Systems in Two Perturbation Situations

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1074)

## Abstract

The fuzzy solution to fully fuzzy linear systems $$\tilde{A}\otimes \tilde{x}=\tilde{b}$$ (shown as FFLS) in two perturbation situations are discussed in detail in this paper, where $$\tilde{A}$$ and $$\tilde{b}$$ are respectively a fuzzy matrix and a fuzzy vector. This paper aims to show how the perturbations of the coefficient matrix or the right hand vector impact the fuzzy approximate solution vector to FFLS, we first transform the original fully fuzzy linear systems into tree crisp linear systems. And then two perturbation situations are studied: (I) the coefficient matrix is slightly perturbed while the right hand side remains unchanged; (II) the coefficient matrix and right hand side are all slightly perturbed. Finally, we deduce the relative error bounds to two perturbation situations based on the distance of LR-type triangular fuzzy vector.

## Keywords

LR-type fuzzy numbers The fully fuzzy linear systems Perturbation analysis The relative error bounds

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© Springer Nature Switzerland AG 2020

## Authors and Affiliations

• Kun Liu
• 1
Email author
• Wei-peng Li
• 1
• Yong-ling Li
• 1
• Hong-ying Duan
• 2
1. 1.College of Mathematics and StatisticsLongdong UniversityQingyangChina
2. 2.School of Information EngineeringLongdong UniversityQingyangChina

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