The Analysis of the Fuzzy Solution to Fully Fuzzy Linear Systems in Two Perturbation Situations
| Autor: | Wei-peng Li, Hong-ying Duan, Kun Liu, Yong-ling Li |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
021103 operations research Linear system 0211 other engineering and technologies Perturbation (astronomy) 02 engineering and technology Tilde Fuzzy logic Fuzzy linear systems Approximation error 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Coefficient matrix Approximate solution Mathematics |
| Zdroj: | Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery ISBN: 9783030324551 ICNC-FSKD |
| DOI: | 10.1007/978-3-030-32456-8_85 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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