An extension method for fully fuzzy Sylvester matrix equation

Liangshao Hou; Jieyong Zhou; Qixiang He

doi:10.1007/s00500-021-05573-z

An extension method for fully fuzzy Sylvester matrix equation

Liangshao Hou, Jieyong Zhou^*, Qixiang He

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Citations (Scopus)

Abstract

An extension method is proposed to solve a class of fully fuzzy Sylvester matrix equation (FFSME) under some mild assumptions. This method consists of two steps. Firstly, the fully fuzzy system is transferred into a series of interval Sylvester matrix equations through α-cut. Secondly, these interval systems are extended into crisp systems which is easy to be solved. The solutions of FFSME are not presumed to be triangular-type fuzzy numbers. Moreover, some examples are presented to show the validity of our method.

Original language	English
Pages (from-to)	5763-5774
Number of pages	12
Journal	Soft Computing
Volume	25
Issue number	7
Early online date	13 Jan 2021
DOIs	https://doi.org/10.1007/s00500-021-05573-z
Publication status	Published - Apr 2021

User-Defined Keywords

Fully fuzzy Sylvester matrix equation
Fuzzy number
Interval analysis
α-cut

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title = "An extension method for fully fuzzy Sylvester matrix equation",

abstract = "An extension method is proposed to solve a class of fully fuzzy Sylvester matrix equation (FFSME) under some mild assumptions. This method consists of two steps. Firstly, the fully fuzzy system is transferred into a series of interval Sylvester matrix equations through α-cut. Secondly, these interval systems are extended into crisp systems which is easy to be solved. The solutions of FFSME are not presumed to be triangular-type fuzzy numbers. Moreover, some examples are presented to show the validity of our method.",

keywords = "Fully fuzzy Sylvester matrix equation, Fuzzy number, Interval analysis, α-cut",

author = "Liangshao Hou and Jieyong Zhou and Qixiang He",

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AU - Hou, Liangshao

AU - Zhou, Jieyong

AU - He, Qixiang

N1 - Supported by the National Natural Science Foundation of China (No. 12071088). Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.

PY - 2021/4

Y1 - 2021/4

N2 - An extension method is proposed to solve a class of fully fuzzy Sylvester matrix equation (FFSME) under some mild assumptions. This method consists of two steps. Firstly, the fully fuzzy system is transferred into a series of interval Sylvester matrix equations through α-cut. Secondly, these interval systems are extended into crisp systems which is easy to be solved. The solutions of FFSME are not presumed to be triangular-type fuzzy numbers. Moreover, some examples are presented to show the validity of our method.

AB - An extension method is proposed to solve a class of fully fuzzy Sylvester matrix equation (FFSME) under some mild assumptions. This method consists of two steps. Firstly, the fully fuzzy system is transferred into a series of interval Sylvester matrix equations through α-cut. Secondly, these interval systems are extended into crisp systems which is easy to be solved. The solutions of FFSME are not presumed to be triangular-type fuzzy numbers. Moreover, some examples are presented to show the validity of our method.

KW - Fully fuzzy Sylvester matrix equation

KW - Fuzzy number

KW - Interval analysis

KW - α-cut

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SP - 5763

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JO - Soft Computing

JF - Soft Computing

IS - 7

ER -

An extension method for fully fuzzy Sylvester matrix equation

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