求解正梯形全模糊Sylvester矩阵方程

IF 1.3 Q2 MATHEMATICS, APPLIED

Fuzzy Information and Engineering Pub Date : 2022-07-03 DOI:10.1080/16168658.2022.2152906

A. Elsayed, N. Ahmad, G. Malkawi

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引用次数: 0

摘要

系统和控制理论中的许多问题都与Sylvester矩阵方程的可解性有关。在许多应用中，至少系统的一些参数应该用模糊数而不是清晰数来表示。在以往的文献中，模糊Sylvester矩阵方程的解仅用三角模糊数表示。本文提出了求解正梯形全模糊Sylvester矩阵方程(PTrFFSME)的两种解析方法。利用现有的算术模糊乘法运算，将PTrFFSME转换为一个等效的清晰Sylvester矩阵方程(SME)系统。研究了PTrFFSME正模糊解存在唯一性的充分必要条件。此外，还讨论了该系统的解与PTrFFSME的等价性。通过一个算例说明了所提出的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Solving Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation

Many problems in systems and control theory are related to solvability of Sylvester matrix equations. In many applications, at least some of the parameters of the system should be represented by fuzzy numbers rather than crisp ones. In most of the previous literature, the solutions of fuzzy Sylvester matrix equation are only presented with triangular fuzzy numbers. In this paper, we propose two analytical methods for solving Positive Trapezoidal Fully Fuzzy Sylvester Matrix Equation (PTrFFSME). The PTrFFSME is converted to an equivalent system of crisp Sylvester Matrix Equations (SME) using the existing arithmetic fuzzy multiplication operations. The necessary and sufficient conditions for the existence and uniqueness of the positive fuzzy solutions to the PTrFFSME are investigated. In addition, the equivalency between the solution to the system of SME and the PTrFFSME are discussed. The proposed methods are illustrated by solving one example.

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来源期刊

Fuzzy Information and Engineering Mathematics-Logic

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

40 weeks

期刊介绍： Fuzzy Information and Engineering—An International Journal wants to provide a unified communication platform for researchers in a wide area of topics from pure and applied mathematics, computer science, engineering, and other related fields. While also accepting fundamental work, the journal focuses on applications. Research papers, short communications, and reviews are welcome. Technical topics within the scope include: (1) Fuzzy Information a. Fuzzy information theory and information systems b. Fuzzy clustering and classification c. Fuzzy information processing d. Hardware and software co-design e. Fuzzy computer f. Fuzzy database and data mining g. Fuzzy image processing and pattern recognition h. Fuzzy information granulation i. Knowledge acquisition and representation in fuzzy information (2) Fuzzy Sets and Systems a. Fuzzy sets b. Fuzzy analysis c. Fuzzy topology and fuzzy mapping d. Fuzzy equation e. Fuzzy programming and optimal f. Fuzzy probability and statistic g. Fuzzy logic and algebra h. General systems i. Fuzzy socioeconomic system j. Fuzzy decision support system k. Fuzzy expert system (3) Soft Computing a. Soft computing theory and foundation b. Nerve cell algorithms c. Genetic algorithms d. Fuzzy approximation algorithms e. Computing with words and Quantum computation (4) Fuzzy Engineering a. Fuzzy control b. Fuzzy system engineering c. Fuzzy knowledge engineering d. Fuzzy management engineering e. Fuzzy design f. Fuzzy industrial engineering g. Fuzzy system modeling (5) Fuzzy Operations Research [...] (6) Artificial Intelligence [...] (7) Others [...]