Least Squares Method for Solving Fuzzy LR Interval Algebraic Linear Systems

IF 1.3 Q2 MATHEMATICS, APPLIED

Fuzzy Information and Engineering Pub Date : 2022-07-03 DOI:10.1080/16168658.2022.2140479

Mehrnoosh Salari, R. Ghanbari, Khatere Ghorbani-Moghadam

引用次数: 0

Abstract

We first investigate the solvability conditions of fuzzy LR interval algebraic linear systems with fuzzy LR interval coefficient matrix and fuzzy LR interval hand-right vector. Next, we compute the solution of FLRIALS (fuzzy LR interval algebraic linear systems) using the least squares approach. We show that solving the least squares problem is equivalent to solving a quadratic programming problem. Indeed, instead of the FLRIALS, this quadratic programming has a non-convex constraint. Thus, we relax this constraint to have a convex search space. Then, from the solution obtained from quadratic programming on convex search space, we give an approximate solution for FLRIALS.

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求解模糊LR区间代数线性系统的最小二乘法

首先研究了具有模糊LR区间系数矩阵和模糊LR区间右向向量的模糊LR区间代数线性系统的可解性条件。其次，我们使用最小二乘法计算模糊LR区间代数线性系统的解。我们证明了求解最小二乘问题等价于求解二次规划问题。实际上，与FLRIALS不同，这种二次规划具有非凸约束。因此，我们放宽这个约束，使其具有凸搜索空间。然后，从凸搜索空间上的二次规划得到的解出发，给出了FLRIALS问题的近似解。

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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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 [...]