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Interval linear systems as a necessary step in fuzzy linear systems

机译：区间线性系统是模糊线性系统的必要步骤

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摘要

This article clarifies what it means to solve a system of fuzzy linear equations, relying on the fact that they are a direct extension of interval linear systems of equations, already studied in a specific interval mathematics literature. We highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals, each of which based on a generalizationof scalar equality to intervals. Each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals. We also consider the smallest multidimensional intervals containing the solution sets. We propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals. This unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies. (C) 2015 Elsevier B.V. All rights reserved.
机译：本文根据模糊线性方程组是区间线性方程组的直接扩展这一事实进行了阐明，该模糊线性方程组已经在特定的区间数学文献中进行了研究。我们重点介绍了线性方程组的四个不同定义，其中系数被间隔替换，每个定义都基于对间隔的标量等式的推广。间隔线性系统的四个扩展中的每个扩展都有一个对应的解集，可以根据一个相对较新的约束间隔概念，通过一种通用的统一方法来进行计算。我们还考虑了包含解集的最小多维间隔。我们建议将间隔设置扩展到系数为模糊间隔的线性方程组。这种统一的设置澄清了各种模糊区间线性系统研究中的许多异常或不一致的已发布结果。 （C）2015 Elsevier B.V.保留所有权利。

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