In this paper, we define fuzzy matrices (FM), intuitionistic fuzzy matrices (IFM) and a new operation \( * \) defined on the set \( I_{n} = \left\{ {1,2, \ldots ,n} \right\}. \) The system \( (I_{n} , * ) \) is an abelian group. This group is pivotal in our paper. Circulant intuitionistic fuzzy matrices is defined also in this paper via the group \( (I_{n} , * ) \) as a new way for defining circulant matrices. However, we study and investigate several properties of circulant intuitionistic fuzzy matrices. The first row (column) of a circulant matrix plays an important role in our studying. From any intuitionistic fuzzy matrix R (not necessarily circulant) we can construct two circulant intuitionistic fuzzy matrices \( R_{L} \) and \( R_{U} \) such that \( R_{L} \le R \le R_{U} \). We also show that some compositions of circulant intuitionistic fuzzy matrices are also circulant. Moreover, we proved that \( RS = SR \) for two circulant intuitionistic fuzzy matrices \( R \) and \( S \). However, we give some examples to clarify our results.

在本文中，我们定义模糊矩阵（FM），直觉模糊矩阵（IFM）和一个新的操作\（* \）所设定的限定\（I_ {N} = \左\ {{1,2，\ ldots， n）\ right \}。\）系统\（（I_ {n}，*）\）是一个阿贝尔群。该小组在我们的论文中至关重要。本文还通过组\（（I_ {n}，*）\）定义了循环直觉模糊矩阵，作为定义循环矩阵的一种新方法。但是，我们研究和研究了循环直觉模糊矩阵的若干性质。循环矩阵的第一行（列）在我们的研究中起着重要作用。来自任何直觉模糊矩阵R（不一定是循环的）我们可以构造两个循环的直觉模糊矩阵\（R_ {L} \）和\（R_ {U} \）使得\（R_ {L} \ le R \ le R_ {U} \）。我们还表明，循环直觉模糊矩阵的某些组合也是循环的。此外，我们证明了两个循环直觉模糊矩阵\（R \）和\（S \）的\（RS = SR \）。但是，我们举一些例子来澄清我们的结果。