In this paper we have presented, firstly, an evolution of the concept of fuzzy normed linear spaces, different definitions, approaches as well as generalizations. A special section is dedicated to fuzzy Banach spaces. In the case of fuzzy normed linear spaces, researchers have been working, until now, with a definition of completeness inspired by M. Grabiec’s work in the context of fuzzy metric spaces. We propose another definition and we prove that it is much more adequate, inspired by the work of A.George and P. Veeramani. Finally, some important results in fuzzy fixed point theory were highlighted.

中文翻译：

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模糊赋范线性空间中的不动点理论：一般观点

在本文中，我们首先介绍了模糊赋范线性空间概念的演变、不同的定义、方法以及概括。一个特殊部分专门用于模糊 Banach 空间。在模糊赋范线性空间的情况下，直到现在，研究人员一直在研究完整性的定义，其灵感来自 M. Grabiec 在模糊度量空间背景下的工作。我们提出了另一个定义，并证明它更充分，受到 A.George 和 P. Veeramani 工作的启发。最后，重点介绍了模糊不动点理论中的一些重要成果。