Fuzzy metrics and statistical metric spaces
Fuzzy metrics and statistical metric spaces
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发表时间：
1975
期刊：
影响因子：
0.5
通讯作者：
Ivan Kramosil;J. Michálek
中科院分区：
文献类型：
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作者：
Ivan Kramosil;J. Michálek
在当代有关数学的逻辑和集合论基础的研究中，形容词“模糊的”似乎是一个非常流行且频繁出现的词汇。在我们看来，这种快速发展的主要原因很容易理解。我们周围的世界充满了不确定性，我们从环境中获取的信息、我们使用的概念以及我们观察或测量所得的数据，一般来说都是模糊且不准确的。因此，对现实世界或其某些方面的每一种形式化描述在任何情况下都只是实际状态的一种近似和理想化。像模糊集、模糊序、模糊语言等概念使得能够以一种纯数学和形式化的方式处理和研究上述不确定性的程度。关于模糊集概念及相关概念最有趣的结果和应用的一个非常简短的综述可在[1]中找到。本文的目的是将模糊性的概念应用于度量和度量空间的经典概念，并将所得概念与由度量空间的其他一些推广（即概率统计推广）所产生的概念进行比较。我们的目的是在一个相当通俗易懂的层面上撰写本文，参考文献仅对那些希望更详细地研究这些问题的读者是必要的。
The adjective "fuzzy" seems to be a very popular and very frequent one in the contemporary studies concerning the logical and set-theoretical foundations of mathematics. The main reason of this quick development is, in our opinion, easy to be understood. The surrounding us world is full of uncertainty, the information we obtain from the environment, the notions we use and the data resulting from our observation or measurement are, in general, vague and incorrect. So every formal description of the real world or some of its aspects is, in every case, only an approxima tion and an idealization of the actual state. The notions like fuzzy sets, fuzzy orderings, fuzzy languages etc. enable to handle and to study the degree of uncertainty mentioned above in a purely mathematic and formal way. A very brief survey of the most interest ing results and applications concerning the notion of fuzzy set and the related ones can be found in [l]. The aim of this paper is to apply the concept of fuzziness to the clasical notions of metric and metric spaces and to compare the obtained notions with those resulting from some other, namely probabilistic statistical, generalizations of metric spaces. Our aim is to write this paper on a quite self-explanatory level the references being necessary only for the reader wanting to study these matters in more details.