Dai Songsong
School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, China.
Entropy (Basel). 2020 Jan 4;22(1):66. doi: 10.3390/e22010066.
In this paper, we give a definition for fuzzy Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a single finite string is the length of the shortest program that produces this string. We define the fuzzy Kolmogorov complexity as the minimum classical description length of a finite-valued fuzzy language through a universal finite-valued fuzzy Turing machine that produces the desired fuzzy language. The classical Kolmogorov complexity is extended to the fuzzy domain retaining classical descriptions. We show that our definition is robust, that is to say, the complexity of a finite-valued fuzzy language does not depend on the underlying finite-valued fuzzy Turing machine.
在本文中，我们给出了模糊柯尔莫哥洛夫复杂度的定义。在经典情形下，单个有限字符串的柯尔莫哥洛夫复杂度是产生该字符串的最短程序的长度。我们将模糊柯尔莫哥洛夫复杂度定义为通过产生所需模糊语言的通用有限值模糊图灵机得到的有限值模糊语言的最小经典描述长度。经典柯尔莫哥洛夫复杂度在保留经典描述的情况下扩展到了模糊领域。我们证明了我们的定义是稳健的，也就是说，有限值模糊语言的复杂度不依赖于底层的有限值模糊图灵机。
