Fuzzy Kolmogorov Complexity Based on a Classical Description

Songsong Dai
2020 Entropy  
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
more » ... aining 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.
doi:10.3390/e22010066 pmid:33285841 fatcat:5bsdkboymzc5tgdechpxb3lzme