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Fuzzy Kolmogorov Complexity Based on a Classical Description.

¹School of Electronics and Information Engineering, Taizhou University, Taizhou 318000, China.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This summary is machine-generated.

This paper introduces fuzzy Kolmogorov complexity, extending classical string complexity to fuzzy languages. The new definition ensures the complexity measure is independent of the specific fuzzy Turing machine used.

Keywords:

Kolmogorov complexity fuzzy Turing machines fuzzy languages

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Area of Science:

Theoretical Computer Science
Fuzzy Set Theory
Information Theory

Background:

Classical Kolmogorov complexity measures the shortest program length for a string.
Extending complexity measures to fuzzy systems is an active research area.
Fuzzy languages require new approaches to define descriptive complexity.

Purpose of the Study:

To define fuzzy Kolmogorov complexity for finite-valued fuzzy languages.
To adapt classical description length concepts to the fuzzy domain.
To establish the robustness of the proposed fuzzy complexity measure.

Main Methods:

Defining fuzzy Kolmogorov complexity using universal finite-valued fuzzy Turing machines.
Calculating complexity based on the minimum classical description length of a fuzzy language.
Demonstrating invariance of the complexity measure across different machines.

Main Results:

A novel definition for fuzzy Kolmogorov complexity is presented.
The proposed measure retains classical descriptive properties.
The fuzzy Kolmogorov complexity is shown to be independent of the specific universal fuzzy Turing machine.

Conclusions:

The introduced fuzzy Kolmogorov complexity is a robust extension of classical Kolmogorov complexity.
This work provides a foundational tool for analyzing fuzzy language descriptional complexity.
The findings contribute to the theoretical understanding of information and computation in fuzzy systems.