Well, this is partly a matter of what discipline one is dealing with. So, sure, for AI or computer science more generally, Kolmogorov or Chaitin or Rissanen measures are more useful and reasonably well defined. For other disciplines, other definitions may be more suitable. Thus for economics, I have (following Richard Day) defined complexity in a dynamic way based on erratic dynamics appearing endogenously out of the system (with “erratic” defined more specifically). I laid this out in a paper in 1999 in the Journal of Economic Perspectives, and have a more recent paper up on my website (“Computational and Dynamic Perspectives on Economic Complexity”) comparing the two approaches, at http://cob.jmu.edu/rosserjb.
Well, this is partly a matter of what discipline one is dealing with. So, sure, for AI or computer science more generally, Kolmogorov or Chaitin or Rissanen measures are more useful and reasonably well defined. For other disciplines, other definitions may be more suitable. Thus for economics, I have (following Richard Day) defined complexity in a dynamic way based on erratic dynamics appearing endogenously out of the system (with “erratic” defined more specifically). I laid this out in a paper in 1999 in the Journal of Economic Perspectives, and have a more recent paper up on my website (“Computational and Dynamic Perspectives on Economic Complexity”) comparing the two approaches, at http://cob.jmu.edu/rosserjb.