I would like to be able to measure the complexity of agents to determine whether a system is really a swarm or if it is a multiagent learning system etc. A discussion of complexity measures: http://tinyurl.com/measurecomplex. By knowing the type of system an outside agent can better adapt to, learn from, or manipulate the system.
2 thoughts on “Measuring Complexity”
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I have come up with two approaches for determining whether a system is really a swarm:
1. Using the Shapely value. Essentially if I sample a portion of the population that I believe to be the swarm and their Shapley values are approximately equal then I may be able to assume that the system is a swarm. The Shapely value however is a measure of usefulness. Therefore, as an observer of a system I might not have all of the information needed to make this calculation. This lead me to my next methodology.
2. Fuzzy measure theory: “The conditions for membership are precise, but the information about an element is insufficient to determine whether it satisfies those conditions” (http://tinyurl.com/fuzzymeasure). The condition for a system to be a swarm is precisely described by 1. but the information that I have available about the system is insufficient to determine whether it satisfies 1..
Maybe look at this:
(http://ces.univ-paris1.fr/membre/Grabisch/articles/ejor95.pdf) Seems like probably there are more conditions than point 1. that could describe the conditions for swarms. The title of the paper is The application of fuzzy integrals in Multicriteria Decision
Making. Which seems like a good start if I can come up with other conditions/criteria.
The Fuzzy Measure theory Wikipedia article has a connection between the Shapely value and fuzzy measure theory which I believe could be useful for 2.. Actually it seems to describe 2…. Maybe I can find who wrote that and maybe see if they describe it better.