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Hello,
I have tried to implement a test case of FCM with iModeler, and would like to understand how calculations are done. I have implemented the example in K. Kok, Global Environmental Change 19 (2009) 122–133 (The potential of Fuzzy Cognitive Maps for semi-quantitative scenario development, with an example from Brazil), attached. To obtain the same results I had to do (fig 2b):
C1: if(time()==1;1;delay0(1;[C2])*(-0.1)+valuebefore(1))
C2: if(time()==1;0;delay0(1;[C1])+0.5*delay0(1;[C3]))
C3: if(time()==1;1;valuebefore(1)-delay0(1;[C2])*0.5)
I am wondering why I had to put these delays..
Thanks in advance for thode who can help!
Grégoire

Dear Grégoire

Finally someone who is familiar with FCM

First your question: Whenever you try to calculate the values within a loop you need a delay to have a beginning and an end of each calculation for each time step. System Dynamics as a methodology puts automatically a delay with each stock.

What I found interesting is that FCM alway show asymptotic behavior as they calculate loops but without stocks. Within a system dynamics simulation you can define stocks where appropriate and as a result the behavior could be escalating.

That is exactly what we do with the qualitative analysis through the iMODELER's Insight Matrix: There you see the would-be-impact of factor's impulses of the value 1 assuming that all loops contain stocks. So the idea of FCM is very similar to that of our qualitative analysis with the only difference that we calculate the probably more realistic potential impact of loops with stocks.

Happy modeling

Kai

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Kai Neumann

Consideo

Thanks a lot Kai, I undestand better. Actually this dynamic behavior sensitivity puzzles me.. when we set factors and influences, we describe a situation that is occuring now. In general it is a somehow slow changing situation (i.e. not much is happening in a year that is different from now except in case of a crisis), however both fcm or iModeler show "transients", large fluctuations in the sort term and stabilization (in most cases I suppose) in the long term. I am wondering to which point we should "ignore" the transients, i.e. it would be the result of an imperfect model not balanced yet, and focus more on the long term which is much more robust, the state variables of the system adjusting to the influences that we have defined. I know I am not very clear but you probably understand what I mean!

Well, I think it depends on what you want to examine or what you want an answer to. Quantitative models, e.g. system dynamics, show developments over time and to what extent. Qualitative models allow to compare potential impacts of factors. The classic cross impact analysis (e.g. the sensitivity model of Prof. Vester) for this isn't able to consider the dynamics from feedback loops and potential delays. That's why FCM was developed - to consider the potential effect of feedback loops from otherwise qualitative models. In my humble opinion the asymptotic behavior of FCM simulations isn't satisfying. That's why we went further with our insight-matrix. It, too, calculates the effect from impulses, going further than FCM.

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Kai Neumann

Consideo

Thanks Kai! Well, removing the delays in iModeler (i.e. considering factors as stocks) I find asymtotic behavior in the above model.. Apart from the delay you introduce, it seems that iModeler is very close to FCM after all.. Related to this I have a quick question: to what time step correspond short, medium and long term? It is related to the max time steps I suppose.. (e.g. medium term is half the max time step?)- or is it averaging the response over a range of time steps? I am also interested in understanding better the idea of impulses for insight matrices.. Sorry if I ask so many questions: I am traveling to Argentina wednesday to start modelling socio-ecologic dynamics with iModeler and need to know better what is under the hood

It is time step 1, 3 and 5 (the classic MODELER had a modus to automatically simulate the values from the insight matrix via system dynamics)

_________________
Kai Neumann

Consideo