The difference between a cognitive map and a fuzzy cognitive map is the FCM’s capacity
to not only to represent the existence and sign of causal relations but also the strength of 0.3 C B A -0.2 0.5 Expert1 FCM1 A C D 0.7 0.3 Expert2 FCM2 B C A 0.25 0.05 Expert1&2 Augmented FCM1 0.4 D 0.05 0.35 0.1
75 the relationship. Strength of the relationship itself is a function of the connection weights
and squashing functions.
Initially, I had planned to have weights assigned by a panel of experts: to this end, I
identified authors of research publications that are pertinent to my topic and sent them
individualized online survey. Each survey contained an excerpt of the collective cognitive
map and asked the participant to assign weights for the connections in this subset of the
model. My plan was to use this information to (1) identify connections that the experts
were uncertain about and that should subsequently be researched through exploratory
modeling, and (2) identify connections that could be included in the model with the average
of all expert assigned weights because the experts assigned the same or very similar
weights. As reported in Appendix IV, I encountered several difficulties: First, few experts
responded to the survey at all. Some emails bounced, some experts never responded, others
declined to participate because they found the questions difficult, out of their field of
expertise, or too time-consuming to answer. As a result, I only have an expert-assigned
weight for 263 of 458 connections (57%). I also did not receive multiple data points for
each causal connection and therefore could not use the agreement among the experts as a
measure of uncertainty.
I therefore decided to rely on the computational capacity of exploratory modeling and
investigate alternative model structures not only for some, but for all 458 connections in
the model. Because I had carefully deduced the sign and direction of causal links from the
existing literature and had validated the model structure (see section 4.3), I did not want to
76 there was a positive causal link, all exploratory models should also contain a positive causal
link, albeit with different weights.
I prepared two sets of models with 100 models each:
Set 1 contains models in which edge weights were randomly selected from the interval of
[-1, -0.75] for negative edges and [0.75, 1] for positive edges. These models assume that
all connections that are derived from the literature are rather strong and there is little
uncertainty. This is not unlikely because academic research typically reports on factors or
practices that have strong contributions on an outcome of interest. Research that shows
only minor impacts is simply less likely to be published.
Set 2 contains models in which edge weights were randomly selected from the interval of
[-1, 0) for negative edges and (0, 1] for positive edges. These models assume very high
uncertainty about edge weights. This high uncertainty accounts for the fact that the
literature currently does not take a system view and rarely investigates the
interdependencies among the factors that contribute to ambidexterity. Accordingly, little is
known about the system structure.
I developed my own simulation package in R: Using a uniform distribution function, it
generated the two sets of 100 random adjacency matrices. (The uniform distribution
allowed equal chances for all weights. I chose it because there is no prior knowledge about
the quantitative characteristics of the causal relations of the FCM).
In this study I generated 200,000 random initial vectors and ran them through 100 random
77 exploratory modeling projects, some of which investigated around 20,000 permutations of
the model (Jan H. Kwakkel and Pruyt 2013) for a model of 20 to 30 variables, in my case
of 366-nodes and 481-edges FCM, even 1000 permutation of the model structure reached
the computational limitations6. But as discussed in chapter 6, it was shown that in my FCM model results were much less sensitive to the changes in the weights of the connection than
morphology of the model—existence or not existence of causal connections. In fact in
results of running the simulation for a set of 1000 models with different adjacency matrices
showed negligible difference with a set of 100 models, a sign of saturation.
The last factor effecting on the strength of a relationship is the transfer function—also
known as squashing function—as discussed in section 3.4.2. For the reasons explained
there, a hyperbolic tangent function was used for all the nodes in the FCM with the
exception of the “organizational ambidexterity” node. The transfer function was specified
as following to produce a range of [-1,+1] for the same domain, where t is the input signal
from the connection and Y represents the value of the node:
( ) = 2Tanh(t)
Figure 10 provides a visualization of this transfer function.
6 1000 permutation on 481 connections, generated an adjacency matrix as large as 1.2GB memory. A 20,000 permutation of such large model, would generate an adjacency matrix as large as 24 GB memory.
78
Figure 10- Hyperbolic tangent transfer function used to build the FCM
The case for the “organizational ambidexterity” node was different since as discussed in
chapter 1, based on definition a balance and relatively higher than average “exploitative
innovation” and “exploratory innovation” are needed at the same time to yield to
“organizational ambidexterity”. Thus positive signals from both nodes at the same time
needed to be sensed by the “organizational ambidexterity” node in order to increase its
value. To meet these criteria I customized the Gompertz function ( ) = for two
input variables ( , ) = and then specified it as ( , ) = . As a
result a degree of organizational ambidexterity could be achieved only if both input
nodes—exploitative and exploratory innovations—see a positive change more than 50%.
Also closer the value of these two nodes leads to higher organizational ambidexterity. See
Figure 11 for a representation of the value of organizational ambidexterity in regard to
79
Figure 11- A representation of the value of organizational ambidexterity in regard to value of its two input nodes