The linguistic variables to make a judgement on startle Causal Factors can thus be represented by a value that is a    not a crisp number but is supplied to the experts in a way that is associated with natural language as Table I below shows. This linguistic format caters to the fuzzy nature of decision making where an intangible concept as startle causality is concerned.
B.        Association:               
Using the FCM Expert Software tool [33], an associative map of the causal concepts as devised from the outputs of the questionnaire process has been created. Figures 5 through to 7 below provide a sample of the FCM what-if scenarios defined to devise appropriate experiments in line with the previously described startle process construct in Figure 3. These figures describe the associative relationships between the human factors’ concepts and the startle mind state. The parameters of choice used in modelling the interaction include Kosko’s activation function rule with self-memory and the Sigmoid Transfer function [41], [56], [57]. The actual Kosko mathematical representation of FCMs assured by [57] takes the following form:
·
 
Ai (k +1)  = f(Ai (k) * Σ  Aj (k) eji ) for j = 1.            N (4)
·
 
where f ( ) is a threshold (activation) function and j != i. The equation thus calculates the values of concepts in the FCM with certain concepts set up as static concepts. In the case presented, concepts 12 through to 19, bar 16, are set as static. A Sigmoid threshold transfer function gives values of concepts in the range [0, 1] and its mathematical equation is:
f (x) = 1 / 1 + e−λ. x        (5)
where λ is a real positive number and x is the value    Ai (k ) on the equilibrium point. In this construct, concepts are activated by making its vector element 1 or 0 or in the range [0, 1].
The threshold function when applied reduces the unbounded weighted sum to a predetermined range, which somewhat hinders quantitative analysis, but facilitates qualitative comparisons between concepts following on from the fuzzy linguistic associations and comparisons applied across the concepts in the graph. The subsequent inference process consists of computing the current state vector through time, for a fixed initial condition, with a successive substitution method [33], [56], [58] to compute any new state vectors showing the effect of the activated concept. This occurs through iteratively multiplying the previous state vector by the relational matrix using standard matrix multiplication.
·
 
Ak = Ak −1 + (Ak −1 W).   (6)
−           ≤
 
The iteration stops when a limit vector is reached, i.e., when Ak = Ak −1 or when Ak Ak −1 e; where e is a residual, whose value depends on the application type (and in most applications is equal to 0.001) [41], [46].