Fig. 1. - A Fuzzy Cognitive Map1
 
As a knowledge representation and reasoning technique, FCM can be used to adequately describe a dynamic system in a form close to how humans perceive it [41]. This characteristic is what lends itself to successfully capturing experts’ knowledge and extracting relevant data which are subsequently transformed to rules. This approach primarily represents knowledge in the form of causal connections and a map structure. The resulting fuzzy model is used to analyse, simulate, test the influence of parameters, and predict system behaviour.
Probabilistic thinking guided by a mixed effect philosophy is applied to the plethora of identified variables from the HFACS framework. This provides minimisation of uncontrollable domain noise factors and ensures an objective determination of what level or degree of  Truth is ascribed to independent causal variables once they are identified. Given a time-critical decision-making situation, such as an unexpected escalating emergency, for example, human factors including automation bias and inexperience could force the pilot to maintain reliance on cues emanating from potentially failing sources. Crucially, the fidelity of the pilot’s perception may also be significantly eroded by the unexpected event, further complicating the problem [2], [11] leading to poor aeronautical decision making (ADM). In such circumstances, the startled pilot can be further hampered by the pressure as per the evolving situation, causing an instinctive reactionary manner with a strong potential for a subsequent mishap [11], [42]. The FCM framework provides a methodical way of codifying the interrelationship between human factors, and their potential for driving a pilot to startle in a dynamically evolving, emergency. As shown in this study, the FCM implementation attempts to provide a  glimpse of the startled mind objectively, through a quasi-Delphi questionnaire and analysis process. Following this process of distilling the key concepts of interest into a framework representing an intuition of the problem space, an experiment can then be deployed which can capture the necessary physiological information, representative of Visual Acuity, as a function of situation awareness and decision-making during a startling event. This fundamental thought had a significant influence on the model build, as discussed in the following sections.
     
 

     II.            FUZZY SETS & FCMs

Fuzzy cognitive mapping is a method developed by Kosko in 1986 as an extension of cognitive maps, created using a fuzzy logic viewpoint for modelling causal knowledge [43]. The FCM creates a directed graph depicting a specification of concepts (nodes) and causal edges, pertinent to the domain. In this directed graph representation, the fuzzy weights of any connected concepts in the map rely on the relationship strength between nodes displayed as edges. The effectiveness of FCMs can be understood from the view that behaviours of systems can be studied, by combining aspects of fuzzy logic, neural networks,  and semantic networks theories in a structured and logical manner, with human expert inputs.
To demonstrate the notion of fuzzy logic which determines the eigenvalues of the FCM framework, and to provide the reader with some contextual foundation, consider that traditional logic typically represents the output of a variable as a binary True (1), or False (0). Fuzzy logic, on the other hand, represents the value of such a variable anywhere between 0 and 1. For instance, the determination of a causal factor of startle in-flight might be ascribed a value of 0.3 or 0.7 to mean partially true or false (i.e. in terms of being impactful to the elicitation of startle). This value provides intuitive regard for the relationship strengths between concepts in the FCM. The mathematical abstraction of the fuzzy logic introduced earlier can be summarised using the logic of fuzzy sets. Thus, in a crisp set, membership or non-membership of an element, say ‘x’ in a set A is described by a characteristic function
µA (x), where µA(x) = 1 if x ∈ A and µA(x) = 0 if x ∉ A.
Fuzzy set-theory extends this concept by suggesting the notion of a defined partial membership. This partial membership conception means that a fuzzy set A on a notional universe U is characterised by a membership function of an element with values in the interval [0, 1]. In essence, this set admits all uncertainties associated with the variable with a graded membership [41], [44].
For FCM reasoning process, a simple mathematical formulation is generally used. To this end, values of the concept Ci in time t shall be represented by the state vector   Ai (k), and the state of the FCM construct, can be represented by a state vector of the form:
A(k) = [Ai (k), . . . An (k)].           (1)
This state vector represents a point within a fuzzy hypercube 1n = [0, 1]n that suggest what the system has achieved at a point [41], [45]. The hypercube represents a system with an input vector A(0), within the multidimensional space; 1n. which once activated, then gradually converges to either:
 
 
Equilibrium point Chaotic point or
 
A periodic attractor within the hypercube to which the whole system converges; and is dependent upon the input vector value to the system.
In general terms, the FCM simulation process, according to [45], takes the form:
·         Begin
·         Step 1: Read the input vector A0
·         Step 2: Give the connection weight matrix  -  W
·         Step 3: Calculate the concept vector at step k using A(k )  = A(k −1)+A(k −1) .W (k ); with j Ç i for summation.
·         Step 4: Apply the threshold to output vector; A(k ) = f(A(k))
·         Step 5: If [A(k) = A(k – 1) OR A(k) – A(k – 1) < 0.001] STOP
·        
 
 
Else: Go to Step 1
·         End
Structurally, a fuzzy cognitive map may be represented by what is termed a fuzzy digraph with feedback (Figure 1).  In this form, it is akin to a collection of neural processing units and weighted relations which could be positive or negative, signifying levels of causality [46]. The FCM, of system representation expediently demonstrates in terms of concepts (i.e. variables of the system) and causal relations between these concepts. Each concept is characterised by its activation degree (determined from experts’ input), which denotes to what extent a variable is considered dominant in the system.
Three possible types of causal relationships between concepts Ci and Cj express the influence of one concept on another as follows:
a)   wij > 0 indicates a positive causality, then an increase (decrease) on Ci will produce an increment (decrease) on the effect concept Cj with intensity |wij |.
b)   wij < 0 indicates a negative causality, then an increase (decrease) on Ci will produce a decrease (increase) on the effect concept Cj with intensity | wij |.
c)    wij = 0 denoting the absence of a causal (or in other words, neutral) relationship between concepts Ci and Cj.
For our case of studying startle events and its associativity with reduced performance, event causality FCM serves two key  functions: explanatory – what is happening in the system and predictive – what will happen next in the system. Invariably, the balance of these functions is restricted by the convergence thresholds anchored to the activation functions of the system nodes. This is accomplished using a rule-based fuzzy inference system, deciphered from expert judgment. The judgement elicited from the experts, help to guide understanding of the possible correlations that exist between the human factors during the execution of a high cognitive workload. This is of crucial importance to comprehend how decision errors may be alleviated, particularly when situation awareness is compromised, and the pilot becomes startled by ongoing inflight events. This supposition allows us to establish an experimental framework for investigating startle in a novice pilot. The FCM facilitates the determination of a concept (node) hierarchy, based on the considered interaction of human factors, for a structured analysis of the case study – embodied in experimental protocols. From this generation process, the aggregated data from the study provides the basis of objective reflection on the FCMs effectiveness, for understanding startle causality, based on a GA pilot in VFR, as an example.
As mentioned, human factors that are considered within this study (that form the basis of the causal variables used for the questionnaire), are adapted from the HFACS taxonomy on human factors [22]. Their work identified six major perspectives for the consideration of human factor errors which include Cognitive, Ergonomic, Behavioral, Aeromedical, Psychosocial, and Organisational perspectives. These six perspectives subsequently distil into four groupings regarding causal factors. These are Acts and Omissions; Preconditions and Local Factors; Supervision and Local Management; Organisational Influences – and then break down into 19 concepts. These contributors provide a contextual guide to help understand the symbiotic structure of our human-aircraft interaction system. Table II provides an overview of these concepts, distilled as far as causality is concerned and provides these factors in rank order as chosen by the expert panel. Figure 2 is an adaptation of the SEEV framework [20], [24] as it applies to the task of piloting an aircraft, which is relevant to this research. The model is pertinent in the sense that it provides a succinct overview of how the attendance to a task in the hugely dynamic environment of a modern cockpit is:
 
 
 
·         firstly, driven by visual acuity (considered in the context of disrupted scanning activity by the pilot due to being startled).
·         The effort required to understand the dynamism of context within which the inflight objective is to be completed.
The model provides a probabilistic estimation of how attending to some point of interest P(AOI) is achieved, under the influence of perception filters in a larger AOI. This probability of attendance is provided as a linear weighted combination of four components (concepts in practical terms). These are salience, effort, expectancy and value, and their respective scaling factors as shown in the following equation :
P(AOI) = s*S – ef*EF + ex*EX + v*V (2)
The SEEV model applied to determine visual attention, was found to produce better accuracy and consistency with actual human behaviour [47] [48]. Compared to probabilistic scan behaviours methods, for predicting scan pattern given an environmental context, the SEEV model performs far more favourably. It highlights the challenge of attending to an unexpected evolving situation and the constraints of expectancy on the choice conundrum of such a scenario or situation. Notably, this model suggests that cognitive processes can exist in parallel if their channels and required resources are different. For example, a pilot can read cockpit instruments while also processing auditory instructions. This is particularly relevant to this research if we are to conceptualise the potential impact on the pilots’ ability (in the context of the discussions presented earlier) considering disorientation and startle resilience within the first level state of the SA construct. A full treatment of this framework is outside the scope of this work; however, assurances can be obtained from [24], [29], [47], [49]. Mainly for its applicability in human-machine interaction studies where the effectiveness of workspace environment scanning and constraints on attention are considered.
The visual comprehension of available information by pilots in a high stressed situation could be examined objectively, based on the SEEV thinking if a normalised weighting of the human factors’ variables (causal inputs) can be obtained. Figure 3 showing the abstraction of the startle and surprise pathways by [11] inspire the author’s abstraction of a conceivable startle process, as in Figure 4 below. In [11], the proposed model examines the nature of surprise and startle from a systems perspective. Thus, laying the foundation for considering the effects of inflight startle and surprise responses. Indeed, this sustains the current course of research to be studied through formulating experiments aligned with the model dynamics. This work seeks to develop such experiments which are capable of testing, training and expanding the bandwidth of pilot’s intuitive reframing skills, given an unexpected event. While abstracting the experimental design, we keep in mind the aspirational target of integrating an eye tracker to capture physiological outputs (based on attention to points of interest considered as visual acuity). The discussion thus presents a considered approach to formulate an assessment of metacognitive skills through task performance outputs and pupillometric information. Thus, we can develop a  goal-based representation of the startle process path, considering only the fast appraisal and perception pathway, leading to the startle reflex being activated.
The highlighted startle process of  Figure 3  is suggested as a possible fault path for a GA pilot to be startled. The conceptualisation allows us to devise experimental protocols, based on attempting to create and stimulate a fast response in the active mental frame of the pilot, enough to trigger a startle. Such interaction is explored in this research, to determine a hierarchy of the associated cognitive features around visual processing of indicators (i.e. visual acuity) and inflight environmental conditions. Indeed, the assessment seeks to offer a basis for considering important aspects, crucial to the implementation of a flight simulation experiment activity to mitigate low startle resilience by the pilot. The use of an FCM model, in this case, is grounded on the vision of this work to support optimal decision making during exigent circumstances, which could lead to a LOC, or indeed, the prompt resolution of a fully developed aeroplane upset during flight operations.
From the guiding logic of figures 2 and 3 models, a conceptualisation of the startle process path, as suggested in Figure 4 below, is provided for a case of clear-air turbulence. In the physical sense of human-machine interaction scenario, adequate measures are taken to adequately capture both active (simulator output scores from pilot inputs) and inactive frames (impulsive physiological gaze response behaviours). The primary goal is to shed some light on the issue of startled responses which exacerbate the decline of performance. The abstraction also has the added benefit of providing a roadmap, for formulating appropriate scenarios, capable of instigating startle. Undeniably, a startled individual is more prone to applying instinctive reactions which might not be suitable in a situation where process and precise application of knowledge, are crucial to delivering a successful outcome.
A description of the startle causal factor FCM model build considerations is provided in the following sections. The mapping process, as mentioned, provides the foundation for judging the appropriateness and the efficacy of experimentation, analysis and any computation efforts in the quest to understand startle resilience. This is because the outputs of the mapping process (Table VI.) allows the homing in on the most important out of the 19 identified human factors considered crucial to the challenge of understanding the startle process drivers in the GA context.

IV. Building a Startle Causality FCM Model

A.       Codification
For developing the  FCM  model of a startle, four key principles [41], [50], [51], are relied upon to populate the map connections. These are as follows:
1.       Choose the number N and kind of concepts Ci of the FCM – In this case; we achieve this based on the HFACS framework.
2.       Determine the direction of relationships and interactions amongst the concepts.
3.       Use an inference rule to describe the relation between two concepts and infer a fuzzy linguistic set (weight) for the interconnection between the concepts.
4.       Linguistic weights for every interconnection are combined and transformed into numerical weights.
Having been briefed on the fundamental aspects of what constitutes a startle, within a piloting task, the expert(s) create a fuzzy correlation of the causal factors based on a linguistic representation of causal variables – Levels of Truth judged to fall between [0, 1]. This implies that we may use an FCM to structure a process wherein the perception of stakeholders on a system (or problem) is uncovered, and intuitive representations of the system are thus created. This sort of rapid prototyping abstraction is very valuable in the context of time-pressured incident management, fault finding and decision making efforts, for instance, as is shown in [52]–[54]. Following the outputs of a questionnaire given to the experts, 19 concepts were deemed relevant to the human factor challenge of inflight startle resilience which can lead to loss of control when it is lacking. To control the dimensionality of the problem space, the top 12 causal factors determined from expert judgement, are modelled as the driving inputs in the map, necessary for evoking a startle response. This implies that these top causal factors are set up as the decision concepts in the mapping. Setting of these factors as decision drivers are useful for the benefit of the algorithms which drive the outputs. These algorithms are discussed extensively in [46], [55], [56]
The following representation adopted from the work of [19] introduces definitions of a triangular fuzzy number concept, used for linguistic variable associations based on items articulated in the questionnaire for the FCM concepts (Appendix A). The triangulation of fuzzy numbers complements the definitions of fuzzy variable values previously discussed, allowing for an objective sliding scale within which the experts’ opinions are bounded for each concept considered.
The triangulation concept represents a fuzzy number A denoted by (a1, a2, a3) with a membership function defined
as: