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Page 8 of 22 Ernest et al. Complex Eng Syst 2023;3:4 I http://dx.doi.org/10.20517/ces.2022.54

Figure 4. 3-FIS tree for Tank Firing Control utilized within the studied model.

Figure 5. MFs for Marine Firing FIS. Input 1 corresponds to normalized potential target health with 5 MFs for ”Very Low, Low, Moderate,
High, Very High”. Input 2 corresponds to current number of assigned friendly attackers already through this bidding cycle with 4 MFs for
”None, Some, Many, All”.

2.2.3. Explainability
After creating the tree structure, individual FISs are constructed using expert knowledge where available in
most cases. Often this will be in the form of the number of MFs which will be utilized in each FIS; often
leaving the specific distribution of said MFs across the input space to the machine learning process.

Explainability can be analyzed through a plethora of manners; the structure of the FISs created for this study
were designed to optimize the general explainability and interpretability of the system alongside raw perfor-
mance. As an example, the input MF sets for the Marine Firing FIS are shown in Figure 5.

A variety of approaches can be utilized to interpret the membership functions and provide explainability, but
one of the simplest approaches would be to report or display the most active membership function for each
input, corresponding with its rules. This represents the membership function with the largest impact on the
output. This can essentially be compared to Shapley Values, a popular explainability metric utilized across
multipleRLapproaches [22,23] . Ingeneralapproaches,thesevaluesenableadeterminationofthemostimpactful
variables leading to a particular output. Through the membership functions of a given FIS, this is innately
provided. Duetothefactthatallsystemvariableshavethepotentialtobehumanunderstandabletermswithina
fuzzy based system such as the GFT, there is further intrinsic value within this approach if the GFT is properly
designed. Note that explainability is not inherently granted through the utilization of fuzzy systems; rather
fuzzy logic is a construct in which systems that are highly explainable can be developed.