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At the Britannica article on Fuzzy Logic, there is a brief introduction to, and history of, fuzzy logic and fuzzy control. It's a good summary for non-technical readers, and you might want to keep it on hand for the inspectors.
At Input Page for Shoe Sizes , there is a small expert system which I wrote to demonstrate fuzzy logic. It is based on a tutorial paper, and runs rules that predict a person's shoe size from their height. Your KPIs rules work the same way, so I use this in some of my explanations. Please try the system by following the instructions on the linked page. When it gives a result, look at the explanatory graphs on the output page, and see how each rule contributes to the result via the input's membership in its fuzzy set. The rules I wrote for you are doing the same.
The paper "Animated Fuzzy Logic" (PDF) by Gary Meehan and Mike Joy introduced the shoe-size rules to the literature and is the tutorial paper I cited above. You can download it from "Animated Fuzzy Logic" .
Unless you're a computer scientist, much of it — especially the stuff about functional programming — won't mean much. However, it's worth skimming to see what the authors say about why fuzzy logic is useful. The more you can make these ideas your own and internalise why they're useful for KPIs, the more you'll impress the government inspectors, and the easier it will be to talk to your programmers when you go on to commercialise. See what you can make of §4 and Figure 8, which show how the fuzzy sets used in the shoe-size system cover the advice space, and how each fuzzy set contributes to a result.
I have written a tutorial in Word format. It doesn't assume any prior knowledge. At the least, see how fuzzy sets can be represented as XY graphs of sloping lines, triangles, and trapezoids, and how inputs to rules can be plotted on the X axis and a membership line derived from that. Note the difference between sets denoting the low end of an attribute, those denoting the high, and those in the middle. See how the weighting of output sets means that different rules can contribute different strengths to a result.
At Input Page for Simple KPis is an expert system which relates one key performance indicator, annual revenue growth, with a measure of investment attractiveness. It uses several rules which cover the advice space in the same way as the shoe-size rules cover different portions of the mapping from height to shoe-size. Try it with inputs first of 10 and then of 90, to see how different fuzzy sets get involved and weight the output. See how the diagnostic graphs explain its conclusions.
At "A very brief introduction to Fuzzy Logic and Fuzzy Systems", there's a nice article by Carmel Gafa which explains fuzzy sets, fuzzy rules, expert systems, and that constructs an expert system to control the speed of a fan based on ambient temperature and humidity. The article covers much of the same space as above, but is worth reading once you've tried my two expert systems above. Work through it, and imagine that instead of doing a fan with temperature and humidity, you're doing start-ups with indicators such as annual revenue growth, customer churn rate, burn rate, and gross margin. What rules would you write? What would the inference engine do when evaluating them? What might their membership graphs look like? Think about this in combination with the section "Leverage Your Expertise" in my Commercialising page. As I said above, the more you can make this stuff your own, the better you'll get on at demonstrations and discussions.