I am working through the work of Baoding Liu on uncertainty theory, specifically uncertain sets. The concept was introduced to represent 'unsharp' concepts such as humans being 'tall' or 'young' or a car being 'fast'.
I have two questions in relation to this. I'm posting as one as I believe this is the first post on uncertain set theory.
I believe I understand Axioms One through Three as defined in this paper. Particularly, I understand Axiom Three (the Subadditivity Axiom) to be:
The set function value of a union of sets is always less than or equal to the sum set function values of the individual sets.
However Axiom Four (the Product Axiom) I am unclear on, stated here for clarity:
Problem One: specifically, I am unclear as to (i) whether the product series operation is producing a Cartesian product, or a true value (and if so, how), and (ii) how the intersection operator returns a value after calling the set function on each event.
Problem Two: I am failing to make the connection between the theory and the provided examples, below:
Some help in deciphering this concept would be much appreciated.
(Far from exhaustive) Readings: