Notice that no "logical" meaning is given for fuzzy rules. In ordinary mathematical logic, a rule "if A then B" or "A => B" is defined by a truth table, and we can used to draw sound conclusion from "A is known to be true" to "B is known to be true". In the fuzzy case, the book gives no indication of a precise meaning of rules.
The principle called "monotonic selection" p. 105 is presented as an ad hoc construction, and it will only work when the two fuzzy sets involved are represented by monotonic functions. The explanations in 4.6 of Mamdani and Sugeno style reasoning are not very successful. I suggest that you try to get an intuitive understanding of the different phases involved, and drop the detailed mathematical formulas which anyhow are not justified but presented in a very ad hoc fashion.