Exercise 2.4 (Inverted Pendulum: Rule-Base Modifications): In this problem we will study the effects of adding rules to the rule-base. Suppose that we use seven triangular membership functions on each universe of discourse and make them uniformly distributed in the same manner as how we did in Exercise 2.3. In particular, make the points at which the outermost input membership functions for e saturate at  and for  at . For u make the outermost ones have their peaks at ±20. (a) Define a rule-base (i.e., membership functions and rules) that uses all possible rules, and provide a rule-base table to list all of the rules (make an appropriate choice of the linguistic-numeric values for the premise terms and consequents). There should be 49 rules. (b) Use triangular membership functions and repeat Exercise 2.3 (a), (b), (c), (d), (e) (but provide the implied fuzzy sets for the four rules that are on), (f), (g) (but use all four implied fuzzy sets in the COG computation), (h), and (i). Exercise2.4 （a）、 error -3 -2 -1 0 1 2 3  -3 3 3 3 2 2 1 0  -2 3 3 2 2 1 0 -1  -1 3 2 2 1 0 -1 -2  0 2 2 1 0 -1 -2 -2  1 2 1 0 -1 -2 -2 -3  2 1 0 -1 -2 -2 -3 -3  3 0 -1 -2 -2 -3 -3 -3   （b）、 a.  b.  c.  d. 规则1. If error is “0” and change-in-error is “1” Then force is “-1”; 规则2. If error is “0” and change-in-error is “2” Then force is “-2”.  其中input1为error input2 为 change-in-error output1为force e. 规则：If error is”1” and change-in-error is “1” Then force is “-2”; If error is”1” and change-in-error is “2” Then force is “-2”; If error is”2” and change-in-error is “1” Then force is “-2”; If error is”2” and change-in-error is “2” Then force is “-3”;  f. 所做结果如d图所示。force=-7.74 g. 所做结果如e图所示。force=-16.7 h.  i.