There are several methods to defuzzify, one of them is indeed triangle, the simpler one is the pole method.
the result is the same but with less calculation.
suppose we have 9 rules that leads us to three values:
washingtimeshort,middle,high.
short time is 1 hour middle is 2 hours and high is 3 hours.
each rule gives us values for 1 washingtime.
put them on a line like short 0,0.1,0
middle 0.5,0.8,0.1
high 0.8,0.5,0.0
adding them up
0.1*1hr=0.1
0.5+0.8+0.1=1.4*2hr=2.8hr
0.8+0.5+0=1.3*3=3.9hr
total = 6.8 hr
total peaks 0.1+1.4+1.3= 2.8
so 6.8/2.8=2.43 hr washingtime.
the book uses triangles math.
first they calculate where z3 is by using the membership on a line from 160 to 4000
example up
=0.5
so 0.5 *(4000-160)+160=2080
z3'is the middle between 4000 and 2080 = 2960
now he claims the Zp is these added and that is wrong.
You have to calculate the weightpoint from this triangle
as this gets way to complicated for you, and way over for this simple type of fuzzy.
The method comes from the way we fuzzyfi the inputs.
we calculate the membership of an input signal the same by looking on a line of a triangle where the membership is.
And yes in my program i can use this method of defuzz, but keep it simple with the averagemethod.
Zadev described a lot of calcualtions, and the starter is the triangle, but also poisse, sinus, experiencelines can be used.
with experiencelines from statistics is meant how many people feel it is cold, so sometimes the line is very steep, and can have all types of shape, depending on the question and the way of asking.