Computation Examples

Let’s see the functioning of the model by hand-working kT over the model assump­tion that the triangle peak coordinate of kT membership functions is computed as an arithmetical mean of the other two coordinates ct = (ai + bi )/2 and b7 = 22.5°C.

The fuzzy model is running for the inputs: At = 14°C and j = 90. The process is illustrated graphically in Fig. 7.8. 1 [1]

Rule#4 mkT,4 = min (тд?,4, mj, s) = min(0.2, 0.4) = 0.2

Rule#5 mkT,5 = min (тді,5, mj, s) = min(0.7, 0.4) = 0.4

Rule#6 mkT,6 = min m&,6, mj, s = min(0.8, 0.4) = 0.4

Rule#12 mkT,5 = min(m&,4, mj, W) = min(0.2, 0.6) = 0.2

Rule#13 mkT,5 = min(тді,5, mj, W) = min(0.7, 0.6) = 0.6

Rule#14 mkT,5 = min(тді,6, mj, W) = min(0.8, 0.6) = 0.6

Each rule leads to an attribute of output linguistic variable clearness index. But

the rules Rule#5, Rule#12, Rule#13, Rule#14 sum up to the same conclusion,

attribute K5. The different degree of fulfillment K5 needs to be summarized in

just one conclusion, which is achieved by unifiying the individual results with

the fuzzy operator OR. Thus the confidence level of output linguistic variable

attribute K5 is obtained as:

mkT,5 = max (0.4,0.2,0.6,0.6) =0.6

c4mkT,4 (1 – mpi) + С5ткт,5 (1 – mp[2]) + С6ткт,6 (1 – mp6) mkT,4 (1 – ) + mkT,5 (1 – – Pp5) + mkT,6 (1 – )

3. Defuzzyfication. The result of the inference process is translated from fuzzy logic into a crisp value using the COG method (Eq. 7.17). After simple manipulation it writes:

and, using the numerical values from the inference task, the optimal kT predicted by the fuzzy algorithm is equal to 0.532.

Updated: August 4, 2015 — 1:52 am