**6. References**

306 Serial and Parallel Robot Manipulators – Kinematics, Dynamics, Control and Optimization

R4: 0.0184 IF (*DX(n-1*) IS *NB*) THEN (*DX(n)* IS *Z*) 0.6044

R5: 0.0105 IF (*DX(n-1)* IS *PB*) THEN (*DX(n)* IS *NB*) 0.4762

*L{DX(n)}* NB NS Z PS PB

PB 0.0051 0.0046 0.0010 0.0 0.0

PS 0.0115 0.0620 0.0609 0.0104 0.0008

Z 0.0017 0.1192 0.3953 0.0895 0.0068

NS 0.0001 0.0235 0.1430 0.0431 0.0023

NB 0 0.0030 0.0112 0.0044 0.0006

*P*(*L*{*DX* (*n* 1)}) 0.0184 0.2123 0.6114 0.1474 0.0105

To determine the predicted value *DX(n)=b\*,* for given value (crisp or fuzzy) *DX(n-1)=a\**, the reasoning procedure, described in 3.3 is used, e.g. for *DX(n-1)=1.55,* predicted value is approximated as equal to *DX(n)=0.30538.* This value depends on many parameters of the fuzzy model and the reasoning procedure. It is very useful to create the computing system with many options of changing the reasoning parameters. In Fig. 2 the predicted, mean

Table 4. Joint empirical probability distribution of two linguistic random variables

values of the increments has been underlined by thick line.

representing increments

ALSO (*DX(n)* IS *PB*) 0.0056

ALSO (*DX(n)* IS *PS*) 0.2363

ALSO (*DX(n)* IS *NS)* 0.1263

ALSO (*DX(n)* IS *PB*) 0.0330

ALSO (*DX(n)* IS *NS*) 0.4286

*P(L{DX(n-1)}, L{DX(n)})*

*L{DX(n-1)}* 

ALSO (*DX(n)* IS *Z*) 0.0952.


**Part 3** 

**Optimization** 

