knowledge base

Knowledge Base:
The KB establishes the fundamental part of the Mamdani FRBS. It serves as the repository of the problem specific knowledge —that models the relationship between input and output of the underlying system.
Notice that the KB contains two different information levels
1. A Database (DB):
Containing :
• The linguistic term sets (the linguistic rules ).
• The membership functions.
• The scaling factors or scaling functions.
that are used to transform between the universe of discourse in which the fuzzy sets are defined to the domain of the system input and output variables.
The types of salling are:

a) Linear scalling:
Scaling allows it to define the fuzzy membership functions over a normalised universe of discourse. This variable is normalised by applying the parameterised scaling function, which incorporates the context information through the parameters min and max(0 and 1), whether fixed, tuned or learned scaling functions are employed.
b) Non-linear scaling:
This scalling provides a remedy to this problem as it modifies the relative distribution and changes the shape of the membership functions.
2. Rule Base(RB):
A rule base (RB) is comprised by a collection of linguistic rules that
are joined by the also operator. In other words, multiple rules can fire simultaneously for the same input.
The RB can present several structures.
List Of Rules.

Decision Table:
It becomes an equivalent and more compact representation for the same set of linguistic rules when only a few input variables (usually one or two) are considered by the FRBS.

Example:
Consider an FRBS where two input variables, x1 and x2, and a single
output variable, y, are involved with the following term sets associated:

Parameter name Type Linguistic Labels

x1 Input Var. {small , medium , large }
x2 Input Var. { short , medium , long }
y Output Var. { bad , medium , good }

Q/ Give five rule for these variables expressed in rule base and decition table:
Sol:
a) Using rule base:

R1 : If ( x1 is small ) and ( x2 is short ) Then (y is bad )

R2 : If ( x1 is small ) and ( x2 is medium ) Then (y is bad )

R3 : If ( x1 is medium ) and ( x2 is short ) Then (y is medium )

R4 : If ( x1 is large ) and ( x2 is medium ) Then (y is medium )

R5 : If ( x1 is large ) and ( x2 is long ) Then (y is good )







b) Usinge decision table:
large medium Small
medium bad short
medium bad medium
good long