2. FORMATION OF RULES
The formation of rules is in general the canonical rule formation.
For any linguistic variable, there are three general forms in which the canonical
rules can be formed.
(1) Assignment statements
(2) Conditional statements
(3) Unconditional statements
3. ASSIGNMENT STATEMENTS
These statements are those in which the variable is assignment with the value.
The variable and the value assigned are combined by the assignment operator
“=.”
The assignment statements are necessary in forming fuzzy rules.
The examples of this type of statements are:
4. CONDITIONAL STATEMENTS
In this statements, some specific conditions are mentioned, if the
conditions are satisfied then it enters the following statements, called as
restrictions.
5. UNCONDITIONAL STATEMENTS
There is no specific condition that has to be satisfied in this form of statements.
Some of the unconditional statements are:
6. PROPERTIES OF SET OF RULES
The properties for the sets of rules are
– Completeness,
– Consistency,
– Continuity,
– Interaction.
7. (a) Completeness
A set of IF–THEN rules is complete if any combination of input values result in an
appropriate output value.
(b) Consistency
A set of IF–THEN rules is inconsistent if there are two rules with the same rules-
antecedent but different rule-consequents.
(c) Continuity
A set of IF–THEN rules is continuous if it does not have neighboring rules with
output fuzzy sets that have empty intersection.
(d) Interaction
In the interaction property, suppose that is a rule, “IF x is A THEN y is B,” this
meaning is represented by a fuzzy relation R2, then the composition of A and R
does not deliver B
8. FUZZY INFERENCE SYSTEM
Fuzzy Inference System (FIS) in usually known by several forms like Fuzzy
Rule Based System, Fuzzy Associative Memory and Fuzzy Models, Fuzzy Expert
System.
This Fuzzy Rule Based System is an integral portion of Fuzzy logic.
Fuzzy Inference System mainly finds its application in decision making.
Appropriate rules are formulated by the Fuzzy Inference System based on
which the decision is taken.
Fuzzy Set, Fuzzy Reasoning and Fuzzy rules are the backbone for Fuzzy
System.
fuzzy rules are utilized in the Fuzzy System for decision making. AND or OR is
used as the connector for the fuzzified rules.
9. The Fuzzy System takes a crisp input which is fuzzified by the fuzzifier and the
fuzzy system gives an output which is a fuzzy score that is defuzzified to a crisp
output.
10. WORKING OF FUZZY SYSTEM
The various modules of the Fuzzy Rule Based System are the fuzzification
module, database, rule base, inference module and the defuzzification module.
Fuzzy rules are contained in the rule base.
The components of Fuzzy Inference System is shown in Figure.
11. The fuzzification method is used to convert crsip input to fuzzy.
The rule base comprises of the collection of fuzzy rules.
This rule base and the data base are jointly knows as the knowledge-base.
Inference module takes the fuzzy input from the fuzzifier and the knowledge as
input and inference a fuzzy score.
Defuzzification converts the fuzzy score back to crisp outputs.
The Fuzzy Inference System performs the following steps for fuzzy reasoning.
The first step is called as fuzzification.
In this step, input variables on the antecedent are compared with the membership
values of every linguistic term.
12. In the second step, membership values of the premise are combined to obtain
good weight for every rule.
This is done using the MIN operator.
In the next step, the consequents of the rule is generated based on the weight.
The next step is defuzzification.
In this step, the consequents are combined to get the crisp output.
