This document discusses fuzzy rule-based classification systems. There are three types of rules that can be formed: assignment statements, conditional statements, and unconditional statements. A fuzzy inference system uses a rule base of fuzzy rules to perform fuzzy reasoning and mapping of fuzzy inputs to outputs. The key components of a fuzzy inference system are fuzzification of inputs, a rule base, an inference engine, and defuzzification of outputs. Fuzzy rule-based systems find application in decision making problems.

1. FUZZY RULE BASED
CLASSIFICATION SYSTEM

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.

13. Fuzzy Rule Bases
 Approximate Reasoning
 Disjunctive Rules
 Conjunctive Rules
 Fuzzy Relational Equations