Example Let us consider a fuzzy system with two inputs x₁ and x2 (antecedents) and a single output y (consequent). Inputs x and x₂ have three linguistic variables small, medium and big with a triangular membership function. Output y has two linguistic variables small and big with a triangular membership function as shown in Figure below. The rule base consists of the following two rules: Rule 1: IF x is small AND x.is medium THEN y is big Rule 2: IF x is medium AND x.is big THEN y is small Demonstrate entire process of fuzzification, aggregation and defuzzification in a fuzzy system and find the output when the inputs x₁and x₂ equal 3.89 and 5.58, respectively. XI small Amedium Amedium Rule 1 min Rule 2 min Aggregation of Mig (v) and small (v) x= 3.89 AND AND big 1 minu (x₁)(x₂)] xy=5.58 big small y (c) small big 7

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Example Let us consider a fuzzy system with two inputs x₁
and x2 (antecedents) and a single output y (consequent).
Inputs x and x₂ have three linguistic variables small, medium
and big with a triangular membership function. Output y has
two linguistic variables small and big with a triangular
membership function as shown in Figure below. The rule
base consists of the following two rules:
Rule 1: IF x is small AND xz is medium THEN y is big
Rule 2: IF xis medium AND x2 is big THEN y is small
Demonstrate entire process of fuzzification, aggregation and
defuzzification in a fuzzy system and find the output when
the inputs X₁ and x₂ equal 3.89 and 5.58, respectively.
X1
(a)
x₁= 3.89
small
Amedium
9
1
min[μ (x₁), M (x₂)]
AND
AND
big
X2
Amedium Rule 1
mini
ARU
9
Rule 2
min
X2=5.58
Aggregation of Mig (y) and small
big
small
(b)
y
(c)
small
big
Transcribed Image Text:Example Let us consider a fuzzy system with two inputs x₁ and x2 (antecedents) and a single output y (consequent). Inputs x and x₂ have three linguistic variables small, medium and big with a triangular membership function. Output y has two linguistic variables small and big with a triangular membership function as shown in Figure below. The rule base consists of the following two rules: Rule 1: IF x is small AND xz is medium THEN y is big Rule 2: IF xis medium AND x2 is big THEN y is small Demonstrate entire process of fuzzification, aggregation and defuzzification in a fuzzy system and find the output when the inputs X₁ and x₂ equal 3.89 and 5.58, respectively. X1 (a) x₁= 3.89 small Amedium 9 1 min[μ (x₁), M (x₂)] AND AND big X2 Amedium Rule 1 mini ARU 9 Rule 2 min X2=5.58 Aggregation of Mig (y) and small big small (b) y (c) small big
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