Example Let us consider a fuzzy system with two inputs x₁ and x2 (antecedents) and a single output y (consequent). Inputs x and xhave 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 xis 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.
Example Let us consider a fuzzy system with two inputs x₁ and x2 (antecedents) and a single output y (consequent). Inputs x and xhave 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 xis 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.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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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 x is 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["M₂ (x₁), M (x₂)]
AND
AND
big
X2
Amedium Rule 1
mini
AR
9
Rule 2
0.
min
X2=5.58
Aggregation of big (v) and small (v)
big
small
(b)
y
(c)
small
big](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F68d4452b-3aad-4182-b6fc-60087e4ddd04%2Fbad98aa0-7820-4ff8-8074-7cec766444c6%2Ftt1phhd_processed.jpeg&w=3840&q=75)
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 x is 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["M₂ (x₁), M (x₂)]
AND
AND
big
X2
Amedium Rule 1
mini
AR
9
Rule 2
0.
min
X2=5.58
Aggregation of big (v) and small (v)
big
small
(b)
y
(c)
small
big
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