8.7 For the nonlinear function y=x^3 develop a fully rule-based system using four simple rules to approximate the output y. To develop the system, partition the range of the input x, [-1,1], into five triangular MFs, and partition the output range of y, [-5, 5], into three triangular MFs. Use input labels, negative-big, negative-small, zero, positive-small and positive-big. Use output labels, negative-big, zero, and positive-big. Use the following rules for the simulation: Rule 1: IF x is zero, THEN y is zero. Rule 2: IF x positive-big, THEN y is positive-big. Rule 3: IF x is negative-small, THEN y is negative-small. Conduct a simulation for the inputs: [-2, -1.5, -0.5, 0.5, 1.5, 2.0]
8.7 For the nonlinear function y=x^3 develop a fully rule-based system using four simple rules to approximate the output y. To develop the system, partition the range of the input x, [-1,1], into five triangular MFs, and partition the output range of y, [-5, 5], into three triangular MFs. Use input labels, negative-big, negative-small, zero, positive-small and positive-big. Use output labels, negative-big, zero, and positive-big. Use the following rules for the simulation: Rule 1: IF x is zero, THEN y is zero. Rule 2: IF x positive-big, THEN y is positive-big. Rule 3: IF x is negative-small, THEN y is negative-small. Conduct a simulation for the inputs: [-2, -1.5, -0.5, 0.5, 1.5, 2.0]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8.7 For the nonlinear function y=x^3 develop a fully rule-based system using four simple rules to approximate the output y. To develop the system, partition the range of the input x, [-1,1], into five triangular MFs, and partition the output range of y, [-5, 5], into three triangular MFs. Use input labels, negative-big, negative-small, zero, positive-small and positive-big. Use output labels, negative-big, zero, and positive-big. Use the following rules for the simulation:
Rule 1: IF x is zero, THEN y is zero.
Rule 2: IF x positive-big, THEN y is positive-big.
Rule 3: IF x is negative-small, THEN y is negative-small.
Conduct a simulation for the inputs: [-2, -1.5, -0.5, 0.5, 1.5, 2.0]
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