FUZZY REGRESSION
BITS Pilani
Hyderabad Campus
TEAM MEMBERS
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ANUPAMA
HARIKA TRIKUTAM
TARUN GHANTA
REVANTH GADAMSETTY
BITS Pilani, Hyderabad Campus
INTRODUCTION
The Regression analysis is a technique of studying the dependence of one
variable, on one or more variables, with a view to estimate or predict the
average value of the dependent variables in terms of the known or fixed
values of the independent variables.
The goal of the regression analysis is:
(a) to find an appropriate mathematical model, and
(b) to determine the best-fitting coefficients of the model from the given
data.
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The following model shows the dependence of the output variable on the
inputs variables:
(1)
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NON-SYMMETRIC FUZZY
REGRESSION
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FULLY FUZZY LINEAR
REGRESSION SYSTEM
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MULTIPLICATION OF TWO
FUZZY NUMBERS
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METHODOLOGY
Methods used to solve the fully fuzzy linear regression
❑ Huang’s method
❑ LU decomposition method
❑ QR decomposition
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HUANG’S METHOD
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(A,M,N)⊗(x,y,z) = (b,g,h)
(Ax, Ay+Mx,Az+Nx)=(b,g,h)
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Ax=b
Ay+Mx=g
Az+Nx=h
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HUANG’S METHOD
METHOD ALGORITHM
Step 1: Express fuzzy matrix as three
crisp matrices A,M,N
• Take
Step 2 : Substitute A,M,N in equation
• (A,M,N)⊗(x,y,z) = (b,g,h)
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Step 3 : compute x,y,z
from the following
equations
•Ax=b
⟹ x=
•Ay=g-Mx ⟹•Az=h-Nx ⟹ z=-
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(code and examples of Huang’s method to be continued on Python)
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LU DECOMPOSITION
METHOD
A= LU
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LU DECOMPOSITION
METHOD ALGORITHM
Step 1: Assume that = (A,M,N)
A=
Step 2: Set
Step 3: Compute
Step 4: Compute
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Step 5: Compute the solution of the fully fuzzy
linear system (A,M,N)⊗(x,y,z)=(b,g,h) as follows:
x=
y=
z=
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(code and examples of LU decomposition method to be continued
on Python)
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QR DECOMPOSITION
THEOREM: If A is an m×k matrix with full column rank, then A can be factored as A =
QR where Q is an m×k matrix whose column vectors form an orthonormal basis for
the column space of A and R is a k×k invertible upper triangular matrix.
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BITS Pilani, Hyderabad Campus
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(A,M,N)⊗(x,y,z) = (b,g,h)
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APPLICATION OF FUZZY
REGRESSION
Estimation of air transport demand
Real state price prediction
Prediction of tool life used in milling
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Predict exchange rates for composite
currencies
Prediction of dissolved oxygen
Market demand estimation for new product
development
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THANK YOU
BITS Pilani, Hyderabad Campus