plrls {fuzzyreg}

Fuzzy Linear Regression using the Possibilistic Linear Regression with Least Squares Method

Description

The function calculates fuzzy regression coeficients using the possibilistic linear regression with least squares method developed by Lee and Tanaka (1999) that combines the least squares approach (fitting of a central tendency) with the possibilistic approach (fitting of spreads) when approximating an observed linear dependence by a fuzzy linear model.

Usage

plrls(x, y, h = 0, k1 = 1, k2 = 1, epsilon = 1e-05)

Arguments

x

two column matrix with the second column representing independent variable observations. The first column is related to the intercept, so it consists of ones. Missing values not allowed.

y

one column matrix of dependent variable values, missing values not allowed.

h

a scalar value in interval [0,1], specifying the h-level, which is the minimum degree of membership for each prediction in the model.

k1

weight coefficient for the centeral tendency.

k2

weight coefficient for the spreads.

epsilon

small positive number that supports search for the optimal solution.

Details

The function input expects crisp numbers of both the explanatory and response variables, and the prediction returns non-symmetric triangular fuzzy number coefficients.

The h-level is a degree of fitting chosen by the decision maker.

Value

Returns a fuzzylm object that includes the model coefficients, limits for data predictions from the model and the input data.

Note

Preferred use is through the fuzzylm wrapper function with argument method = "plrls".

References

Lee, H. and Tanaka, H. (1999) Fuzzy approximations with non-symmetric fuzzy parameters in fuzzy regression analysis. Journal of the Operations Research Society Japan 42: 98-112.

See Also

fuzzylm

Examples

x <- matrix(c(rep(1, 15), rep(1:3, each = 5)), ncol = 2)
y <- matrix(c(rnorm(5, 1), rnorm(5, 2), rnorm(5, 3)), ncol = 1)
plrls(x = x, y = y)