moflr {fuzzyreg}

Fuzzy Linear Regression Using the Multi-Objective Fuzzy Linear Regression Method

Description

This function calculates fuzzy regression coeficients using the multi-objective fuzzy linear regression (MOFLR) method developed by Nasrabadi et al. (2005) 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

moflr(x, y, omega = 0.5, sc = 1e-06)

Arguments

x

matrix of n independent variable values, followed by n spreads. First column is exptected to consist of ones, representing intercept. Missing values not allowed.

y

two column matrix of dependent variable values and the respective spread. Method assumes symmetric triangular fuzzy input, so the second spread (if present) is ignored. Missing values not allowed.

omega

a scalar that specifies weight that determines trade-off of between outliers penalization and data fitting in interval [0,1], where high values of omega decrease the penalization of outliers.

sc

scaling constant used to input random spreads for the intercept, necessary for computational stability.

Details

The function input expects both the response and the predictors in form of symmetric fuzzy numbers. The prediction returns symmetric triangular fuzzy number coefficients. The Nasrabadi et al.'s method can process datasets with multiple outliers. Values omega>0.5 decrease weight of outliers on the solution.

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 = "moflr".

References

Nasrabadi, M. M., Nasrabadi, E. and Nasrabady, A. R. (2005) Fuzzy linear regression analysis: a multi-objective programming approach. Applied Mathematics and Computation 163: 245-251.

See Also

fuzzylm

Examples

data(fuzzydat)
fuzzylm(y~x, fuzzydat$nas, "moflr", "xl", , "yl")