TEF {fuzzyreg}

Total Error of Fit of Fuzzy Regression Model

Description

Calculates total error of fit of a fuzzy regression model based on the concept of difference in membership functions of triangular fuzzy numbers between the estimated and observed fuzzy dependent variables.

Usage

TEF(object, sc = 1e-06, ...)

Arguments

object

a fuzzylm object.

sc

scaling constant used for numerical stability when spreads are equal to zero.

...

additional arguments passed to the integrate function.

Details

Calculates \sum{E}, where E is the difference in membership functions between two triangular fuzzy numbers. Here, between the observation and the prediction from a fuzzy regression model fuzzylm.

Value

A numeric with sum of pairwise differences between the triangular fuzzy numbers.

Note

TEF is not suitable for assessing fuzzy linear regression models that were fitted from crisp input data. Such data will result in division by zero. The scaling constant sc numerically allows the calculation to proceed, but it is not advisable. Use GOF instead.

References

Kim B. and Bishu R. R. (1998) Evaluation of fuzzy linear regression models by comparing membership functions. Fuzzy Sets and Systems 100: 343-352.

See Also

fuzzylm, GOF

Examples

data(fuzzydat)
f <- fuzzylm(y ~ x, fuzzydat$lee)
TEF(f)