IVFN Subtraction (Interval Calculus)

This subtracts one Interval-Value Fuzzy Number (IVFN) from another via interval calculus. An IVFN represented by the interval X:

$$X\ =( x_{1}, x_{2}) \ =\ [ x_{1} ;x_{2}] =\{x\in \mathbb{R} \ |\ x_{1} \ \leq x\ \leq x_{2}\}$$

where \(x_1\) and \(x_2\) represent the lower and upper bounds, respectively.

The IVFN X may have another IVFN Y subtracted from it via:

$$X\ -\ Y\ =\ [ x_{1} \ -\ y_{2} ;\ x_{2} \ -\ y_{1}]$$

Usage

subtract_ivfn(ivfn_1 = ivfn(), ivfn_2 = ivfn())

Arguments

ivfn_1

[ivfn]
An interval-value fuzzy number (ivfn) object

ivfn_2

[ivfn]
An interval-value fuzzy number (ivfn) object

Value

[ivfn]
An IVFN object representing the subtraction of ivfn_2 from ivfn_1

Details

It is not required for one IVFN to be "greater than" the other.

This difference may also be estimated by translating the IVFN's into their corresponding distributions (e.g. ivfn(-1, 1) = runif(n, -1, 1)), subtracting one distribution from the other, and estimating the minimum and maximum values of the difference distribution.

References

Moore R, Lodwick W (2003). “Interval Analysis and Fuzzy Set Theory.” Fuzzy Sets and Systems, 135(1), 5–9. ISSN 01650114, doi:10.1016/S0165-0114(02)00246-4.

Dimuro GP (2011). “On Interval Fuzzy Numbers.” In 2011 Workshop-School on Theoretical Computer Science, 3–8. ISBN 978-0-7695-4628-5 978-1-4673-0225-8, doi:10.1109/WEIT.2011.19.

Moore RE (1966). Interval Analysis, volume 4. prentice-Hall Englewood Cliffs.

See also

Other interval-valued-fuzzy-numbers: c.ivfn(), create_ivfn_fcm_from_conventional_fcm(), ivfn(), make_adj_matrix_w_ivfns(), print.ivfn()

Examples

subtract_ivfn(ivfn(0.5, 0.8), ivfn(0.2, 0.5))
#> ivfn: [0, 0.6]
subtract_ivfn(ivfn(-0.5, 0.3), ivfn(0.4, 0.6))
#> ivfn: [-1.1, -0.1]
subtract_ivfn(ivfn(-1, 1), ivfn(-0.5, 0.5))
#> ivfn: [-1.5, 1.5]