Triangular Fuzzy Number (TFN) - S3 Class

This constructs an triangular fuzzy number (ivfn) that represents a continuous, triangular distribution of values within a given range

Usage

tfn(lower = double(), mode = double(), upper = double())

Arguments

lower

[double(1) - Unrestriced (positive or negative)]
The lower limit of a Triangular Number set (the lower value must be less than or equal to the upper value)

mode

[double(1) - Unrestriced (positive or negative)]
The most likely value of a Triangular Number set

upper

[double(1) - Unrestriced (positive or negative)]
The upper limit of a Triangular Number set (the upper value must be greater or equal to the lower value)

Value

[tfn]
A triangular fuzzy number (TFN)

Details

The TFN class does not perform any operations on its input, rather it checks whether the input follows the defining criteria of TFNs

For TFNs, the lower bound must be less than or equal to the mode which must be less than or equal to the upper bound. If the lower bound, mode, and upper bound are equal, the TFN represents a "crisp" numeric value.

$$ \mathbf{TFN} :\ \left[ x^{L} ,\ x^{M} ,\ x^{U}\right] $$ where \(x^{L}\), \(x^{M}\), and \(x^{U}\) are the lower bound, mode, and upper bound of the TFN.

References

Chakraverty S, Sahoo DM, Mahato NR (2019). “Fuzzy Numbers.” In Concepts of Soft Computing, 53–69. Springer Singapore, Singapore. ISBN 9789811374296, doi:10.1007/978-981-13-7430-2_3.

Hanss M (ed.) (2005). Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, SpringerLink B\"ucher. Springer-Verlag Berlin Heidelberg, Berlin, Heidelberg. ISBN 978-3-540-24201-7, doi:10.1007/b138914.

Trillas E, Eciolaza L (2015). “Fuzzy Logic.” In volume 320, chapter Fuzzy Arithmetic, 141–158. Springer International Publishing, Cham. ISBN 978-3-319-14202-9, doi:10.1007/978-3-319-14203-6_6

See also

Other triangular-fuzzy-numbers: create_tfn_fcm_from_conventional_fcm(), make_adj_matrix_w_tfns(), print.tfn(), subtract_tfn()

Examples

tfn(lower = -1.0, mode = 0.0, upper = 1.0)
#> tfn: [-1, 0, 1]
tfn(0, 0.5, 0.8)
#> tfn: [0, 0.5, 0.8]
tfn(-0.3, 0.1, 0.4)
#> tfn: [-0.3, 0.1, 0.4]