This subtracts one Triangular Fuzzy Number (TFN) from another via interval calculus. A TFN represented by the fuzzy set (triangular distribution):
$$X\ =( x_{1} ,x_{2} ,x_{3}) \ =\ \left\{\begin{matrix} 0 & for\ & x< x_{1}\\ \frac{2( x\ -\ x_{1})}{( x_{3} -x_{1})( x_{2} -x_{1})} & for\ & x_{1} \leq x< x_{3} \ \\ \frac{2}{x_{3} -x_{1}} & for & x\ =\ x_{2}\\ \frac{2( x_{3} -x)}{( x_{3} -x_{1})( x_{3} -x_{2})} & for\ & x_{2} < x\leq x_{3}\\ 0 & for & x >x_{3} \end{matrix}\right.$$
where \(x_1\) and \(x_3\) are the lower and upper bounds, respectively, and \(x_2\) is the mode.
The TFN X may have another TFN Y subtracted from it via:
$$X\ -\ Y\ =\ ( x_{1} -y_{3} ,\ x_{2} -y_{2} ,\ x_{3} -y_{1})$$
Details
It is not required for one IVFN to be "greater than" the other.
This difference may also be estimated by translating the TFN's into their corresponding distributions (e.g. tfn(-1, 0, 1) = EnvStats::rtri(n, min = -1, max = 1, mode = 0)), subtracting one distribution from the other, and estimating the minimum, mode, and maximum values of the difference distribution.
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(),
tfn()