Fuzzy membership functions (MFs) usually stem from
experimental data, perception of the linguistic terms and the simulation of reality, which are characterised by the
defined linguistic variables and accommodated to the
environment under consideration. If a variable can take
words in natural languages as its value, it is called a linguistic
variable, where the words are characterised by
fuzzy sets defined in the universe of discourse in which
the variable is defined. Several geometric mapping functions
have been widely adopted, such as triangular, trapezoidal
and S-shaped MFs. However, triangular and
trapezoidal MFs are the most frequently used in construction
project risk analysis practice [1]. For example, in the
construction project risk management, the score system,
FI, RL, RS and RM are constructed by triangular and
trapezoidal MFs as shown in Figs. 2 and 3, where the linguistic
variables of the score system and FI are defined as
very poor (VP), poor (P), fair (F), good (G) and very
good (VG), RL and RS are defined as very low (VL),
low (L), medium (M), high(H) and very high (VH), and
RM is defined as negligible (N), minor (Mi), major
(Ma) and critical (C).
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