Seismic risk analysis and management of civil infrastructure systems: an overview - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 140

GIT is an outcome of two generalizations (Klir 2004): the fi rst one entails
the realization of information defi ned as a statistical measure (Shannon and
Weaver 1964), and the second one entails the generalization of classical set
theory by fuzzy set theory (Zadeh 1965). The GIT framework for uncer-
tainty theories is provided in Fig. 6.1. Figure 6.1 indicates different well-
developed uncertainty theories (each arrow in the fi gure indicates a change
to a higher level of generality). As well, the numbers inside the square box
indicate ordering of these theories by their levels of generality.
Essentially, the ultimate goal of GIT is to enable risk analysts to quantify
prevalent uncertainty. In order to do this, the following four levels are pro-
posed (Klir 2004):

• Level 1 : fi nd an appropriate mathematical representation of the con-

ceived type of uncertainty.

• Level 2 : develop a calculus by which this type of uncertainty can be

properly manipulated.

• Level 3 : fi nd a meaningful way of measuring relevant uncertainty in any

situation that can be formalized in the theory.

General lower and
upper probabilities

7

Feasible interval-values
probability
distributions

Feasible fuzzy
probability
distributions

Capacities of
order 2

5

6 12

Capacities of
order 3

5

Capacities of
order

Fuzziied
DST ∞ : DST

4 11

Sugeno Fuzziied

λ -measures λ -measures

3 10

Classical probability
theory

Probability of
fuzzy events

1 8

Crisp probability
theory

Graded probability
theory

2 9

6.1 Ordering of uncertainty theories by levels of their generality (after
Klir 2004).