Earthquake risk management of civil infrastructure: integrating soft and hard risks - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 234

9.5 Uncertainty: fuzziness, incompleteness and

randomness (FIR)

In order to reveal the uncertainties within the theories of reliability and
seismic vulnerability as described in the previous sections, then we need to
consider the classifi cation of uncertainty very carefully. It is not suffi cient
to state that all uncertainty can be modelled as randomness. In previous
work, the author has classifi ed uncertainty with three orthogonal character-
istics FIR - fuzziness, incompleteness and randomness. It was argued that
other characteristics of uncertainty, such as ambiguity, ambivalence, inde-
terminacy, unpredictability, and confl ict emerge from interactions among
these basic three attributes (Blockley, 2010).
Fuzziness is imprecision or vagueness of defi nition. It is implicit in
assumptions about levels of performance, such as IO , LS and CP . It is
explicit in the treatment of seismic vulnerability by Bernardini and Lago-
marsino (2008), as their analysis is based on the use of fuzzy and random
sets. Randomness, as discussed earlier is the lack of a specifi c pattern in
some data and is explicit in probability and reliability theory.
Incompleteness refers to things we do not know - it is perhaps the most
neglected characteristics of uncertainty. Some theorists even deny it exists.
It is not recognised in the axioms of classical probability theory, because
the probabilities of events or statement in the sample space must sum to
unity, i.e. everything in the sample space is totally known and identifi ed.
This requirement of totality is dropped in fuzzy sets and its derivative,
random sets, as used by Bernardini (2005). However, the axiom that replaces
it is also restrictive, since it requires total dependency between sets - in
effect they are nested (Blockley, 1985). Unfortunately, although incomplete-
ness is explicit in random set theory, it is not suffi ciently stressed as a major
source of uncertainty. There is a need, in any methodology, explicitly to
decouple measures for and against the truth or dependability of an event
or logical statement and hence to allow a state of 'don't know'. Interval
probability theory, interpreted as Italian fl ags, as described by Blockley and
Godfrey (2000) and Blockley (2008) was designed to facilitate a direct
handling of incompleteness.

9.6 Systems thinking

Systems thinking (Blockley and Godfrey, 2000) has been used to identify
and characterise the three different sources of FIR in risk management
previously classifi ed as random parameter, system model and human
(Blockley, 1980). They are hard system parameter uncertainty, hard system
model uncertainty, and soft system uncertainty. Our purpose will be to argue
not just for a need to integrate theories of reliability and vulnerability for