A MULTICRITERIA BASED
METHODOLOGICAL APPROACH FOR QUALITY
CONTROL IN HISTORICAL BUILDINGS
The historic preservation works demand a tight organizational
structure of supervising and management, in order to increase
building’s lifetime, by ensuring that incidents of future failure are
avoided (preventive maintenance) (Moropoulou, Chandakas et al.).
In the proposed methodology, four Decision Support Systems (DSS’s) are enrolled to
asses a quality control index that will indicate whether and to which extend a building
needs intervention. For assessing the value of this index for a building, values for
three different groups of factors are gathered. The first group, the inspection group,
includes criteria responsible for calculating the inspection index for the specific
building, i.e. construction year, time and appraisals of previous inspection, building
category, etc . The second group of factors involves criteria that affect the diagnosis
process, including environment and pollution data, climate, etc., while the last
category, the intervention group of factors is related to parameters such as ISO
existence etc .
The values of the aforementioned groups of factors serve as input to a multicriteria
algorithm that calculates: a) significance weights for every factor, and b) an overall
index in each case. Three different indices are calculated at this point, which
subsequently act as parameter values for the three criteria (inspection, diagnosis and
intervention) and by applying an aggregation function, a quality index is assessed. In
flowchart of figure below the overall methodology is presented.
Start
Inspection
criteria
values
Diagnosis
criteria
values
Intervention
criteria
values
InspectDSS
DiagnoseDSS
InterveneDSS
All of the four
DSS’s exploit the so
called disaggregation –
aggregation approach
of Multiple Criteria
Decision Analysis field.
Inspection,
Diagnosis,
Intervention
indices
QualDSS
Need
intervention?
Quality index
End
End
In decision-making involving multiple criteria, the basic problem
stated by analysts and decision-makers concerns the way that the final
decision should be made. Two basic approaches under which numerous
methodologies have been developed are
a) the bottom up approach and
b) the top-down approach. The first, the most trivial one, includes all
methodologies and techniques that aim at building a decision model by
aggregating preferential information on criteria.
This means that the criteria aggregation model is known a priori
and the analyst guides the decision maker via a process of incrementally
declaring preferences to construct his/ her global preference model.
This approach is referred to the literature as the aggregation approach
and several representatives of it include MAUT, SMART, TOPSIS,
MACBETH, or AHP(Figueira, Greco et al. 2005). The second approach,
can be though as a reverse process in which the final decision in know a
priori and is decomposed to reveal the underlying attributes that led
the decision maker to the specific decision and utilize this information
to construct a value system that will be used in future decision support
cases.
The UTA (UTilités Additives) methods are considered the most representative methods
of the second approach, also known in the literature as the Disaggregation-Aggregation
approach (Jacquet-Lagreze and Siskos 1982 ) or simply the Disaggregation approach.
UTA methods refer to the philosophy of assessing a set of value or utility functions,
assuming the axiomatic basis of MAUT and adopting the preference disaggregation
principle.
UTA methodology uses linear programming techniques in order to optimally infer
additive value/utility functions, so that these functions are as consistent as possible with
the global decision-maker’s preferences (inference principle).
More details as well as a historical background on the development of the preference
disaggregation philosophy can be found in the review of Jacquet-Lagreze and Siskos
(Jacquet-Lagreze and Siskos 2001).
In the traditional aggregation paradigm, the criteria aggregation model is known a priori, while
the global preference is unknown. On the contrary, the philosophy of disaggregation involves the
inference of preference models from given global preferences.
The Disaggregation-Aggregation approach aims at analyzing the behavior and the cognitive style
of the Decision Maker (DM) (Jacquet-Lagreze and Siskos 2001). Special iterative interactive procedures
are used, where the components of the problem and the DM’s global judgment policy are analyzed and
then they are aggregated into a value system as shown in figure below.
The goal of this approach is to aid the DM to improve his/her knowledge about the decision
situation and his/her way of preferring that entails a consistent decision to be achieved.
In order to use global preference given data, Jacquet-Lagrèze and Siskos (JacquetLagreze and Siskos 2001) note that the clarification of the DM’s global preference
necessitates the use of a set of reference actions AR .
Usually, this set could be:
•A set of past decision alternatives (AR: past actions),
•A subset of decision actions, especially when A is large (AR⊂A),
•A set of fictitious actions, consisting of performances on the criteria, which can be
easily judged by the decision-maker to perform global comparisons (AR: fictitious
actions).
In each of the above cases, the DM is asked to express and/or confirm his/her
global preferences on the set AR taking into account the performances of the
reference actions on all criteria.
Following the Disaggregation- Aggregation methodological schema, the
modeling process of level 2 must conclude to a consistent family of criteria
{g1,g2,...,gk}. More details on the criterion family requirements can be also found
in (Figueira, Greco et al. 2005). We briefly mention here that each criterion
must be a non-decreasing, real valued function, defined on A, as follows:
g : A  [ g , g * ]  R / a  g( a )  R
j
j* j
[ g j*, g *j ] is the criterion evaluation scale
g j* g * the worst and the best level of the jth criterion respectively
j
gj(α) is the evaluation or performance of action α on the jth criterion and g(α) is the
vector of performances of action α on the k criteria.
The multi-criteria data input matrix is processed by the UTA* algorithm through an
iterative ordinal regression procedure. Analytical details and an illustrative example of
the UTA* algorithm can be found in (Siskos, Grigoroudis et al. 2005) and (Lakiotaki,
Matsatsinis et al. 2011).
In abstract, the UTA* algorithm, considers as input a weak-order preference
structure on a set of actions, together with the performances of the alternatives
on all attributes, and returns as output a set of additive value functions based
on multiple criteria, in such a way that the resulting structure would be as
consistent as possible with the initial structure given by the user.
This is accomplished by means of special linear programming techniques.
Four basic steps are followed in UTA* according to which, all the necessary
parameters to estimate global value functions for each item and user are
calculated.
The UTA* algorithm aims at estimating additive utilities of the form:
m
U (g)   ui ( gi )
i 1
subject to the following constrains:
ui ( gi* )  0 i
m
 u ( g )  u ( g )  u ( g )  ...  u
i 1
i
*
i
1
*
1
2
*
2
m
( g m* )  1
where ui(gi) i=1,…,m are non decreasing real valued functions, named marginal utility
functions.
Τhe UTA* algorithm may be summarized in the following steps:
Step 1: Express the global value of reference actions u[g(αk)], k = 1,2,...,m, first
in terms of marginal values ui(gi), and then in terms of variables wij according
to the formula 4.2.2-4. The transformation of the global value of reference
actions into weights values expression is made according to formula:
wij  ui ( gij 1)  ui ( gij )  0, i  1,2,..., n
and j  1,2,..., ai 1
u ( g1)  0
 i i

j 1

j
wit
ui ( gi ) 

t 1


i  1,2,..., n
i  1,2,..., n and j  2,3,..., ai 1
Step 2: Introduce two error functions σ+ and σ- on ARi (reference set of
alternatives) by writing for each pair of successive actions in the given
ranking the formula:
(ak , ak 1)  u[g(ak )]    ( )    ( )
 u[g(a 1)]    ( 1)    ( 1)
Step 3: Solve the linear program (LP):



[min]z 
[  ( k )    ( k )]

 1

subject to

 (a , a
if ak ak 1

k k 1)  


if ak ~ ak 1 
(ak , ak 1)  0

 n ai 1

wij  1

 i 1 j 1

wij  0,   ( k )  0,   ( k )  0



k

i, j and k
Step 4 (stability analysis): Check the existence of multiple or near optimal
solutions of the linear program. In case of non uniqueness, find the mean additive
value function of those (near) optimal solutions which maximize the objective
functions, on the polyhedron of the constraints of the LP bounded by the following
constraint, where z* is the optimal value of the LP in step 3 and ε a very small
positive number.
ui ( gi*) 
m

k 1
ai 1
wij

j 1
i  1,2,..., n
[  (ak )   (ak )]  z*  
By applying the UTA* algorithm all the necessary parameters to estimate
global utility functions U(g(α)) for each alternative are calculated. Thus, a value
is assessed quantifying alternative’s utility to each user and ensuring
consistency with his/ her value system.
In the case of a historical building the quality control index is the actual
utility function calculated as a linear combination of the three indices and their
respective weights. The three indices are calculated separately as utility
functions for each of the three aforementioned DSS’s.