atlas of urban vulnerability in spain: methodology and contents

ISVUN-G, Global criteria Classification, includes the whole set of the 20 urban
vulnerability indicators.
The maps included in this domain represent the position of each Spanish Census
section classified according to one of these five possible Multiple Criteria
classifications. Taking into account that each classification is performed on two
different universes (classifying every Census section with respect to the regional
Autonomous Community- or national context), there are 10 maps available.
From the methodological point of view, the Multiple Criteria classification consists in
grouping the elements of a set into equivalence classes or ranges, attending to the
value of p indicators or magnitudes, assigning the same global value to each of the
element of each class or range.
The classification of a set of elements by an indicator or criterion A, is different from the
classifications established by the criterion or indicators C and B. Thus, an element "a"
can be placed before another element "b" if classified using A indicator, but placed
behind when using indicators B or C. Multiple criteria classification method establishes,
in a mathematical way, groups of elements which are "not worse" within each other.
This means that they situated in positions or ranges, according to different criteria,
which do not establish if they are "better" or "worse" according to this criteria than
those in the same position, but certainly not worse than others situated in a lower
position.
Thus, let C be a finite set, in which each and every one of its elements can have p
scalar values V1,. . . , Vp, assigned. Each of these values represents the performance
of the element considered regarding a certain criterion. From now, we will assume that
one element is most suitable according to the i criterion when the value Vi is highest.
For any a, b ϵ C, we will say that a is strictly preferible than b or a dominates b-,
a b, if and only if Vi(a) Vi(b) for i ϵ {1, 2, . . . , p} and also Ǝj such that Vj(a) > Vj (b).
This means that a is not worse than b under any criterion of the whole set considered
and, also, a is strictly better than b under a certain criterion j.
To calculate the ranges or classes of equivalence, considering a set of elements C
and a set of criteria or characteristics P, the following recursive algorithm has to be
applied:
1. C1 C, i 1.
2. The optimal class or range for P is composed of every element a ϵ Ci, for which are
there not other element b ϵ Ci, such as b a. Let Oi be such a class or range, then:
a) If Oi=Ci, the sets O1, ...., Oi are the ranges or classes of equivalences
looked for: END.
b) In any other case, Ci+1=Ci-Oi, i i+1, repeat 2.
For each one of the 5 set of criteria considered (Sociodemographic, Socioeconomic,
Housing, Subjective or Global) and for each of the two possible universes (Spain, or
the respective Autonomous Community), the maps represent the value of the
respective Urban Vulnerability Synthetic Index (ISVU) for each set of criteria, in a rank
between 0 and 1.
The methodology for the calculation of the ISVU of each Census section, for each set
of criteria considered (G: global, SD: sociodemographic, SE: socioeconomic, R:
ATLAS OF URBAN VULNERABILITY IN SPAIN.
METHODOLOGY AND CONTENTS. PAG. 28