problem, which should indicate the ideal municipal district. Afterwards, the results of the choice of the decision-maker are visualized in GIS.
1. Pre-selection of the alternatives: Multi-attribute class allocation problematic
The physical andor qualitative constraints of our problem act as restricting factors on the number of alternatives. A set of feasible alternatives is produced, characterizing the multi-
attribute class allocation problematic [37], in which each municipal district is allocated to one of the two classes, namely, acceptable for the subsequent analysis feasible or rejected a
priori. This phase is conducted in GIS environment.
This constraint is easily analyzed in GIS, because it represents a physical constraint, typically a topological operation. Superimposing these two thematic layers,
municipal_districts and road_network, a process known as overlay process of comparing spatial features in two or more map layers Manguire and Dangermond, 1991, we select the
alternatives that fully satisfy the pre-defined conditions.
After overlaying these two thematic layers, we want to select the objects of the layer municipal_districts that are intercepted by objects of the layer road_network. Besides
this, the descriptive attributes of the latter layer type of highway, physical aspects, etc. should fulfill the following conditions: highway_type = federal paved AND physical_aspect
= good OR regular. This procedure combines typical GIS functions overlay, spatial query and search, which, according to Maguire and Dangermond 1991, undertake complex
analysis.
This first constraint reduces the set of alternatives from 69 to 40, the procedure for which may be visualized in Figure 6 see appendix.
Apart from the constraint of the conservation aspect of the highways, the municipal districts should also meet the condition that the values of the Indexes of Education, Longevity and
Income must be larger than the average values for the State, 0.652, 0.641 and 0.705, respectively.
These indexes are the basic components of the Human Development Index HDI supplied by the UNDP. They refer, respectively, to the access to knowledge as measured by the
adult literacy rate and the combined primary, secondary and tertiary gross enrolment ratio, long healthy life as measured by life expectancy at birth and a decent standard of living as
measured by GDP per capita - PPP US UNDP, 1998. The average values for the State are lower than the values computed for Brazil as a whole, 0.83 education, 0.71 longevity
and 0.71 income, which by its turn does not have high values considering the international context Human Development Report, 2001. So, it seems unacceptable to consider as
candidates the municipalities that present indexes lower than the average for the Sate.
This constraint presents a Boolean algebra equation: the municipal districts must meet the 1st
AND 2nd
AND 3rd criteria. Similar to the previous step, this one is easily visualized in
GIS. This condition was extremely restrictive, and the query resulted in an extremely reduced set of alternatives. Making use of the hybrid approach already cited reducing the
strictness of the conjunctive method and not allowing the excessive permissiveness of the disjunctive method, this constraint was relaxed: the municipal district should simultaneously
fulfill at least two of these conditions.
The query conducted in GIS presents the following structure: to select the objects of the layer, municipal_districts that fulfill the condition expressed by [Longevity or = 0.641
AND Education or = 0.652 OR Income or = 0.705 AND Education or = 0.652 OR Longevity or = 0.641 AND Income or = 0.705], where the numbers represent the
average values of these indexes for Rio de Janeiro State, acquired directly from UNDP, 1998, which has its own methodology to obtain these normalized values. The closer the
value of the indicator is to 1, the greater is the human development level in the municipality or region in the considered dimension UNDP, 1998. This search resulted in the selection of
34 of the 69 municipal districts, as may be visualized in Figure 7 see attachment.
Universitas Sumatera Utara
The following stage is to overlay the two layers of information generated, creating a third layer that contains the municipal districts that fulfill both constraints: to be crossed by paved
federal highways, in a good or regular state of conservation, AND to present at least two of the constituent indicators of HDI greater than the average indexes for the State. The result of
this overlay operation displayed in figure 8see original paper produced a set of 26 alternatives that, in the 2nd stage, are appraised by multi-criteria analysis.
It can seem that we loose information in the next steps, not considering the municipalities excluded by the exclusion criteria. One should notice that these in formations are used in
different phases that have their usefulness in the global solution. The information about infrastructure highways, health longevity, education and work income are considered in
Model 2 section 2.2.3 through other variables. This would be the case of the longevity index that evaluates the life expectance, used to preselect some alternatives, and the
infant mortality rate in Model 2.
2. Choice of multi-criteria evaluation method
