IntroductionDecision Support Systems have been defined as interactive computer-based systems that help decision makers in the use of data and models in solving unstructured problems. A simplified model for the decision making process (DM) includes the following stages: 1) Identifying the problem, 2) identifying and modelling the objective(s) of the decision, 3) collecting, generating and or combining data to generate alternative scenarios 4) evaluating alternatives according to objectives established, 5) choosing an alternative and conducting a sensitive analysis. If decision maker(s) estimate(s) there is enough information, the process ends with a final decision, otherwise the flow goes back to the identifying objectives (2) or to the generating alternatives stages [1](see Fig 1). Like for Artificial Intelligence, the boundaries for defining what falls under Decision Support Systems (DSS) seem to be diffuse. However, most of the authors who have tried to give a definition agree that one of the most important characteristics is that the human judgment remains in the decision making process cycle, as a key actor, generating alternatives, re-defining and re-modelling objectives since this is a task involving creativity, which cannot be mechanized. Computers, in turn, can help humans in gathering data, generating various decision alternatives, evaluating their outcome according to the decisions goals, visualizing these results and communicating the results to others.

Fig. 1 Decision Making Process [1]

Frequently, DSS are deals with ill-structured problems; this means that the goals might be not totally clear and/or there is insufficient information to solve them in a certain optimal way. Furthermore, in ill-structured problems there are many stakeholders and many decision makers, so the solution tends to be subjective and unique. Also DSS systems use various models and analysis techniques and are intended to be used by non-computer experts. Hence, a DSS must be very interactive, flexible and adaptable in order to support different solution approaches. Furthermore, DSSs oriented to spatial problems must be able to model the environment and evaluate the impact of changes under various hypotheses. Also, spatial information is inherently fuzzy and uncertain [2], this means that fuzzy analysis techniques are needed.

From the available literature about GISs used to support DM, we realize that there is an important number of modelling tools available, which can generate a certain scenario for a geographical area applying certain evaluation functions and showing the output, like for vegetation winter survival [3], wind farms locations [4] or forest production estimation [5]. However, the great majority of the existing GISs are not explicitly designed to support a DM

cycle. Furthermore, the process of generating various alternative scenarios according to different criteria and comparing them is in most cases, a difficult and time consuming task. In order to implement a DM process we need to abstract the modelling part from the DM cycle and allow the decision maker to generate multiple scenarios according to different hypotheses and compare the outcomes in a simple and systematic way.

There are many types of decision problems involving spatial issues that might be solved with the help of a GIS. The most recurrent problem can be generally stated in the following way: Find a suitable area to “do” something. For example: in [6], authors explain how to find specific locations for constructing artificial water recharge aquifers using floods. In this example decision makers must be experts on aquifers recharge, but they will need historical information and spatial data in order to design a formula which reflects the correct criteria for selecting the suitable area(s). This formula is used to build a suitability map using a GIS. This map typically shows the suitability level on each point of the map that satisfies the requirements. However in ill-structured problems this criteria is complex to build because the goals are not clear, also the multiple decision makers will tend to define different goals according to their knowledge.

A decision making process supported by GIS, typically starts with two inputs: data and expert knowledge. Models are built using experts´ knowledge and alternative scenarios are constructed using different data input. These scenarios can be compared because there are based on the same model, however the model is based on different expert knowledge. This can change, for example by including or removing a person in the experts’ team. If the knowledge is changed, is actually hard represent this changes in the model, and it is even harder compare results after a knowledge change.

In the DSS area there are mathematical tools designed to include expert knowledge and manage incomplete and uncertain. And in the last 20 years we can find a considerable amount of works that test different tools as belief functions in different spatial decision making problems [6] [7] [8] [9] getting good results. However this experiments are specific test for GIS applications.

Spatial Decision Support systems are especially relevant to a vast number of scientific, economic and humanistic areas. Among other, the most referenced by the literature are [10]:

Socio-economics: urban planning, industrial planning, agricultural land use, housing, educations, recreation natural resources, and many of new smart city applications.

Environmental: forestry, fire and epidemic control, floods and earthquake predictions, pollution, and also smart city application.

Management: organization logistics, electricity and telecommunication network planning, real time vehicle tracking, and other public services planifications like health services, security and fire protection, and also smart city applications.

According to some authors [11] a GIS is always a DSS, because they are used to supporting some stage of a decision making process. According to [2] GIS offer in general appropriate techniques for data management, information extraction, routine manipulation, and visualization, but they do not have the necessary analytical capabilities to manage a decision making process. Furthermore, in [12] authors claim that at the moment of publication (2010), the existing Spatial-DSS does not provides the needed characteristics, and the recent literature does not shows a progress in this issue.

According to [13] and our research the most needed characteristic to support spatial ill-structured problems are:

A. Combine data from different sources, providing degrees of certainty of each and a method to evaluate and combine data of same type and area but with different levels of certainty.

B. Generate suitability scenarios using different hypothesis in a flexible and systematic process. This is needed because its replace the criteria/formula specification, providing a method to combine the hypothesis of multiple experts and decision makers.

C. Offer suitable tools to compare different scenarios, this is needed to complete a decision making process. The comparison of two or more scenarios can provide a better solution and more information of the problem itself. Moreover, in ill-structured problems the information discovery is important to avoid specific solutions.

In this work we propose a method to discuss about scenarios and hypothesis using a collaborative software based on decision support techniques.

Scenario buildingIn previous works, we specifically describe how to build a scenario based on experts hypothesis using the Dempster Schäfer theory. In this section we are going to explain the benefits of using this technique and how it works.

Geographic information is usually represented in a discrete manner, with discrete geometries and deterministic values. However, a variable like temperature over a period of time becomes a random variable with frequency distributions and average values. Geographical points can be seen as random variables as well because they are mostly created using sampling procedures (e.g. GPS). Information associated to the geometries of the areas being represented could also have probabilistic and/or epistemic properties, e.g., which is the probability that the boundary runs exactly over a certain line?

The Dempster-Shafer theory was developed in 1967 by Dempster and extended by Shafer. It proposes to use sets of hypotheses regarding a variable (e.g. the temperature values in X are always between t1 and t2) associated with a probability of being correct. In order to explain this theory, we will use an example: Table 1 shows mean number of persons values associated to a certain location. In addition we have a query Q = [13-23] looking for locations with more than 13 and less than 23 persons. In this case, 3/5 of the locations meet this condition (locations 1 and 3 do not). Now Table 2 contains a "range" of persons registered for each location. In this case, only 2/5 of the locations fully satisfy the condition (positions 4 and 5) and 2/5 more may have a possibility to satisfy it (positions 1 and 2). One location does not fall within any interval of the query range (position 3) . The theory defines three types of answers to queries:

─ Plausible: is the probability that the random variable takes values within the range of the query. ─ Certain: is the probability that the whole range of the distribution of variable (D) is within the range of

the query.─ Uncertain: no valuable information can be derived from this data

Location Mean of #persons

1 122 203 74 195 17

Location Range of #persons

1 [9-21]2 [12-23]3 [5-10]4 [17-20]5 [14-22]

Table 1. Location versus mean number of persons

Table 1. Location versus range of number of persons

Using the Dempster-Shafer evaluation, we can calculate the hypotheses (Plausibility, Certainty and Uncertainty) for each location for the example shown in tables 1 and 2. We see that the Certainty level is 40% and Plausibility level is 80% (Table 3). These values are considered as lower and upper bounds of possibility, i.e. between 40% and 80% of the locations have some possibility to have a similar number of persons to the queried range. Additional to this information, the theory states that a certain weight should be given to each hypothesis. This weight should be assigned by a human expert or a heuristic. Table 4 shows an example where this weight is assigned by an expert. We will show an example where these weights are calculated by a heuristic formula later on this paper.

Loc. Persons Hypothesis1 [10,20] Plausible2 [15-25] Plausible3 [10-25] Uncertain4 [17-29] Certain5 [20-32] Certain

Persons Weight[10,20] 20%[15-25] 15%[10-25] 35%[17-29] 20%[20-32] 10%

Table 1. Location/Persons

D-S.

Table 4. Location/Persons weights

In this case, since Q = [13-23], the certainty is 30% (20% from location 4 plus 10% from location 5) and the plausibility is 65% (20% from position 1 plus 15% from position 2 which are plausible, plus 30% from the certain positions 4 and 5).

Using the Dempter-Shafer Theory the expert can define a set of Hypothesis expressing his knowledge, for example, if the expert is looking for persons one hypothesis can be “persons are in shops with a 20% of belief” or “persons are in schools or workplaces with a 40% of belief”. We also defined query hypothesis: “persons are in shops just like in place X,Y”. In the hypothesis statement the expert can define multiple hypotheses, which are combined using Dempter-Shafer combination rules. Furthermore, this complex scenarios are designed by the expert without requirement any kind of GIS expertise.

The result of combining the hypothesis with real data and fuzzy techniques for spatial representation, give us a suitability map. A suitability map typically shows the suitability level on each point of the map that satisfies the requirements, in or case, shows the belief degree of the hypothesis for evaluated each location. This kind of suitability map is what we call a simple scenario.

Fig. 5. 3D scenario build using Html5.

Collaborative scenario building tools

A complete scenario is the combination of various simple scenarios. Building a complete scenario requires a cooperative work between different stakeholders like experts in the particular scenario area and decision makers. In order to provide useful tools for collaborative scenario building for a single area we must divide the work in two different dimensions: Hypothesis Dimension and Time Dimension (see Fig X).

The hypothesis scenario is directly related to the collaboration between decision maker and experts. In order to support this stage we propose to use suitability map operators to combine different scenarios.

In this work we propose to use 4 different operators to collaborative build a scenario. In order to simplify and appreciate the differences between the operators, we are going to use 3 initial scenarios. Each initial scenario is the result of a specific set of hypothesis.

Scenario 1 Scenario 2 Scenario 3

Fig X, Initials Scenarios.

Sum OperatorSum is probably the simplest operator that a decision team must require, it consists on sum the belief degree of each scenario for each evaluated location. This operator can be useful when 3 independently but related scenarios must be merged. For example criminality, transit and street maintenance must be combined to evaluate the governmental resources are needed in a general and comparative scope. Using sum the decision maker can easily identify the need of resources for each location independently of the type of need.

S1+S2+S3

Fig X. Sum of 3 scenarios.

Average OperatorThe average operator is the simple average between the belief degrees of each location in each scenario. The result of this operator is visually similar to sum. However, it is proposed when a same resource can be applied to the 3 scenarios. For example an excavator can be used to multiple jobs, if the 3 scenarios problems can solved using the same resource, the average will indicate the most suitable place of it.

AVG(S1;S2;S3)

Fig X. Average of 3 scenarios.

OWA OperatorsAn OWA operator is the weighted average given an order. There are two basic types of OWA, when the values and weights are ordered from ascending or descending. Assuming that the values are ordered, only two results can be obtained. Given this, we defined 2 operators OWA ASC and OWA DESC.

OWA DESCThe values are ordered (desc) and the weight are also ordered in a descending way.

This combination can emphasize the biggest belief values of each scenario, avoiding that conceptual mistake given a simple average of numbers. For example, if a criminality scenario have a large belief degree in a certain location, using average this information can be mixed with lower degree values of the other scenarios.

OWA DESC

Fig X. OWA DESC applied to 3 scenarios.

OWA ASCThe values are ordered (desc) and the weight are also ordered in a ascending way. This

combination emphasize the belief when the values are constantly high in all scenarios. This operator is similar to average, but it not susceptible to isolated big values. It can be applied to allocate specific and limited resources that can support multiple scenarios. It can also be used to identify critical areas.

OWA ASC

Fig X. OWA ASC applied to 3 scenarios.

Collaborative Scenarios DiscussUsing the previously described operator we propose to provide a scenario discuss based on suitability maps.

Study caseChile is the country with the highest seismic activity in the world and it also have 6435 kilometers of coast. These conditions generates a complex evacuation scenario under natural disasters like tsunam2is. When a big earthquake occurs, the population in coast areas must go to higher grounds, however, there are some cities in the north of the country with another complications, the tsunami speed is higher than the possible evacuation speed. This is the case of Iquique.

Fig 1: Left Iquique from the sea, Right: Evacuation area.

In order to plan the evacuation of population, the emergency entity has traditional GIS, these systems allows to know how much population are registered in the area, how many schools, and other registered information. For example, Fig X shows the current SIG system of ONEMI (national emergency entity).

In tsunami case, the evacuation problem can be classify as an ill-problem, because there are not real information about how much people must be evacuated, there is not real knowledge about how much time it could last, an earthquake can occurs at different hours of the day and the population in the area changes according to the day and time.

In order to aboard this variables, incomplete information and multiples scenarios, we propose to use a Dempster-Shafer based Smart Geographical Information System (SGIS). Using the previously described SGIS, we can visualize the belief of concentration of population according to several hypotheses like:

During day people are in: Commercial areas, Schools, Universities, Libraries, Banks, Bus stations, etc.

Each location hypotheses must have a belief value assigned, and using the geographical databases like Openstreetmap it is possible to compute a “regular day population distribution” scenario of Iquique.

Regular day scenario

The time&belief based scenarios can provide a better information to the decision making when there are uncertainty, incomplete information, and complex modelling. However, the SGIS can be used to evaluate solutions has well.

For example, there is an area in the coast of Iquique were there are a high belief of population during day, these is because a high concentration of universities, restaurants, shopping center, popular beach (playa Brava), etc. This area is also located in the evacuation area and it is far from higher grounds.

In this area, one proposed solution is a vertical evacuation, these means that people must enter to high buildings. This solution scenario can be described has an evacuation possibility, this mean, that is there are a high building, the population near to it can enter to this building. However, an obvious problem will occur were there are higher concentrations of persons and a few buildings. Using the SGIS we can evaluate this scenario by combining the previous scenario (population belief), and a building location scenarios as 2 different hypotheses:

A vertical evacuation will occur when:

There are population There are buildings

The result evaluation of these scenario will depend on the belief degree values assigned to each hypotheses, however, as non-experts in the area we assigned a 100% to the building hypotheses, and a 20% to population. The Dempster-Shafer theory combines these hypothesis and the visual result is a single belief value for each evaluates area.

The result in Fig X, can be interpreted as a survival belief based on a single evacuation scenario/strategy.