# Forest Fire Risk Forecasting with the Aid of Case-Based Reasoning
## 2 Background
### Case-Based Approach: Basic Principles  
Case-based reasoning (CBR) [20; 55] is a decision-making methodology that allows one to reuse and adapt (if necessary) previously obtained solutions to similar problems based on the principle of decision making \"by analogy\". The basic concept views a case as a structured representation of accumulated experience in the form of data and knowledge that provides its subsequent automated processing using specialized software [24; 56]. The following features of cases can be defined:  
* They represent domain specific knowledge related to the context that allows one to use this knowledge at the application level;* They can be presented in various forms, cover different time periods, and be associated with solutions with descriptions of problems, results, situations, etc. Each case is a unit of experience, the structure of which depends on the specifics of a particular problem but includes two main parts:
* Identifying (characterizing), which describes the experience in a way that allows one to assess the possibility of its reuse in a specific situation;
* Training (solution), which is a solution to a problem, proof of a solution (conclusion), alternative, or unsuccessful solutions. Solving problems with the use of CBR consists of a number of main stages: retrieve, reuse (including adaptation), revise, and retain, which are preceded by the stages of conceptualization and the formation of a case base. The task of the first preparatory stage (the conceptualization stage) is to form a case model based on some domain model describing a problematic situation. In our case, a problematic situation can be either a forest fire or a forest quarter. In fact, the case model is formed by redistributing significant characteristics or concepts of the domain according to the parts discussed above: identifying and training. As a result, a certain pattern is formed in the form of a domain class or frame [55; 57]. In this paper, information on the main factors influencing the occurrence and development of a wildfire (see Section 2.1) were used to form a case. At the second preparatory stage, the case base is formed according to the obtained model with possible indexing of cases [22]. To increase the speed when working with a case base, a database management system is usually used; however, typed text files can also be used for prototyping [55; 57]. Retrieval is the first main stage, the main purpose of which is to extract one or more cases similar to the current problem (situation) from the case base. Various metrics are used to calculate similarity [20; 22; 55; 57]: Euclidean, Hemming, probabilistic, Rogers-Tanimoto, Manhattan, Chebyshev, Mahalonobis, Zhuravlev, Bray-Curtis, Chekanovsky, Jacquard, etc. In this paper, we apply the modified Zhuravlev metric [58], which we used earlier [22]:  
\[\mathrm{s_{i}(c^{*},c_{i})=\sum}w_{i}\mathrm{h_{j}(p^{*},p_{ij})/N}, \tag{1}\]  
where \(\mathrm{s_{i}}\) is a similarity; \(\mathrm{c^{*}}\) is a description of a new object or a new case (current situation); \(c_{i}\) is an i-case from a case base; \(w_{j}\) is an information weight of a j-property of compared cases; \(p\) is a property of compared cases; \(N\) is the amount of properties of the compared cases; \(i\) is an index of cases in the case base; \(j\) is an index of a case properties; \(\mathrm{h_{j}}\) is a function for calculating similarity between property values. This function has three different forms depending on a type of a property value: quantitative, qualitative, and interval. For quantitative values:  
\[\mathrm{h_{j}(p^{*},p_{ij})=1,\ |\ v^{*}_{j}-v_{ij}|<\xi, \tag{2}\] \[\mathrm{h_{j}(p^{*},p_{ij})=0,\ |\ v^{*}_{j}-v_{ij}|\geq\xi,}\]  
where \(v^{*}_{j}\) is a value of a j-property of a new object or a new case (current situation); \(v_{ij}\) is a value of a j-property of an i-case from a case base; \(\xi\) is an acceptable difference in values, which is adjusted on the basis of empirical experimental data.