Knowledge Based System is the system fitted with the mechanisms that enable solving problems on the base of the knowledge saved in the form of symbolic expressions (Popper a Kelemen 1988). It consists of:

• knowledge base,

• base of facts,

• inference engine.

In the growth simulator SIBYLA, the evaluation of the overall stand quality follows the principle of knowledge based systems. The methodology was published in the work of Fabrika (2006). 

Knowledge Base contains knowledge in the form of symbolic expressions. The growth simulator SIBYLA uses symbolic expressions of the production net type, which is composed of production rules. The production net is shown in Fig. 1 and Fig. 2.

Three criteria are evaluated: The overall quality of the stand is good (X), if all natural production (I), ecological structure (J), and economic returns (K) from the stand are good. 

The evaluation of criteria is based on their aspects. Natural production (I) is good, if all its aspects, i.e. the utilisation of production area (A), the utilisation of increment potential (B), the quality level of the production (C), and the production safety (D), are good. Ecological structure (J) is good, if vertical and tree species structure (E), type of horizontal mixture of trees (F), and safety of the structure (G) are all good. Economic returns (K) are good, if the relative financial returns from the stand (H) are good. Figure 2 presents the prodution network in the form of symbolic expressions. The nodes A, B, C, D, E, F, G, and H are called leaf nodes; the nodes I, J, and K are called intermediate nodes, and the node X is called a root node. The production network (Figure 2) can be described by four production rules:

The aspects are quantified using their indicators. The utilisation of the production area is assessed on the base of stand density (SD). The utilisation of the increment potential is assessed by the ratio between the total current increment obtained from the prognosis and the increment standard derived from yield tables (iP/iN). The quality level of the production is assessed using the percentage of the highest-quality assortments I, II and IIIA (%I-IIIA). The evaluation of the production safety is based on the height diameter ratio (h/d). The vertical and tree species structure is evaluated by "Arten Profil" index (APi). The type of horizontal mixture is assessed using the index of Clark and Evans (C&Ei). The safety structure is evaluated on the base of heigh diameter ratio (h/d). Relative financial returnes are evaluated by the ratio between the economic increment percentage (iV%) and the bank rate (BIR%).    

Figure 1 Knowledge base (production network) for the evaluation of the overall stand quality 

Figure 2 Symbolic expression of the production network 

The base of facts comprises such facts, which are related to the problem that is currently being solved. In the case of the knowledge based system of the growth simulator SIBYLA, the specific values of the indicators represent the facts. The values are obtained from the results of the growth simulations: 

• SD - represents stand density derived from yield tables.

• iP/iN - is calculated as the ratio between the total current increment (iP) and the increment standard (iN) derived from yield tables on the base of age (t), mean stem volume (v), number of trees of the main stand per hectare (N) and the proportion (%R) of all tree species (i=1..m) using the method of Šmelko et al. (2003):

• %I-IIIA - represents the volume percentage of the highest-quality assortments (I+II+IIIA) on stand volume.

• h/d - represents height diameter ratio of the stand.

• APi - is "Arten Profil" index of the stand.

• C&Ei - is the index of Clark and Evans.

• iV% - stands for the economic increment percentage derived from total current economic increment (CBP_e) and total economic production (CEP) as follows:

• BIR% - represents bank rate given in per cent set by a user (by default 2.5%). It is entered in the polynomial form:  

BIR% = a₀ + a₁ . x² + ... + a₆ . x⁶ 

where x is the sequential year of the simulation, and a_i are the coefficients defined by a user.

The overall stand quality is evaluated by plausibility (P). Its value fluctuates in the range from -1 to +1, where -1 indicates absolutely (100%) bad condition, and +1 indicates absolutely (100%) good condition. The value 0 means neutral or indefinite condition. The closer the value to -1, the worse the condition, and vice versa, the values closer to +1 indicate better condition. The inference engine utilises the following axioms: 

• the plausibility of conditions (see Figure 2) in the production network is indefinite,

• hence, the plausibility of the assumption (see Figure 2) in the production network is indefinite,

• the plausibility of the rule in the production network is absolute (100%),

• the conjuction linkages AND (see Figure 2) utilise minimum-biased weighted average according to Reynolds (1999):

where p_i are the plausibility values of conditions, AVG(p_i) and min(p_i) are average and minimum plausibility values, respectively.   

How is the plausibility of conditions determined in the assumption of the production rule ?

The plausibility of conditions is determined using the principle of fuzzy sets. The values of indicators are transformed to plausibility values using the graphs below: 

Figure 3 Fuzzy sets used for the transformation of indicators quantifying the aspects of natural production

Figure 4 Fuzzy sets used for the transformation of indicators quantifying the aspects of ecological structure 

Figure 5 Fuzzy sets used for the transformation of the indicator quantifying the aspect of economic returns

 The change of the overall stand quality can be determined as a percentual difference of the new condition P(2) from the initial condition P(1) as follows: 

p(dif)% = [ P(2) - P(1) ] . 50

The initial condition can represent the overall stand quality at the beginning of the simulation, and the new condition can represent the overall stand quality at the end of the simulation. This enables a user to compare several variants of stand development, e.g. by applying different thinning regimes.