Analysis of Actors

Direct Influence: The Direct Influence option gives matrix, bar and Cartesian representations of the number of variables (factors, actors) that directly influence on each variable (factor, actor) of a particular system. This option represents a Boolean matrix (matrix of zeros [0] and ones [1]) as a result of the normalization of influence values provided by the experts. The sum of the values within a row (i) indicates the number of times that the variable (i) exerts an action on the system, this value constitutes and indicator of influences of the variable i. The sum of the values within a column (j) indicates the number of times that the variable (j) is influenced by other variables of the system, this value constitute and indicator of dependency of the variable j. Both the sum of values of the row and the column of a variable provide two indicators, motricity and dependency, which will be used to classify each variable according to those two criteria. Bar and Cartesian representations reflect this classification for each result option.

Indirect Influence: Besides the Direct Influences that take place in a system, a system presents other type of relationships known as Indirect Influences. Indirect or hidden relationships indicate the wave of effects on the studied system through a chain or nodes of influences. It is quite complicate for the human mind to visualize the complexity of such a huge network of hidden influence. This option provides the matrix multiplication operations applied to the structural matrix that permits to carry out different type of analysis regarding hidden influences. The Indirect Influence option distinguishes the number of roads or paths of length two (2) that reach or permit influence on other variables. The length of the road or path indicates the number of variables being influenced in order to reach the target variable (i.e. A g B g C; the linking arrows represent the number of paths the variable A goes through in order to influence on variable C). Indirect Influence option is the result of Direct Influence matrix to the power of two (2). This option gives also matrix, bar and Cartesian representations of the hidden Influence and Dependency indicators.

Potential Direct Influence: The Potential Direct Influence (PDI) option provides with the average values of the responses of the experts according to the set of criteria considered in the study. In this sense, this option represents the original matrix of direct influences provided straightforwardly by the experts. The use of the Potential Direct Influence classification is essential for the formulation of a first approach for the identification of key variables of a system. Each row of the PDI matrix represents the weight of influence of the variable (i) on the rest of the variables (A g B, A g C, A g D; first level path only considers the direct influence of A on the rest of the variables). Of course, although matrix, bar and graphical results of this option give an important overview of the system, comparison of results with higher level indirect influence analyses put in evidence the fact that there are strong hidden relationships belong the set of variables of each system.

Potential Indirect Influence: Based on the Potential Direct Influences that take place in a system, potential hidden influences of variables can be obtained by multiplying the PDI matrix by itself, this type of relationships are known as Potential Indirect Influences. The Potential Indirect relationships indicate the strength of effects on the studied system through a chain or nodes of influences. It is quite complicate for the human mind to evaluate the size of such a huge network of hidden influence. This option provides the matrix multiplication operations applied to the PDI matrix that permits to carry out different type of analysis regarding Potential Indirect influences. The Potential Indirect Influence option identifies the sizes of roads or paths of length two (2) that reach or permit influence on other variables. The length of the road or path indicates the number of variables being influenced in order to reach the target variable (i.e. A g B g C; the linking arrows represent the number of paths the variable A goes through in order to influence on variable C, as seen in the Indirect Influence option). The difference between the Indirect Influence option and the Potential Indirect Influence option is that the last one takes also into account the size of that road or path through which each variable influences other variables. The size of the path is given by the average value of expert responses (Potential Direct Influence). In summary, the Potential Indirect Influence option is the result of PDI matrix to the power of two (2). This option gives also matrix, bar and Cartesian representations of the hidden Potential Influence and Dependency indicators.

Potential Indirect Influence on the Power of 7: This option gives the forecaster the possibility to choose the length of paths or roads s/he would like to consider in the analysis of the studied system. In other words, the analyst hereby can choose from 1 to 10 the power of the exponential operation of the Boolean (zeros [0] and ones [1]) matrix (i.e. choosing number seven [7] will provide the indirect or hidden influence results to the seventh [7th] power). It has been proven that at a certain length of the paths (matrix multiplication) the number of roads of influences stabilizes. This number generally depends on the size of the system: generally systems with more than 10 variables reach stable values at the power of 7 or 8 to determine the number of influence paths for small systems it is usually enough to consider the 4th or 5th power of the indirect influence for very small systems it is recommended to evaluate the Potential Indirect Influence option. Note: the combobox next to this option provides the forecaster with the possibility of evaluating the matrix to the power of ten (10).

Relationship of Forces: This option provides the relationship of forces of the variables of the studied system. The coefficient of force is directly proportional to the relative indirect potential influence and inversely proportional to the dependency. Such relationships of forces are represented in three (3) different coefficients:

Real coefficient of force: r (i)

r (i) = (M_i/sum(M_i)) * (M_i/sum(M_i + D_i) )* (1/n)

Coefficient of force relative to the strongest variable: R (max)

R (max) = r (i) / max r (i)

Coefficient of force relative to the system: R (i)

R (i) = r (i) / sum r (i)

Where Mi is the indirect potential influence of the variable (f/actor, i.e. Ai), and n is the total number of variables (f/actors).

For simplicity, this coefficient is normalized using two (2) different criteria: dividing r (i) by the maximum real coefficient, and thus giving the relative strength of the variable (f/actor) based on the strongest variable (f/actor) of the system: R (max) dividing r (i) by the sum of the real coefficients, and thus giving the relative strength of the variable (f/actor) in the system: R (i)

The three different coefficient values for each variable are represented in the last three columns of the matrix of this option. The bar chart provided in this option represents the coefficient of force of each studied variable related to the strongest variable. In this sense, the strongest variable will be represented with the highest bar and the value 1.