3. The model of decision-making on HO's efficiency

Currently, there are sufficient number of models representing HO's activity in the STS structure and their efficiency in the professional activity.

Speaking generally, it is possible to state that evaluation of the HO's vocational aptitude can be based both on the assessment of their PIQ level and on the analysis of their efficiency at different stages of the operational activity.

Such structure of knowledge about the process of vocational aptitude evaluation is related to the hierarchical structures that allow employing bulk information at the certain levels of the hierarchy.

For the purpose of representation and analysis of knowledge about the HO's professional activity in the STS structure, the process of interaction between the human-operator, the technical system, and the environment is represented as a semantic network, Figure 2.

As for the term of act within the operator's activity, we understand an act within the operator's activity as a completed sequence of individual nonrepeated operator's actions implementing a single control cycle.

According to this, further we consider the operator's activity as a cyclic implementation of such operator's acts.

Taking into account, the known division of the operator's activity into several typical stages, we can assume relevance of division of the operator's act into separate steps (Eq. (1)):

Figure 2. The analysis model of the interaction process within STS.

$$\mathcal{S}\_t = \{ \mathcal{S}\_{t\_i} \} , i = 1, N \tag{1}$$

where Sti is the system element representing a single stage of the operator's activity (system element refers to a simplest atomic operation), i is the number of the operator's activity stages.

complexity of formalization of the operator's activity, numerous cross-connections between

Currently, there are sufficient number of models representing HO's activity in the STS struc-

Speaking generally, it is possible to state that evaluation of the HO's vocational aptitude can be based both on the assessment of their PIQ level and on the analysis of their efficiency at

Such structure of knowledge about the process of vocational aptitude evaluation is related to the hierarchical structures that allow employing bulk information at the certain levels of the

For the purpose of representation and analysis of knowledge about the HO's professional activity in the STS structure, the process of interaction between the human-operator, the

As for the term of act within the operator's activity, we understand an act within the operator's activity as a completed sequence of individual nonrepeated operator's actions implementing a

According to this, further we consider the operator's activity as a cyclic implementation of

Taking into account, the known division of the operator's activity into several typical stages,

we can assume relevance of division of the operator's act into separate steps (Eq. (1)):

technical system, and the environment is represented as a semantic network, Figure 2.

3. The model of decision-making on HO's efficiency

ture and their efficiency in the professional activity.

Figure 2. The analysis model of the interaction process within STS.

different stages of the operational activity.

hierarchy.

single control cycle.

such operator's acts.

PIQs and criteria of their selection.

132 Management of Information Systems

By means of a generalized structural analysis, the operator's activity is suggested to be divided into a set of hierarchical levels, each of them determines the modification of an operational control model [14, 15], Figure 3.

According to this system model, the operator's activity can be considered as sequential execution of the operator's activity stages: acceptance and perception of information, assessment and processing of information, decision-making, and implementation of the decision made.

In this model, the input data are the information from a sensory system about the control object status and the current state of the environment. At this stage of the operator's activity, the operator's actions are subject to the initial program control model.

After the input data are accepted and perceived, at the stage of information assessment and processing the data are transformed into the meaningful data. At this stage, it is possible to initiate a re-regulation process, in case if there is divergence between the accepted data and their admissible starting values specified by the program control model, and to replace the control model by interrupt control.

The control decision on modification of the control program should be made at the stage of decision-making when the situation model is constructed in dependence on the situation development.

Further, at the stage of the made decision implementation, the control impact on the system is formed on the base of the conceptual control model intended for defining the vector of the control impact for the purpose of the implementation of the further control program.

Figure 3. The system model of human-operator functions.

The outcome of this stage is the formation of the adaptive control model intended for defining the value of mismatching between the control impact made by the operator and the changes in the behavior of the control object.

The above described sequence of the actions is represented in the diagram by a solid line indicating the situation development. At the same time, it should be noted that a number of stages may be omitted when the full cycle of the operators' actions is implemented and repeated many times. Besides, it is possible to return to the previous stage of the operator's activity, or recursion. The mentioned situations are represented in the diagram by a dash line; the frequency of such situations, first of all, depends on the operator's experience and their effectiveness at the operator's activity stage. For example, if the control decision-making on the base of the available information is difficult, there is an alternative choice between decisionmaking under existing ambiguous conditions, additional assessment of the available information or returning to the stage of information acceptance and perception with the aim of data updating.

Obviously, the PIQ set for each certain case should be unique and depend on the specificity of professional work. Nevertheless, the diagram representing the interconnection between the operator's activity stages and the PIQs can be taken as an example for wide range of occupations related with control of moving objects, Figure 4.

Among these parameters the emphasis should be made on the following:


Among the parameters of sensory perception, the parameters describing the sight and hearing perception are the most valuable.

Figure 4. The diagram of interconnection between operator's activity stages and PIQs.

Figure 5. The hierarchical system of the logic inference for the STS operator's vocational aptitude level.

The outcome of this stage is the formation of the adaptive control model intended for defining the value of mismatching between the control impact made by the operator and the changes in

The above described sequence of the actions is represented in the diagram by a solid line indicating the situation development. At the same time, it should be noted that a number of stages may be omitted when the full cycle of the operators' actions is implemented and repeated many times. Besides, it is possible to return to the previous stage of the operator's activity, or recursion. The mentioned situations are represented in the diagram by a dash line; the frequency of such situations, first of all, depends on the operator's experience and their effectiveness at the operator's activity stage. For example, if the control decision-making on the base of the available information is difficult, there is an alternative choice between decisionmaking under existing ambiguous conditions, additional assessment of the available information or returning to the stage of information acceptance and perception with the aim of data

Obviously, the PIQ set for each certain case should be unique and depend on the specificity of professional work. Nevertheless, the diagram representing the interconnection between the operator's activity stages and the PIQs can be taken as an example for wide range of occupa-

Among the parameters of sensory perception, the parameters describing the sight and hearing

the behavior of the control object.

134 Management of Information Systems

perception are the most valuable.

tions related with control of moving objects, Figure 4.

Among these parameters the emphasis should be made on the following:

• the parameters describing the ability to the cognitive activity;

Figure 4. The diagram of interconnection between operator's activity stages and PIQs.

• the parameters describing the ability to the motor activity.

• the parameters describing the ability to sensory perception of information;

updating.

Among the parameters of the cognitive activity, the parameters describing the rate of information processing, memory, mechanical intelligence, and the ability to forecasting the situation development are the most important.

At the motor level, the parameters describing accuracy and the rate of motor program are the most significant.

The analysis of the system model and the pathways of the operator's actions makes it possible to reveal the most significant stages of the specific type of the operator's activity taking into account its peculiarities and to define a set of the operator's functions that determine the effectiveness of the operator's work in the greatest extent as well as to define the correspondence between the priority levels of operator's actions and the stages of the operator's activity.

In order to improve the confidence of vocational aptitude evaluation of the STS operator, the number of PIQs should tend to infinity. On the other side, it causes a combinatorial explosion and excessive complexity of computational algorithms.

According to this, we offer a methodological approach to evaluation of the integral index of vocational aptitude within the hierarchical system class on the base of the analytic hierarchy process; it includes the selection of 12 PIQs that are the most significant for the certain type of the operator's activity and their division into three groups: most important qualities (MIQ), important qualities (IQ), and less important qualities (LIQ), Figure 5.

Each group consists of its own set of four PIQs having weighting factors (Eq. (2)):

$$\mathcal{W} = (w\_1, \dots, w\_n) \tag{2}$$

The dependence of vocational aptitude value on the PIQs is modeled as follows (Eq. (3)):

$$\text{OLIT} = f(P) = f(a\_1, a\_2, a\_3, a\_4, a\_5, a\_6, a\_7, a\_8, a\_9, a\_{10}, a\_{11}, a\_{12})\tag{3}$$

on the basis of four knowledge bases that describe such dependences (Eq. (4)):

$$z\_1 = f\_2(a\_1, a\_2, a\_3, a\_4), \\ z\_2 = f\_2(a\_5, a\_6, a\_7, a\_8), \\ z\_3 = f\_2(a\_9, a\_{10}, a\_{11}, a\_{12}), \\ z = f\_3(z\_1, z\_2, z\_3) \tag{4}$$

In other words, OUT is a tree root, the operator's vocational aptitude; z1, …, z3—nonterminal nodes, the second stage convolutions; a1, …, a12—nonterminal nodes, the first stage convolutions; x1, …, xn—terminal nodes, individual impact factors, and W ¼ Wx ¼ wx<sup>1</sup> ;…; wxn ½ ð Þ, Wy ¼ wy<sup>1</sup> ;…; wyn , Wz <sup>¼</sup> wz<sup>1</sup> ; wz<sup>2</sup> ; wz<sup>3</sup> <sup>ð</sup> ;Þ�—weighting factors.

For assessment of certain PIQs, we suggest employing an analytical laboratory experiment. According to it, a certain fragment of the professional activity is reproduced in vitro, while the rest elements are purposefully eliminated, it allows to some extent segmenting the certain stages of the operator's activity.

One of the analytical in vitro experiments is testing, or tests. According to the traditional terminology, test refers to a task used for verification of the development level of the operator's psychophysiological properties. This type of experiment is usually deployed for investigation of the impact of different conditions on certain elements of the activity.

In this case, we can formally describe the relationships between the PIQs and the assessment tests undertaken for assessing the PIQ development level as follows: ai ¼ f xð Þ <sup>1</sup>;…; xn , where ð Þ x1;…; xn are the results of the assessment tests.

The system output is an integral assessment of the vocational aptitude within the range from 0 to 100%.

In addition to it, we need assessments of the certain PIQ development level within the range from 0 to 100% marking the efficiency of the operator's functions at the different stages and constituting an individual PIQ portrait of a testee.

For this purpose, we offer the inference A ¼ f g a1;…; a<sup>12</sup> , where f g a1;…; a<sup>12</sup> are the set of certain PIQs constructing an individual psychophysiological portrait of a testee, Figure 6.

An individual psychophysiological portrait may be used both for operational personnel training and for adaptive adjustment of an informational and technical component of the ergatic system to the user's abilities taking into account their current functional state.

To accomplish this, the combination of individual psychophysiological portraits that provide the general vocation aptitude level "not worse than normal," was defined by using simulation methods.

From the point of view of assuring, the whole system reliability such conditions as "the PIQ level is not worse than bad" and "the PIQ level is not worse than normal" are chosen as marginal ones.

Under the condition PIQtestee ij <sup>&</sup>lt; PIQnorm: ij PIQtest: ij <sup>&</sup>lt; PIQnorm: ij atestee ij < anorm: ij , the controlling action is formed in accordance with the set quality functional. Such controlling action is intended for operational personnel training that is for the development of the certain PIQs ensuring improvement of the general level of the operator's vocational aptitude (Eq. (5)):

$$
\Delta a\_{\vec{\imath}} = a\_{\vec{\imath}\,}^{\text{norm}} - a\_{\vec{\imath}\,}^{\text{testee}},\tag{5}
$$

Figure 6. The individual PIQ portrait of the operator.

z<sup>1</sup> ¼ f <sup>2</sup>ð Þ a1; a2; a3; a<sup>4</sup> , z<sup>2</sup> ¼ f <sup>2</sup>ð Þ a5; a6; a7; a<sup>8</sup> , z<sup>3</sup> ¼ f <sup>2</sup>ð Þ a9; a10; a11; a<sup>12</sup> , z ¼ f <sup>3</sup>ð Þ z1; z2; z<sup>3</sup> (4)

In other words, OUT is a tree root, the operator's vocational aptitude; z1, …, z3—nonterminal nodes, the second stage convolutions; a1, …, a12—nonterminal nodes, the first stage convolutions; x1, …, xn—terminal nodes, individual impact factors, and W ¼ Wx ¼ wx<sup>1</sup> ;…; wxn ½ ð Þ,

For assessment of certain PIQs, we suggest employing an analytical laboratory experiment. According to it, a certain fragment of the professional activity is reproduced in vitro, while the rest elements are purposefully eliminated, it allows to some extent segmenting the certain

One of the analytical in vitro experiments is testing, or tests. According to the traditional terminology, test refers to a task used for verification of the development level of the operator's psychophysiological properties. This type of experiment is usually deployed for investigation

In this case, we can formally describe the relationships between the PIQs and the assessment tests undertaken for assessing the PIQ development level as follows: ai ¼ f xð Þ <sup>1</sup>;…; xn , where

The system output is an integral assessment of the vocational aptitude within the range from 0

In addition to it, we need assessments of the certain PIQ development level within the range from 0 to 100% marking the efficiency of the operator's functions at the different stages and

For this purpose, we offer the inference A ¼ f g a1;…; a<sup>12</sup> , where f g a1;…; a<sup>12</sup> are the set of certain PIQs constructing an individual psychophysiological portrait of a testee, Figure 6.

An individual psychophysiological portrait may be used both for operational personnel training and for adaptive adjustment of an informational and technical component of the ergatic

To accomplish this, the combination of individual psychophysiological portraits that provide the general vocation aptitude level "not worse than normal," was defined by using simulation

From the point of view of assuring, the whole system reliability such conditions as "the PIQ level is not worse than bad" and "the PIQ level is not worse than normal" are chosen as marginal ones.

is formed in accordance with the set quality functional. Such controlling action is intended for operational personnel training that is for the development of the certain PIQs ensuring

ij <sup>&</sup>lt; PIQnorm:

ij � atestee

ij atestee

ij < anorm: ij , the controlling action

ij , (5)

ij PIQtest:

improvement of the general level of the operator's vocational aptitude (Eq. (5)):

<sup>Δ</sup>aij <sup>¼</sup> <sup>a</sup>norm

system to the user's abilities taking into account their current functional state.

ij <sup>&</sup>lt; PIQnorm:

, Wz <sup>¼</sup> wz<sup>1</sup> ; wz<sup>2</sup> ; wz<sup>3</sup> <sup>ð</sup> ;Þ�—weighting factors.

of the impact of different conditions on certain elements of the activity.

ð Þ x1;…; xn are the results of the assessment tests.

constituting an individual PIQ portrait of a testee.

Wy ¼ wy<sup>1</sup> ;…; wyn

136 Management of Information Systems

to 100%.

methods.

Under the condition PIQtestee

stages of the operator's activity.

where atestee: ij is the PIQ development level, anorm ij is the PIQ level "the PIQ level is not worse than normal."

So, the quality functional for practicing the certain PIQ of the greatest importance can be presented as the following (Eq. (6)):

$$f1 = \max\_{ij} f\left(w\_{ij}, c\_{ij}, \boldsymbol{\uprho}\left(a\_{ij}^{\text{testee}}, d\_{ij}^{\text{norm}}\right)\right),\tag{6}$$

where wi is a weight coefficient of the PIQ significance in the general structure of the vocational aptitude, ci is a weight coefficient of the PIQ development difficulty that divides the PIQs into developing, conventionally developing, and nondeveloping ones, φ aij testee: ; anorm ij � � is a function describing possibilities of the PIQ development in compliance with the initial level law.

The quality functional for practicing the PIQ combination may be presented as follows (Eq. (7)):

$$J2 = \sum\_{\vec{\imath}\vec{\jmath}\in k} f\left(w\_{\vec{\imath}\vec{\jmath}}, c\_{\vec{\imath}\vec{\jmath}}, \varphi\left(a\_{\vec{\imath}}^{\text{testte}}, a\_{\vec{\imath}\vec{\jmath}}^{\text{norm}}\right)\right),\tag{7}$$

At the same time, according to the initial level law, φ aij testee; anorm ij � � represents a nonlinear dependence of the possible change of the current atestee ij value on its relative level and may be expressed in the exponent form (Eq. (8)):

$$\varphi\left(a\_{i\bar{\jmath}}^{\text{test}}, a\_{i\bar{\jmath}}^{\text{norm}}\right) = \exp\left(a\_{i\bar{\jmath}}^{\text{norm}}\right) - \exp\left(a\_{i\bar{\jmath}}^{\text{test}}\right),\tag{8}$$

Practical evaluation of the operator's activity using of the hierarchical system of the logical inference for the STS operator's vocational aptitude level is offered to perform on the base of analyzing the PIQs' development level that have been defined by the test outcomes.

According to this, we face the challenge of developing a decision-making support system, which should connect local assessments from tests with the PIQ assessment and the evaluation of the operator's vocational aptitude in general.

Due to the difficulty of formal expression and structuring of the STS operator's activity both at the certain stages of the operator's activity and in general, it is proposed to use the fuzzy set theory for the operator's vocational aptitude evaluation.

The analysis of possible approaches to handle the problem of evaluation of the operator's activity shows that the use of so-called soft computing is one of the promising approaches to such tasks.

For modeling the operator's vocational aptitude, the mathematic model on the base of the fuzzy logic and the system of fuzzy inference have been developed, Figure 7.

In accordance with the proposed inference scheme, we can accept that on the first stage of evaluation the input variable xi is the values of the assessment test (AT) outcomes (Ti).

We can accept the variation range of the input variable xi as the universe of discourse. Space partition of the input variables was performed on the base of certain minimal and maximal values of the input variables—the AT values: xiE x ð Þ min <sup>i</sup> ; x ð Þ max i h i, where <sup>x</sup> ð Þ min <sup>i</sup> is the minimal

Figure 7. Structure of the fuzzy inference system.

value of the input parameter; x ð Þ max <sup>i</sup> is the maximal value of the input parameter. The membership function was preset for each part. According to the fuzzy logic theory, we can accept the existence of the crisp set X that is the universe of discourse.

φ aij

138 Management of Information Systems

of the operator's vocational aptitude in general.

such tasks.

theory for the operator's vocational aptitude evaluation.

values of the input variables—the AT values: xiE x

Figure 7. Structure of the fuzzy inference system.

testee; anorm ij � �

¼ exp aij

analyzing the PIQs' development level that have been defined by the test outcomes.

Practical evaluation of the operator's activity using of the hierarchical system of the logical inference for the STS operator's vocational aptitude level is offered to perform on the base of

According to this, we face the challenge of developing a decision-making support system, which should connect local assessments from tests with the PIQ assessment and the evaluation

Due to the difficulty of formal expression and structuring of the STS operator's activity both at the certain stages of the operator's activity and in general, it is proposed to use the fuzzy set

The analysis of possible approaches to handle the problem of evaluation of the operator's activity shows that the use of so-called soft computing is one of the promising approaches to

For modeling the operator's vocational aptitude, the mathematic model on the base of the

In accordance with the proposed inference scheme, we can accept that on the first stage of

We can accept the variation range of the input variable xi as the universe of discourse. Space partition of the input variables was performed on the base of certain minimal and maximal

> ð Þ min <sup>i</sup> ; x

ð Þ max i h i

, where x

ð Þ min

<sup>i</sup> is the minimal

evaluation the input variable xi is the values of the assessment test (AT) outcomes (Ti).

fuzzy logic and the system of fuzzy inference have been developed, Figure 7.

norm � � � exp aij

testee � �, (8)

In accordance with the hierarchical inference scheme, we can accept the existence of multiple pairs corresponding to the certain PIQs, (Eq. (9)):

$$T\_i = \left\{ \left( \mathbf{x}\_i, \mu\_{T\_i}(\mathbf{x}\_i) \right); \mathbf{x}\_i \in \mathbf{X} \right\} \mathbf{i} = \mathbf{1}, \ldots, \mathbf{n}, \tag{9}$$

where xi is the input variable - the outcome of the Ti test, μTi is the membership function.

The values of a linguistic variable are presented as a range of five fuzzy variables "very bad," "bad," "normal," "good," and "excellent."

As all the input parameters, X = (x1, …, xj, …, xn) make a different influence on the ultimate outcome, we used input ranking with weight factors.

The formation of a rule base for the certain operator's activity is performed by using special methods of expert assessment for each case. It allows transferring the general vocational aptitude model to the specific spheres of the operator's work. The whole process can be expressed as (Eq. (10)):

$$R\_1: \text{IF } (\mathbf{x}\_1 \mathbf{IS}.\mathbf{L}\_{11}).\text{AND}.(\mathbf{x}\_2 \mathbf{IS}.\mathbf{L}\_{12}).\text{AND}.\dots\text{AND}.(\mathbf{x}\_n \mathbf{IS}.\mathbf{L}\_{1n}), \text{THEN } a = B\_1$$

$$R\_i: \text{IF } (\mathbf{x}\_1 \mathbf{IS}.\mathbf{L}\_{i1}).\text{AND}.(\mathbf{x}\_2 \mathbf{IS}.\mathbf{L}\_{i2}).\text{AND}.\dots\text{AND}.(\mathbf{x}\_n \mathbf{IS}.\mathbf{L}\_{in}), \text{THEN } a = B\_i \tag{10}$$

$$R\_m: \text{IF } (\mathbf{x}\_1 \mathbf{IS}.\mathbf{L}\_{m1}).\text{AND}.(\mathbf{x}\_2 \mathbf{IS}.\mathbf{L}\_{m2}).\text{AND}.\dots\text{AND}.(\mathbf{x}\_n \mathbf{IS}.\mathbf{L}\_{mn}), \text{THEN } a = B\_m$$

where xk is the input variables; a is the output variable; Lik is the specified fuzzy sets with membership functions.

The inference scheme has been chosen taking into account that the Sugeno algorithm restricts the linearity between the input and output data, while the Mamdani mechanism allows using nonlinear membership functions. Besides, it is known that the Mamdani inference mechanism is more appropriate for expert systems due to transparency of the Mamdani fuzzy models. It is believed that the Mamdani inference mechanisms are more appropriate for applied problems, where the possibility of content interpretation is more important than simulation fidelity.

In this connection, it is proposed to present the inference on the base of the Mamdani mechanism using a mini-max composition of fuzzy sets.

As the scheme of the hierarchical fuzzy inference implies the operations with intermediate variables, it was considered to use two methods of their organization: with the intermediate procedure of defuzzification and fuzzification for the intermediate variables and without this procedure.

As according to the requirements to the decision-making support system, it is necessary to perform assessment of the PIQs; then at the first hierarchical level, we accept the scheme including two procedures: (i) the procedure of the output of inference result from the intermediate knowledge base as a fuzzy set without defuzzification and fuzzification of the intermediate variables and the transfer of the found membership degrees to the fussy inference mechanism of the next hierarchical level, and (ii) the procedure of defuzzification of the results with the aim to construct an individual professional portrait of a testee and their PIQs.

This can assure equivalency of fuzzy sets before and after the procedures of defuzzification and fuzzification of the intermediate variables transferred to the next hierarchical level.

On the other side, this allows obtaining crisp values in the output of the first hierarchical level for construction of an individual professional portrait of a testee and their PIQs.

At the second stage, PIQi is used as a linguistic variable, it is preset by a range of five elements, and the fuzzy variables are preset as follows (Eq. (11)):

$$PIQ\_i = \left\{ \left( a\_i, \mu\_{PIQ\_i}(a\_i) \right); a\_i \in A \right\} \\ i = 1, \ldots, 12,\tag{11}$$

where ai is the input variable—the PIQ (PIQi) values, μPIQi ð Þ ai is the input value degree of membership in this fuzzy set.

The input for the third stage of evaluation is the result of the second stage output. The fuzzy sets in this case are (Eq. (12)):

$$\text{GPIQ}\_{i} = \left\{ \left( z\_{i}, \mu\_{\text{GPIQ}\_{i}}(z\_{i}) \right); z\_{i} \in Z \right\} \mathbf{i} = \mathbf{1}, \mathbf{2}, \mathbf{3} \tag{12}$$

where zi is the input variable—the Grouped PIQ (GPIQi) values, μGPIQi ð Þ zi is the input value degree of membership in this fuzzy set.

Defuzzification makes it possible to transform the obtained fuzzy set into a crisp value by means of the known methods.

The formation of rule bases for the certain operator's activity is performed by using special methods of expert assessment for each case. It allows transferring the general model to the specific spheres of the operator's work.
