Expert System for Neurocognitive Rehabilitation Based on the Transfer of the ACE-R to CHC Model Factors

Abstract

This article focuses on developing an expert system applicable to the area of neurocognitive rehabilitation. The benefit of this interdisciplinary research is to propose an expert system that has been adapted based on real patients’ results from the Addenbrooke’s cognitive examination (ACE-R). One of this research’s main results is a unique proposal to transfer the ACE-R result to the CHC (Cattell–Horn–Carroll) intelligence model. This unique approach enables transforming the CHC model domains according to the modified ACE-R factor analysis, which has never been used before. The expert system inference results allow the automated optimized design of a neurorehabilitation plan to train patients’ cognitive functions according to the CHC model. A set of tasks in 6 difficulty levels (Level 1–Level 6) was proposed for each of the nine CHC model domains. For each patient, the ACE-R results helped determine specific CHC domains to be rehabilitated as well as the starting game level for the rehabilitation within each domain. The proposed expert system has been verified on real data of 705 patients and achieved an average error of 5.94% for all CHC model domains. The proposed system is to be included in the outcomes of the research project of the Technology Agency of the Czech Republic as a verified procedure for healthcare providers.

1. Introduction, Motivation and Research Focus

We perceive neurocognitive rehabilitation (NR) as a systematic effort to correct cognitive deficits based on assessment and understanding of the impairment of cognitive functions due to brain damage. The individuality of persons who undergo the NR is emphasized [1]. In its broader sense, the term cognitive rehabilitation focuses on the support of coping with mental deficits, development and re-establishment of self-control, return to the job position, realization of leisure time, etc. NR should be part of the complex rehabilitation of persons with brain damage and have a multi-disciplinary dimension.

Neurocognitive rehabilitation should be applied as early as possible when brain damage occurs. The stage of a person’s stay at the intensive care unit is the best starting point. It should be based on a theoretical–methodological concept, and respect the principles of individual approach, regularity, continuity, intensive and conscious activity. Appropriate qualified therapists and respect for the interdisciplinary cooperation model are needed. The NR in persons with brain damage is not a complex and common activity in the Czech Republic, unlike physiotherapy, for example. Impairments of cognitive functions are severe and very frequent deficits hampering or preventing the concerned persons from performing their job or having a quality life are common.

NR in persons with brain damage primarily belongs to the area of neuropsychology, ergo therapy, and speech therapy. It can have individual or group forms, be paper-based or computer-based. Unlike the long-term paper-based method, computer cognitive training enables bigger variability and difficulty of the tasks, increases training motivation, and decreases the requirement for a therapist [2].

A clinical diagnosis depends on the knowledge and experience of the examining doctor. The more experience the doctor acquires, the more medical knowledge they have. It might be difficult for a doctor to keep up with all the acquired information. An inexperienced doctor does not have the same expert knowledge to specify the diagnosis due to the lack of clinical experience. Therefore, an expert system might be useful both for inexperienced doctors when diagnosing, and for experienced doctors as support and verification of complex decisions. Apart from a clinical diagnosis, other tasks to be supported by an expert system might be the selection of the therapy, care of the patient, or treatment monitoring.

Since neurocognitive rehabilitation should respect the principles of individual approach, regularity and intensive and conscious activities, we address the following questions from a practical point of view:

1. How will we rehabilitate the patient directly at the bedside in the acute phase of the disease, e.g., after a stroke?

2. How, specifically, do we target rehabilitation for this patient, e.g., which cognitive domains will we rehabilitate? Do we prefer only some? And if so, which ones?

The answer, in the case of a patient who comes to outpatient care will not be so complicated. We will perform a neuropsychological examination, on the basis of which we will compile a rehabilitation plan for the given person. In patients in the early stages of treatment, the use of relatively complex neuropsychological diagnostic methods is not possible; indeed, in many cases, it is not feasible to use known screening methods such as ACE-R, MMSE, MoCa, [3]. If we do not have diagnostic results, then how will rehabilitation for hospitalized patients take place? Is it even possible to provide this group of patients with quality targeted care in the form of cognitive rehabilitation? We will try to answer these questions in the following text.

One of the most well-known and used theories of the present day is based on the CHC model. Based on this modern theory, we currently measure individual cognitive abilities and use it to plan cognitive rehabilitation. We dealt with the idea of how to connect the CHC model with the ACE-R test, primarily by the above-described diagnostic and subsequently rehabilitation process in acute care. Both approaches have some advantages and disadvantages, which are summarized in the following

Table 1. Comparison of ACE-R and CHC with the proposed approach.

Diagnostic Method	Advantages	Disadvantages
ACE-R	Quick Suitable for early-stage treatment	Imprecise CHC incompatible
Woodcock-Johnson test	Complex Precise CHC-compatible	Suitable for ambulant-level treatment Time complexity Suitable for early stage
Proposed approach (expert system)	Quick Complex Precise Suitable for early stage CHC-compatible Ready for all patient types	Hardware and software demands

.

Our proposed neurorehabilitation system with elements of artificial intelligence will offer a patient with acute brain disease the possibility that, if he undergoes a screening test (ACE-R) at the bedside, we can automatically compile a cognitive rehabilitation plan based on the CHC model. The main topic of this article is the presentation of the proposed expert system, which allows the results of a simple screening ACE-R test to be transferred to the domains of the CHC model and, based on it, to build an individual neurorehabilitation plan for the patient.

Cognitive rehabilitation based on this process will be precisely targeted to a specific cognitive deficit from the very beginning of treatment. An experienced clinician would probably be able to set up a cognitive rehabilitation plan very well, however, in hospitals, we find that cognitive screening and subsequent rehabilitation at the bedside are often performed by occupational therapists or general nurses who have only basic education. This approach could facilitate, simplify and improve the system/procedure for healthcare professionals working with acute patients. This is the main motivation of this article.

The research team of this article developed a unique neurorehabilitation system for patients with brain damage in the early stages of treatment, in cooperation with four partner subjects; the University of Ostrava, Technical University of Ostrava, Ambulance of Clinical Psychology, and University Hospital of Ostrava. The whole system consists of a hardware interface directly interacting with an information system that collects patients’ data and enables us to adapt the whole neurorehabilitation process based on uniquely proposed algorithms. The authors selected two approaches from the area of artificial intelligence, specifically, expert systems and neural networks. This article presents the implementation of expert systems in the designed procedure. The proposed system is to be included in the outcomes of the research project of the Technology Agency of the Czech Republic as a verified procedure for healthcare providers.

Many techniques are currently used for neurocognitive patient screening, but the authors of this research propose a unique transfer of simple patient screening for a complex intelligence model verified on real-life cases by the proposed expert system.

2. Related Works

The most frequent application of expert systems in medicine is to help in diagnosing and formulating a treatment proposal. The research in [4] summarizes the characteristics of “weak artificial intelligence” and expert systems necessary in clinical practice. Part of the research is a treatise on the requirements of doctors and current medical rule bases available for the development of methods such as expert systems.

The research in [5] presents the success rate of artificial intelligence techniques that have been used in almost all areas of medicine. An artificial neural network is the most used analytical tool. In contrast, other artificial intelligence techniques, such as fuzzy expert systems, evolutionary computations, or hybrid intelligent systems, are used in various clinical conditions, not only in diagnostics. One chapter in [6] presents systems to support decision-making in medicine, and describes their main principles and structure. From the perspective of patients’ safety, decision-making systems can bring unexpected sources of errors which must be considered during the phases of designing, implementing, and validating. However, a safe and easily usable system can significantly improve the quality of medical diagnoses, prognoses, and therapy. Another study [7] provides a state-of-the-art overview of the use of clinical decision-making systems in medicine, including the cases of their use with a proven effect on patients.

The development of expert systems in the area of medicine is not a trivial task. The first expert systems were developed to help in areas of chemical identification (DENDRAL), speech recognition (HEARSAY I and II), and diagnosis and treatment of blood infections (MYCIN) [8].

The following works provide an overview of the use of expert systems in neurorehabilitation. Most works are devoted to developing expert systems to control robots in rehabilitating upper and lower limbs [9,10,11], which enables patients to self-train to regain control over their bodies after traumatic brain damage. Thus, a patient has to repeat individualized moves of the damaged limb, according to the robotic therapist.

Based on the proposal of [12], cognitive therapy is defined as a set of activities created to rehabilitate a specific cognitive impairment. Each activity can be divided into elementary tasks, each of them then defined as a sequence of certain steps. The therapist defines the rules to control the rehabilitation progress. All these rules are the rule base of an expert system which continuously makes decisions about the best transition between individual actions to be performed by the user to meet the prescribed activities. Each exercise consists of a sequence of activities with a particular meaning from the global perspective of rehabilitation. An expert system was presented in [13] based on artificial intelligence, which was connected with mobile devices and personal digital assistants to help persons with permanent memory damage increase their memory capacity to be able to enjoy an independent everyday life. It concerns a significant extension of an expert system or memory rehabilitation for “non-expert” users. The work of [14] provides examples of research and commercial systems that are designed for the physical and cognitive rehabilitation of the senior population. In addition, the article proposes a system for cognitive rehabilitation with physical exercise. The work of [15] presents a modification of their system. The authors extended it to a cognitive rehabilitation system for more users. It mainly solves problems related to patients’ isolation when using rehabilitation systems outside specialized medical centers. The proposed system also enables combining cognitive and physical rehabilitation and integrates functions enabling group rehabilitation.

Recommending systems as a subarea of expert systems applications has growing usage also in artificial intelligence in the health sector. There are a variety of applications based on a broad palette of methods ranging from standard symbolic artificial intelligence methods ones to connectionist approaches. In addition, the broad applications in a variety of domains are growing from health care [16], through the industry to human resources [17].

Symbolic approaches are used in different scenarios like diabetes treatment recommendation [18] solved through ontologies, knowledge-based solutions for physical activity recommendation [19], or knowledge-based systems for diabetes drug suggestion [20]. Connectionist and biology-inspired methods also provide a wide variety of techniques for many health-oriented problems like ant colony-optimization for food recommendation [21], deep neural networks for cancer patient data evaluation [22], or focus on Convolutional Neural Networks for the recommendation of an appropriate physician [23]. Deep learning techniques were utilized, for example, in Deep Learning Based Health Recommender System Using Collaborative Filtering (DeepReco) proposed by [24], using an approach based on Restricted Boltzmann Machine (RBM)-Convolutional Neural Network (CNN).

An m6A site predictor named DeepM6ASeq-EL in [25], which integrates an ensemble of five LSTM and CNN classifiers with the combined strategy of hard voting, which had high prediction success when tested on six independent datasets.

A DeepBAN communication framework for dynamic WBANs was proposed by [26]. In their proposed framework, a temporal convolution network (TCN)-based deep learning approach was adopted for channel prediction, whereby the computationally intensive task was processed by mobile edge computing (MEC) to reduce the response time. Their proposed method can improve the system’s energy efficiency by 15% compared with the stochastic scheduling scheme.

In [27], a novel perturbation method was proposed to reduce the dynamical degradation of digital chaotic maps. Numerical experiments further proved that this improved perturbation method had a better performance in suppressing dynamical degradation.

An interesting aspect in this area is the effects of the COVID-19 pandemic on mental health, which are mentioned in [28,29]. This is a new phenomenon that could affect the effect of neurorehabilitation. Published works in the area of neurorehabilitation using expert systems are rare, which means that this article will be a quality benefit for future research in this interdisciplinary area.

3. Theoretical Background

Every patient that is hospitalized after an acute brain accident is subjected to a so-called screening based on the test of cognitive skills. Examples of a cognitive skills test are, for instance, the Addenbrooke’s cognitive examination (ACE-R) or the Woodcock-Johnson test. The resulting value reveals the current condition of the patient’s cognitive functions, which can imply the patient’s brain damage. Each test differs in its time requirements and usability in reading a patient’s condition, or they can provide data on variously monitored cognitive functions. A frequent issue is a condition when a patient in the early stages of treatment cannot undergo a detailed screening by the more complex, yet detailed, Woodcock-Johnson test. In such cases, it is necessary to use less demanding screening tests, such as the ACE-R.

3.1. Addenbrooke’s Cognitive Test

The Addenbrooke’s cognitive examination (ACE-R), in its revised version, is a widely used test for global screening of cognitive functions [30,31]. The ACE-R test integrates a Mini Mental State Exam (MMSE) and items that are more sensitive to reveal a mild cognitive impairment. The original ACE-R version has a maximum of 100 points, see (

Table 2. ACE-R and MMSE point scores.

ACE-R	SCORE ACE-R	SCORE MMSE
Attention & Orientation	18	18
Memory	26	3
Fluency	14	-
Language	26	8
Visuospatial	16	1
TOTAL	100	30

). ACE-R also provides five partial scores of cognitive domains (Attention & Orientation, Memory, Fluency, Language, and Visuospatial), which can tell more about the profile of cognitive deficits [32].

An MMSE is a short test of cognitive functions used worldwide to determine cognitive functions and reveal dementia. The test is suitable to distinguish normal ageing from pathological loss of cognitive performance. This test disposes of norms according to age and education for the Czech population aged 60–96.

• 27–30 points: standard level of cognitive functions
• 25–26 points: borderline (standard for older than 75 years)
• 18–24 points: mild dementia
• 6–17 points: moderately severe dementia
• <6 points: severe dementia.

3.2. Cattell–Horn–Carroll Theory of Cognitive Skills (CHC)

The entire developed neurorehabilitation system is built on cognitive function neurorehabilitation based on the CHC Intelligence model. The CHC (Cattell–Horn–Carroll) [33] theory of cognitive functions is an integration of two leading psychometric approaches to intelligence, based on the results of the factor analysis—the Cattell–Horn Gf–Gc theory and the Carroll’s Three-Stratum Theory of Cognitive Abilities. This theory, which lays the grounds for our approach to measure intelligence, stems from the Woodcock-Johnson test and divides cognitive skills into hierarchical layers (strata) based on their generality. The peak of the hierarchy (stratum III) consists of a g-factor (general intelligence). The second layer (stratum II) consists of so-called broad abilities, and the lowest layer (stratum I) is composed of so-called narrow abilities, which are more specific factors under stratum II. A detailed description of individual domains can be found, for example, in [34].

The broad abilities are the following, see Figure 1:

• Crystallized Intelligence (Gc): includes the breadth and depth of a person’s acquired knowledge, the ability to communicate one’s knowledge, and the ability to reason using previously learned experiences or procedures;
• Fluid Intelligence (Gf): includes the broad ability to reason, form concepts, and solve problems using unfamiliar information or novel procedures;
• Quantitative Reasoning (Gq): is the ability to comprehend quantitative concepts and relationships and to manipulate numerical symbols;
• Reading and Writing Ability (Grw): includes basic reading and writing skills;
• Short-Term Memory (Gsm): is the ability to apprehend and hold information in immediate awareness and then use it within a few seconds;
• Long Term Storage and Retrieval (Glr): is the ability to store information and fluently retrieve it later in the process of thinking;
• Visual Processing (Gv): is the ability to perceive, analyze, synthesize, and think with visual patterns, including the ability to store and recall visual representations;
• Auditory Processing (Ga): is the ability to analyze, synthesize, and discriminate auditory stimuli, including the ability to process and discriminate speech sounds that may be presented under distorted conditions;
• Processing Speed (Gs): is the ability to perform automatic cognitive tasks, particularly when measured under pressure to maintain focused attention;
• Decision/Reaction Time/Speed (Gt): reflects the immediacy with which an individual can react to stimuli or a task. This ability is considered part of the theory, but is not currently assessed by any major intellectual ability test, although it can be assessed with a supplemental measure such as a continuous performance test.

Although the aim of this article is focused on an expert system solution, we plan to enhance the reasoning also through the neural network. This should provide a complement to the presented approach.

4. The Proposed Model

The authors of this research propose a unique approach which uses the screening tool ACE-R (which, for patients, is less demanding) to determine the rehabilitation domains according to the CHC model. The result transfer of the ACE-R results into the CHC model domain was achieved by uniquely modifying the factor analysis according to [36].

4.1. Transforming the CHC Model Domains According to the Modified ACE-R Factor Analysis

Figure 2 depicts the relationship between the Addenbrooke’s cognitive test and the Cattell–Horn–Carroll theory of cognitive skills [36], which was modified by the authors in all domains. Individual color arrows represent how individual cognitive skill areas are transformed from the ACE-R model into the CHC model. The weights (in %) assigned to individual arrows are stated in Table 2. Figure 3 then graphically depicts a corresponding transfer of the CHC domains according to the ACE-R factor analysis, expressed in per cent.

The maximum point score of the CHC domains is calculated according to the modified ACE-R factor analysis [36] using Table 2 and

Table 3. Transfer of the CHC domains according to the modified ACE-R factor analysis.

Transfer ACE-R to CHC	GC	GF	GRW	GQ	GSM	GLR	GV	GS	GA
Attention & Orientation	28%	28%		28%	16%
Memory	15%				39%	46%
Fluency	25%					25%		50%
Language	61%		8%						31%
Visuospatial		12%	12%	13%			63%

as a weighted sum of values from column MAX ACE-R (Table 2), where the corresponding weights for individual CHC domains are stated in Table 3. The maximum values of individual CHC domains are calculated as follows: in Table 2, values from column MAX ACE-R are marked as ACEi (i = 1, … 5); in Table 3, we mark CHCij, where i is the column index and j is the row (i = 1, …, 5, j = 1, …, 9). The maximum values for individual domains are then calculated according to the following Formula (1):

$$CH{C}_j={{\displaystyle \sum }}_{i=1}^5\left(AC{E}_i·CH{C}_{ij}\right)/100,$$

(1)

4.2. Classification of Patients to Individual Levels of Rehabilitation Tasks

A set of tasks in 6 difficulty levels (Level 1–Level 6) has been proposed for each of the nine CHC model domains. For each patient, the ACE-R results helped determine specific CHC domains to be rehabilitated as well as the game level to start the rehabilitation within each domain. The maximum values of the CHC domains for individual levels of the proposed games are stated in

Table 4. Maximum values of the CHC domains for individual game levels.

	Max	Level 1	Level 2	Level 3	Level 4	Level 5	Level 6
GC	28.3	4.72	9.43	14.15	18.86	23.58	28.30
GF	6.96	1.16	2.32	3.48	4.64	5.80	6.96
GRW	4.00	0.66	1.33	2.00	2.66	3.33	4.00
GQ	7.12	1.18	2.37	3.56	4.74	5.93	7.12
GSM	13.02	2,17	4,34	6,51	8,68	10,85	13,02
GLR	15.46	2.57	5.15	7.73	10.30	12.88	15.46
GV	10.08	1.68	3.36	5.04	6.72	8.40	10.08
GS	7.00	1.16	2.33	3.50	4.66	5.83	7.00
GA	8.06	1.34	2.68	4.03	5.37	6.71	8.06
Normalized all	1	0.17	0.33	0.50	0.67	0.83	1.00

. They were achieved so that the maximum value of each domain is equally distributed between Level 1 and Level 6 [37,38].

5. Input Data

The cognitive rehabilitation took place at the workplace of the University Hospital of Ostrava. The test group included 705 patients.

Anamnestic questionnaire.

A non-standard questionnaire filled in by the patient was administered for the purposes of acquiring information on the patient’s gender, age, education, and laterality. Patient anonymity was preserved by omitting their names in the final results. There are only their ID numbers. The research involved 705 patients, 351 of whom were men and 354 women. The age range of patients was 19–97 years, and the age histogram is shown in Figure 4. Figure 5 shows a pie chart representing their education.

6. Proposed Diagnostic Expert System

The objective of the proposed expert system (ES) was to select an effective path of neurorehabilitation based on the CHC intelligence model. The rehabilitation path means a selection of modules and levels for rehabilitating areas that are affected by acute brain accident. The proposed expert system relies on a rule base created based on previously acquired data of real patients who underwent a screening using the ACE-R.

6.1. Linguistic Fuzzy Logic Controller

In order to provide an intelligent system for the recommendation of a patient’s rehabilitation progress, we used a system based on linguistic IF–THEN rules. The main tool for the usage of the fuzzy logic rule bases is LFLC2000, developed at the Institute for Research and Applications of Fuzzy Modeling [39].

Fuzzy logic is known for many applications in various areas, including industry, automation, and expert systems in many tasks. Its power lies in the capability of modelling a part of natural language semantics. It is based on evaluative linguistic expressions and conditional statements with these expressions. The conditional statements are used in control, managerial decision-making, identification, etc. Typical examples of evaluative expressions are “very small, more or less medium, roughly big”, etc. The expressions containing words “small, medium, big” are essential.

Conditional statements consisting of evaluative expressions in fuzzy logic are called fuzzy IF–THEN rules; for example,

IF obstacle is near AND car speed is big THEN brake very much

Such a rule can be schematically written as

IF X is A₁ AND … AND X_n is A_n THEN Y is B

where X_i is a variable representing objects (e.g., values of distance, depth, size, etc.) and A_i, B_i are the evaluative linguistic expressions. Sets of fuzzy IF–THEN rules are called rule bases or linguistic descriptions [40]. Linguistic descriptions (rule bases) contain knowledge for the recommendation system. In our research, we use rule bases containing antecedent variables with values obtained from five areas of patients’ tests (with various contexts). A succedent variable represents a normalized value of the performance of a particular patient in specific standardized nine categories such as GC, GF, etc. (described in the previous text). Every value in a category is used to determine the best suitable rehabilitating game profile.

Linguistic descriptions are further used in an approximate reasoning scheme:

Conditions: R₁:= IF X₁ is A₁₁ AND … AND X_n is A_1n THEN Y is B₁,

…………………………………………………………….....

R_m: = IF X₁ is A_m1 AND … AND X_n is A_mn THEN Y is B_m,

Observation: X₁ is A_’1 AND … AND X_n is A_’n

______________________________________________________

Conclusion: Y is B’

The conditions comprise the linguistic description. The A‘_I’s in the observation are, in general, certain modifications of the antecedents Ai of the rules (the part of the rule preceding the word THEN).

The theory of evaluative linguistic expressions is further applied to the formalization of the meaning of fuzzy IF–THEN rules and linguistic descriptions [41]. These rules here are taken from conditional clauses of natural language consisting of evaluative expressions. We have also used a special reasoning method, and also a method for learning linguistic descriptions from the data [42,43]. We used Perception-based logical deduction as the inference core. The defuzzification method used is Defuzzification of Evaluative Expressions (DEE).

The structure of the evaluating linguistic expressions, which can be used inside the fuzzy IF–THEN rules, is the following:

[(sign)](linguistic modifier)(basic expression)

Basic expressions are the following: small (sm), medium (me), and big (bi). The linguistic modifiers are the following: extremely (ex), significantly (si), very (ve), rather (ra), more or less (ml), roughly (ro), quite roughly (qr), typically (ty), rather (ra), very roughly (vr), and very, very roughly (vv).

When we use one observation for learning a rule, we are searching for the best fitting linguistic term for a particular value. As an example, in the GC category and following 5 data observations (in the defined context of fuzzy variables, we will obtain 5 rules), see

Table 5. Data observations and contexts.

X1	X2	X3	X4	X5	est.
<0.00, 18.00>	<0.00, 26.00>	<0.00, 14.00>	<0.00, 26.00>	<0.00, 16.00>	<0.00, 1.00>
5	6	1	15	9	0.576923077
11	12	8	13	9	0.5
16	17	9	23	16	0.884615385
17	22	13	26	16	1
17	13	6	22	11	0.846153846

and

Table 6. Learned rules.

X1	X2	X3	X4	X5	Y
<0.00, 18.00>	<0.00, 26.00>	<0.00, 14.00>	<0.00, 26.00>	<0.00, 16.00>	<0.00, 1.00>
vr sm	qr sm	ra sm	ra me	ra me	ml me
ra me	ra me	ra me	ty me	ra me	ra me
ra bi	ml me	ml me	ra bi	ex bi	ra bi
ve bi	ml bi	ra bi	ex bi	ex bi	ex bi
ve bi	ty me	ra me	ml bi	vr bi	ml bi

.

Raw learned rules are then processed with several filters, e.g., redundant rules filter, inconsistent rules filter. Exactly duplicated rules are omitted automatically during linguistic learning, i.e., the same rules for several similar data observations are added only in one case into the rule base.

6.2. Settings of LFLC

We used default settings of evaluative expressions, which enables restricted use of modifiers with atomic expressions. Figure 6 shows selected modifiers and its allowed expressions (Y—allowed; N—not allowed). There is also a possibility to change the parameters of modifiers, but in our work, we used default settings (more details can be found in LFLC2000 manual).

Linguistic variables for all 9 rule bases were set according to the context of input variables X_n, and normalized context 〈0, 1〉 for output variable Y for a particular category. Then we have rule schemes of IF–THEN rules: X1 & X2 & X3 & X4 & X5 => Y, where X1, …, X5 is performance in a particular test and Y is value for a particular category (GC, GF, etc.), see

Table 7. Linguistic variables for all 9 rulebases.

Rule base	Vigilance	Memory	Word Proc.	Language	Visual	Evaluation
	X1	X2	X3	X4	X5	Y
	<0.00, 18.00>	<0.00, 26.00>	<0.00, 14.00>	<0.00, 26.00>	<0.00, 16.00>	<0.00, 1.00>
GC	<0.00, 18.00>	<0.00, 26.00>	<0.00, 14.00>	<0.00, 26.00>	<0.00, 16.00>	GC value
GF						GF value
GRW						GRW value
GQ						GQ value
GSM						GSM value
GLR						GLR value
GV						GV value
GS						GS value
GA						GA value

.

Example: For rule base in category GC—rule 280.

ve bi & vr bi & ml me & si bi & ex bi --> ra bi

Full linguistic expressions explication:

IF X1 is very big & X2 is very roughly big & X3 is more or less medium & X4 is significantly big & X5 is extremely big THEN Y is rather big

Interpretation of fuzzy sets for these linguistic expressions is highlighted in Figure 7.

These 9 prepared rule bases were subjected to linguistic learning by LFLC2000 from 705 observations for patients, with an evaluation done by expert psychologists. Figure 8 shows partial data for learning, and Figure 9 part of the rule base for the GC rule base.

The number of rules is different for every particular rule base since there are duplicate, redundant and/or inconsistent rules, e.g., for GC rule base, we have only 335 non-duplicate, non-redundant and best chosen consistent resulting rules for 705 originally learned observations. While the number of rules may seem high in comparison with other tasks for expert systems, it should be noted that we are considering five independent variables for every resulting Y dependent variable. The number of possible variations of linguistic expressions is much larger than this number, e.g., for 10 possible linguistic expressions and 5 variables, we have 10⁵ possible antecedent variations and 10⁶ for the additional dependent variable. Moreover, there are many more than 10 possible linguistic expressions combinations with modifier and atomic expressions, even if we do not use logical connectives.

6.3. Rule base Evaluation and Performance

Learned rules were treated with redundancy and inconsistency filters and then applied to the expert-evaluated data. The resulting validation for every rule base showed they were very good results to be successfully applied in an intelligent system. The mean differences between psychologist-based values and ES generated value—delta—are between 0.00548 and −0.04479. This is an acceptable value, even in specific cases when it grows to bigger values. We also performed ANOVA tests for statistically significant differences of the delta values with the following results (Figure 10 and Figure 11,

Table 8. Expected Mean Squares Section.

Source		Term	Denominator	Expected
Term	DF	Fixed?	Term	Mean Square
A: type	8	Yes	S(A)	S + sA
S(A)	6336	No		S(A)

Note: Expected Mean Squares are for the balanced cell-frequency case.

and

Table 9. Analysis of Variance Table.

Source		Sum of	Mean		Prob	Power
Term	DF	Squares	Square	F-Ratio	Level	(Alpha = 0.05)
A: type	8	2.082745	0.2603431	56.74	0.000000 *	1.000000
S(A)	6336	29.07018	4.588096 × 103
Total (Adjusted)	6344	31.15292
Total	6345

* Term significant at alpha = 0.05; Plots of Means Section.

).

The rule base was also reviewed by an expert psychologist to evaluate the results of our ES rule bases. The slight undervaluation of ES for mean observation is rather positive since, in practice, a human expert also performs a similar undervaluation. The rule base may work inadequately for significantly small values in all five abilities or most abilities performance. Nevertheless, for our patients’ observations, higher values are more prevalent (data screening for Xi data and Y categories performance).

From these observations (

Table 10. Bonferroni (All-Pairwise) Multiple Comparison Test.

Response: All
Term A: type
Alpha = 0.050; Error Term = S(A); DF = 6336; MSE = 4.588096 × 103; Critical Value = 3.1970
			Different From
Group	Count	Mean	Groups
GA	705	−4.479466 × 102	GSM, GLR, GS
GV	705	−4.391013 × 102	GSM, GLR, GS
GRW	705	−4.067609 × 102	GSM, GLR, GS
GF	705	−3.605051 × 102	GSM, GLR, GS
GQ	705	−3.496651 × 102	GSM, GLR, GS
GC	705	−3.486643 × 102	GSM, GLR, GS
GSM	705	−1.626205 × 102	GA, GV, GRW, GF, GQ, GC, GLR, GS
GLR	705	1.064321 × 103	GA, GV, GRW, GF, GQ, GC, GSM
GS	705	5.478905 × 103	GA, GV, GRW, GF, GQ, GC, GSM

), we can see statistically significant delta differences, especially between the GSM category and other categories, and GLR and GS categories in contrast to the GA, GV, GRW, GF, GQ, GC and GSM groups. GS and GLR attained the best mean delta around 0.005–0.001 (and both are slightly positive), which means we can expect the best ES approximation. GSM also has a positive delta of about −0.016. The other 6 categories have similar deltas in the range −0.04479 and −0.03487, which appears to slightly undervalue the psychologist-based evaluation. The obtained results are shown in Figure 12 and

Table 11. Differences (delta) between psych. evaluation and ES values (descriptive statistics).

delta	GC	GF	GRW	GQ	GSM	GLR	GV	GS	GA
Mean	−0.03487	−0.03605	−0.04068	−0.03497	−0.01626	0.00106	−0.04391	0.00548	−0.04479
Error of Mean	0.00221	0.00244	0.00203	0.00243	0.00297	0.00243	0.00304	0.00281	0.00242
Median	−0.02006	−0.0269	−0.02667	−0.02682	−0.01338	−0.00284	−0.02333	0.00238	−0.02667
Modus	−0.00333	−0.00333	−0.00333	−0.00333	−0.02	−0.00333	−0.01083	0.02714	−0.02
Standard dev.	0.05868	0.06484	0.05384	0.06464	0.07882	0.06442	0.08085	0.07453	0.06416
Variance	0.00344	0.0042	0.0029	0.00418	0.00621	0.00415	0.00654	0.00555	0.00412
Kurtosis	1.9152	2.16931	3.28159	2.08186	0.76964	2.01668	1.9746	2.67699	3.58614
Skewness	−1.05177	−0.25456	−1.30242	−0.24032	0.01758	0.53233	−0.84893	0.54267	−1.39652
Max − Min diff.	0.41216	0.48356	0.47333	0.48266	0.46671	0.55605	0.57417	0.58476	0.51244
Minimum	−0.27307	−0.27276	−0.35333	−0.27174	−0.22717	−0.26741	−0.33667	−0.21786	−0.35
Maximum	0.13909	0.2108	0.12	0.21092	0.23954	0.28864	0.2375	0.3669	0.16244
Sum	−24.5808	−25.4156	−28.6766	−24.6514	−11.4647	0.7503	−30.9566	3.8626	−31.5802
Number	705	705	705	705	705	705	705	705	705
Rules of ES	335	338	358	340	307	304	294	277	299

.

The proposed expert system will be used to diagnose the recommended level for rehabilitation in a particular category (GC, GF, etc.). The normalized value for a particular category relates to the values in

Table 12. Positive differences in the game-level assignment.

	GC	GF	GRW	GQ	GSM	GLR	GW	GS	GA
Level error <= 0	691	678	699	676	624	623	676	605	696
Level error > 0	14	27	6	29	81	82	29	100	9
Total observations	705	705	705	705	705	705	705	705	705
Level error > 0	1.99%	3.83%	0.85%	4.11%	11.49%	11.63%	4.11%	14.18%	1.28%

.

Game-level assignment is then done with the ES-produced value. The main problem for the assignment to a patient would be an assignment to a higher level than necessary. We have obtained the following results of testing on 705 observations in Table 9. We should note that, compared to psychologist-based assignments, error rates are reasonable for GC, GF, GRW, GW and GA categories (<5%), but for GSM, GLR and GS, they are slightly higher. The total ratio for all categories is 5.94%.

7. Conclusions and Future Work

The presented expert system is currently being deployed, and data is being collected from several groups of patients for overall effectiveness verification. The whole proposed neurorehabilitation system is available through the following link: (https://eddie.osu.cz), (accessed on 1 December 2022). The research project is still active and is under the rules of the Technology Agency of the Czech Republic (TACR). We are unable to provide live data because the system works with sensitive (patient) data. The authors currently process proposed models of artificial neural networks to create back conversion results from CHC domains results to ACE-R evaluation, which are now verified on actual patient data and will be part of further research. These results will be published in subsequent articles.

The main result of this article is the proposed expert system, which integrates the completely unique transfer of the ACE-R result to the CHC (Cattell–Horn–Carroll) intelligence model based on aggregated knowledge of psychology professionals. This unique approach enables transformation of the CHC model domains according to the modified ACE-R factor analysis, which has never been performed before.

We have described our research results with uncertain data for the neurorehabilitation game-level assignment. The prepared expert system learned from 705 observations and provided a reasonable tool for our further development of the game-level recommendation. We plan to use it on new patients when the HW and SW product of the project is completed, and then we will be able to compare the efficiency of this system with the expert knowledge. This planned performance comparison between human-evaluated performances and the expert system results will enable us to prove or disapprove the positive effects of the automated intelligent system application. The main advantage also lies in more evidence-based evaluation through diverse psychologists’ knowledge. The completed ES module will be an integral part of the software for neurorehabilitation and will help in automating the process of the appropriate game level assignment.

We are currently devising a complementary approach based on neural networks; after its implementation and evaluation, we plan to prepare a comparison of these concurrent approaches.