Longitudinal Data Analysis Based on Triadic Rules to Describe of the
Psychological Reactions During COVID 19 Pandemic
Lincoln A. N. Coutinho, Mark A. J. Song
and Luis E. Zárate
Applied Computational Intelligence Laboratory – LICAP, Computer Science Department,
Pontifical Catholic University of Minas Gerais, Brazil
Triadic Analysis, Longitudinal Study, Mental Health, COVID-19, Data Mining.
Longitudinal studies are essential to understand the evolution of individuals’ psychological behaviors, espe-
cially in pandemic scenarios. The work proposes the application of the triadic analysis, derived from the
theory of Formal Analysis of Concepts, to describe, through rules, a longitudinal database about the attitudes
and reactions of individuals during COVID 19. As a main result, one can observe how the different factors
considered in the study are related in different scenarios of the pandemic, showing degrees of stress related to
the prevention of the disease.
A pandemic has various implications in a global-
ized society (Malta et al., 2020). Mental health is a
highly relevant aspect, especially in an abnormal pe-
riod where there may be a decrease in interpersonal
contact due to imposed health restrictions. This as-
pect should not be downplayed, as it is correlated with
public health issues such as anxiety, depression, dis-
tress, among other psychological problems. There-
fore, studies on the mental health of a social group ex-
posed to extreme situations, if used to identify behav-
ioral patterns, can generate relevant information for
public policies (Prati and Mancini, 2021). In this con-
text, longitudinal studies can be employed to achieve
these objectives. In this work, we present a method
to identify psychological effects during the COVID-
19 pandemic for the proposed longitudinal study in
(O’Brien et al., 2021).
In general, longitudinal studies are used to investi-
gate, for example, activities and behaviors of the same
group of individuals over various periods of time, re-
ferred to as waves. Through periodic updating of
records, it is possible to discover highly relevant pat-
terns and temporal relationships from the available
databases using data mining techniques and machine
To analyze the longitudinal databases, we propose
in this work to utilize the foundations of Formal Con-
cept Analysis (FCA) theory (Ganter and Wille, 2012),
a branch of applied mathematics based on the theory
of conceptual lattices. Its main objective is to repre-
sent and extract knowledge from a dataset involving
objects (individuals), attributes (clinical conditions,
symptoms, etc.), and their incidence relations. This
tuple of elements can be represented through a formal
dyadic context, from which it is possible to extract
association rules between the attributes. In summary,
the main purpose of FCA is to summarize items in
a database into information implications, such as the
evidence of an individual symptom in a patient to bet-
ter understand clinical diseases and their representa-
tion in society.
In general, FCA has been used in data analysis and
knowledge representation, where associations and de-
pendencies are identified from a binary incidence re-
lationship between objects and attributes. Several
works, such as (Carpineto and Romano, 2003), have
discussed the use of extracting dyadic association
rules through FCA.
Since datasets are often expressed by ternary and
more generally n-ary relations, there has been a re-
cent and growing interest in proposing new solu-
tions for the analysis and exploration of these multidi-
mensional data, especially in triadic contexts (Bazin,
Triadic Concept Analysis (TCA), proposed by
(Lehmann and Wille., 1995), is an extension of FCA
theory that uses triadic formal context. This intro-
Coutinho, L., Song, M. and Zárate, L.
Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic.
DOI: 10.5220/0012314900003657
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 17th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2024) - Volume 2, pages 323-329
ISBN: 978-989-758-688-0; ISSN: 2184-4305
Proceedings Copyright © 2024 by SCITEPRESS Science and Technology Publications, Lda.
duces a third element (to the dyadic context) - a con-
dition determining the incidence relationship between
objects and attributes. In the context of healthcare
area, objects may correspond to patients, attributes to
symptoms, and conditions to different waves of the
longitudinal study. From the triadic context, it is pos-
sible to extract triadic association rules (Biedermann,
1999) that can be used to observe the relationships be-
tween attributes (symptoms) within a given wave or
between waves of the longitudinal study. In this way,
the TCA extends the FCA, showing not only the in-
cidence of a symptom, but its recurrence in different
scenarios (waves).
In (Trabelsi et al., 2012), the authors compared
three algorithms for triadic data: TRICONS, TRIAS,
and DATA-PEELER. In (Ignatov et al., 2015), the au-
thors presented various strategies for discovering op-
timal patterns considering this type of data. In (Sel-
mane et al., 2013), the authors proposed extracting tri-
adic association rules by transforming the triadic con-
text into an equivalent dyadic context. In (Zhuk et al.,
2014), a comparison of algorithms for triadic context
analysis is conducted, and the work by (Missaoui and
Emamirad, 2017) proposes a tool, Lattice-Miner, used
in this work, for extracting triadic association rules.
The articles (Lana et al., 2022) and (Noronha
et al., 2022) are likely the first works to explore triadic
analysis in describing longitudinal study databases in
the field of health. The first article deals with the anal-
ysis of the effectiveness of COVID-19 prevention pro-
cedures, and the second work focuses on pattern dis-
covery related to human aging by observing the tem-
poral evolution of clinical and environmental condi-
tions of individuals. In this work, we propose the ap-
plication of triadic rules to describe the psychological
reactions of individuals to the COVID-19 pandemic
based on a longitudinal study available in (O’Brien
et al., 2021).
This article is divided into the following sections:
in Section 2, the theoretical framework supporting the
work is presented. In Section 3, the methodology
used for discovering psychological patterns during the
pandemic and the description of the dataset used are
presented. Section 4 contains the experiments and
analysis of the results from different scenarios. Fi-
nally, the conclusions and possible future work are
2.1 Formal Concept Analysis and
Triadic Rules
Formal Concept Analysis (FCA) is a branch of ap-
plied mathematics related to the theory of concep-
tual lattices (Ganter and Wille, 2012). This theory is
used to derive implicit relationships between objects
and their attributes from a dataset. This relationship
is formally defined by a tuple K := (G, M, I), which
is called a formal context, where (I G × M), with
G representing objects, M representing attributes,
and I representing incidence in the context—meaning
which objects possess certain attributes, or, analo-
gously, which attributes are present in certain objects.
Within FCA, two main operators are defined:
:= {m M|∀g A : (g, m) A} (1)
:= {g G|∀m B : (g, m) B} (2)
Considering A G and B M, a formal concept
corresponds to the pair (A, B), where A represents a
subset of objects (extension) and B a subset of at-
tributes (intention) in such a way that A
= B, and
= A, where A
and B
are the derivation operators
described by Equations 1 and 2.
Triadic Concept Analysis (TCA) (Wille, 1995) is
defined by a quadruple K := (G, M, I, C), where, in
addition to objects and attributes, the incidence be-
tween them occurs under a condition C. For exam-
ple, considering a longitudinal study with two waves,
the start and end of a clinical treatment. Thus, a tri-
adic concept represented by (I G × M ×C) can be
translated as objects that possess a certain subset of at-
tributes under a condition, or similarly, attributes that
are related to a subset of objects under a specific con-
dition or wave.
From TCA, it is possible to generate two types
of triadic implication rules known as BCAAR (Bie-
dermann Conditional Attribute Association Rule) and
BACAR (Biedermann Attributional Condition Asso-
ciation Rule), which have the following structure
((Biedermann, 1999)):
) M
[support, con fidence]
) C
[support, con fidence]
The first rule, BACAR, occurs when C
, C
and M
M. This means that when the subset of
attributes M
occurs under condition C
, it also oc-
curs under condition C
with a certain support and
confidence. The second rule, BCAAR, occurs when
, M
M and C
C. This indicates that in the
HEALTHINF 2024 - 17th International Conference on Health Informatics
wave C
, the subset of attributes M
implies M
a certain support and confidence. Our goal is to iden-
tify patterns of psychological relationships among in-
dividuals from the longitudinal database using both
types of association rules.
As mentioned, for this work, a longitudinal study aim-
ing to assess the psychological conditions of individ-
uals during the COVID-19 pandemic was considered.
The first wave was conducted at the beginning of the
pandemic between April 9th and 18th, 2020, and the
second between June 19th and July 11th, 2020, ap-
proximately 2 months after the first data collection.
In this database, several socioeconomic questions for
individuals are present, highlighting aspects of isola-
tion, medication, pre-existing conditions, psychologi-
cal tests, working hours, among other issues (O’Brien
et al., 2021).
The database comprises 151 interviewed indi-
viduals and 81 attributes, of which 12 were selected
for a more detailed analysis of the results, totaling
24 for both waves. Tables I, II, and III describe the
sets of questionnaires considered and the conditions
in which they were conducted. It is worth noting
that only the Five Facet Mindfulness Questionnaire
(FFMQ) test, presented in Table I, has derivations,
which is why Table II includes attributes related only
to this specific scale test.
3.1 Methods
Preprocessing: For representing the longitudinal
database in a triadic context, a discretization process
is required. To achieve this, thresholds (reference
values) had to be defined for marking the incidences
of symptoms for each study wave. The objective is
to describe the negative psychological influence of
the pandemic, so values equal to or above the refer-
ence, which represent or are associated with a neg-
ative psychological condition, were considered and
marked with ’X’ for incidence, while values below
this threshold did not determine an incidence and re-
mained unmarked. A sample of this discretization is
shown in Table IV.
For the PHQ15 (Patient Health Questionnaire
Somatic Symptom Severity Scale), the literature-
suggested scale was used as the reference threshold:
Minimal (0-4), Low (5-9), Medium (10-14), and High
(15-30). Specifically, the threshold value of 10, corre-
sponding to the Medium level on the scale, was con-
Table 1: Key Attributes Selected for Triadic Analysis.
Attributes Metric Description
Total Sum of
15 items from
PHQ Scale
Severity Scale for
Symptoms of the
person in the last
Total Sum of
24 items from
FFMQ Scale
Scale about the
person’s inner
perception in the
last month
Total Sum of
12 items from
GHQ Scale
Scale about the
person’s health in
the last month
Total Sum of
15 items from
PVD Scale
Scale about the
perception of
vulnerability to
Total Sum of
12 items from
IOUS Scale
Scale about the
to uncertainties
Total Sum of
22 items from
IOES Scale
Scale about the
impact of stress on
the person in the
last month
Mean of 13
items from
PATS Scale
Scale about the
preventive actions
of the person
agains diseases
sidered. For the IOES questionnaire, the study by
(Weiss and Marmar, 1997) was used. The threshold
was specifically set at 33, corresponding to the aver-
age value in the first wave of the study (O’Brien et al.,
2021). For other questionnaires, thresholds were de-
termined for extreme situations. To achieve this, an
outlier analysis was performed using a box plot. This
strategy aimed to define values deviating from the
mean and variance that were associated with negative
psychological conditions.
Subsequently, once the data were represented in
the triadic concept, Lattice Miner ((Missaoui and
Emamirad, 2017)), available on GitHub, was used for
generating triadic rules. Before using the software,
the database was converted to JSON (JavaScript Ob-
ject Notation) format, containing all the relationships
between objects, conditions, and attributes to be in the
appropriate format for the software to generate the tri-
adic rules. Consequently, the BCAARs and BACARs
triadic rules can be generated based on desired confi-
dence and support measures. The first, BCAARs can
show the relation between two attributes (clinical con-
ditions) in a certain wave (time) which could imply a
certain dependence on two different symptoms. The
second, BACARs, the recurrence of a attribute (clin-
Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic
Table 2: Derived Attributes Selected for Triadic Analysis.
Attributes Metric Description
Weighted Mean
of FFMQ Scale
Items for
Scale on how easy
it is for the person
to observe
themselves in the
last month
Weighted Mean
of FFMQ Scale
Items for
Scale on how easy
it is for the person
to describe
themselves in the
last month
Weighted Mean
of FFMQ Scale
Items for
Scale on how easy
it is for a person
to focus
on tasks in the
last month
Weighted Mean
of FFMQ Scale
Items for
Scale on the
in the last month
Weighted Mean
of FFMQ Scale
Items for
Scale on the
person’s reactions
in the last month
Table 3: Conditions chosen for triadic analysis.
Wave -
Date Description
A (before)
April 9th to
18th, 2020
2 to 3 weeks after
the beggining of
the pandemics
in the USA
D (after)
June 19th to
July 11th,
2 to 3 months
after the condition
"A" in the USA
ical condition) in different waves (times), that could
mean a lasting clinical condition.
For the analysis, four different scenarios were chosen.
The first scenario considers the complete database
with employed and unemployed individuals. The re-
maining scenarios were subdivided into employed in-
dividuals and those not in the labor market. Employ-
ment conditions were selected based on the litera-
ture, including references such as (Borsoi, 2007) and
(Hirschle and Gondim, 2020).
Each of the scenarios will be presented below,
along with the most significant results observed in
each of them.
Table 4: Transformation for Triadic Concept Analysis.
A - First Wave D - Second Wave
Person ID
ID 1 X X X
ID 2 X X
ID 3 X
ID 4 X X X
4.1 Scenario 1: Complete Database
In this context, 151 individuals were considered, and
1765 triadic rules were generated. This high number
of rules is due to the fact that the rule explores all
possible association rules within the dataset. In order
to analyze the most significant rules, a minimum
support of 30% was chosen for BACARs, and for
BCAARs, a support of 25% was chosen:
R1 - ( A D ) IOES_Total [support = 36,9%
confidence = 80,9%]
R2 - ( D A ) IOES_Total [support = 36,9%
confidence = 88,7%]
R3 - ( A D ) PATS_Mean [support = 30,9%
confidence = 79,3%]
R4 - ( D A ) PATS_Mean [support = 30,9%
confidence = 68,7%]
R1 - ( IOES_Total PATS_Mean ) A [support =
29,5% confidence = 64,7%]
R2 - ( IOES_Total PATS_Mean ) D [support =
31,5% confidence = 75,8%]
R3 - ( PATS_Mean IOES_Total ) A [support =
29,5% confidence = 75,9%]
R4 - ( PATS_Mean IOES_Total ) D [support =
31,5% confidence = 70,1%]
From the complete database, it was observed
through BCAAR rules, R1 and R3, at the begin-
ning of the pandemic, that people (29.5%) who
experienced strong stress symptoms in the last 7
days (IOES_Total) also engaged in preventive actions
against diseases (PATS_Mean) with a confidence of
64.7%. The reverse was also observed (PATS_Mean
IOES_Total) in both study waves. This might sug-
gest that concerning a pandemic, stress, which can be
caused by traumatic events, may result in a person
taking more preventive actions to avoid psychologi-
cal conditions. Conversely, individuals accustomed
to taking more preventive measures against diseases
may also experience higher levels of stress.
HEALTHINF 2024 - 17th International Conference on Health Informatics
4.2 Scenario 2: Individuals Employed
Before the Pandemic
In this context, 138 individuals who were employed
before the COVID-19 pandemic were analyzed. The
minimum support threshold was set at 30%:
R1 - ( A D ) IOES_Total [support = 40,4%
confidence = 84,6%]
R2 - ( D A ) IOES_Total [support = 40,4%
confidence = 90,2%]
R3 - ( A D ) PATS_Mean [support = 32,4%
confidence = 80,0%]
R4 - ( D A ) PATS_Mean [support = 32,4%
confidence = 69,8%]
R1 - ( IOES_Total PATS_Mean ) A [support =
31,6% confidence = 66,2%]
R2 - ( IOES_Total PATS_Mean ) D [support =
33,8% confidence = 75,4%]
R3 - ( PATS_Mean IOES_Total ) A [support =
31,6% confidence = 78,2%]
R4 - ( PATS_Mean IOES_Total ) D [support =
33,8% confidence = 73,0%]
Analyzing the results for individuals who were
employed before the pandemic, the outcome was very
similar to the complete database (section 4.1). The
only difference is that the support and confidence lev-
els are generally higher, meaning the relationship be-
tween stress and disease prevention worsened even
further in this scenario.
4.3 Scenario 3: Individuals who Were
Working at the Beginning of the
In this scenario, 127 individuals who were working
at the beginning of the COVID-19 pandemic (April
9th to 18th, 2020) were analyzed. BACARs and
BCAARs were analyzed with a minimum support of
R1 - ( A D ) IOES_Total [support = 41,6%
confidence = 83,9%]
R2 - ( D A ) IOES_Total [support = 41,6%
confidence = 92,9%]
R3 - ( A D ) PATS_Mean [support = 32,8%
confidence = 78,8%]
R4 - ( D A ) PATS_Mean [support = 32,8%
confidence = 69,5%]
R1 - ( IOES_Total PATS_Mean ) A [support =
33,6% confidence = 67,7%]
R2 - ( IOES_Total PATS_Mean ) D [support =
33,6% confidence = 75,0%]
R3 - ( PATS_Mean IOES_Total ) A [support =
33,6% confidence = 80,8%]
R4 - ( PATS_Mean IOES_Total ) D [support =
33,6% confidence = 71,2%]
Analyzing the results for individuals who were
working at the beginning of the pandemic, the out-
come was very similar to the complete database (sec-
tion 4.1) and to individuals who were employed be-
fore the pandemic (section 4.2). However, the support
and confidence levels are mostly even higher, imply-
ing a deterioration in terms of stress, disease preven-
tion, and the relationship between these two factors.
4.4 Scenario 4: Individuals who Were
Not Employed at the Beginning of
the Pandemic
In this scenario, 24 individuals who were not em-
ployed at the beginning of the COVID-19 pandemic
(April 9th to 18th, 2020) were analyzed, and the
BACARs and BCAARs had a minimum support of
R1 - ( A D ) FFMQ_NonreactMean [support =
25,0% confidence = 66,7%]
R2 - ( D A ) FFMQ_NonreactMean [support =
25,0% confidence = 50,0%]
R3 - ( A D ) PVD_Total [support = 29,2%
confidence = 100,0%]
R4 - ( D A ) PVD_Total [support = 29,2%
confidence = 87,5%]
R1 - ( FFMQ_NonreactMean PATS_Mean ) A
[support = 25,0% confidence = 50,0%]
R2 - ( PATS_Mean FFMQ_NonreactMean ) A
[support = 25,0% confidence = 75,0%]
Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic
Considering the BCAAR rules, R1 and R2, for
individuals who were not employed at the begin-
ning of the pandemic, the rules associate preventive
actions that individuals can take against COVID-19
(PATS_Mean) with attention-related factors such as
non-reactivity (FFMQ_NonreactMean), where non-
reactivity to inner experience is defined in terms of
allowing thoughts and feelings to come and go with-
out being caught up or carried away by them, where
a higher score indicates higher attention (Bohlmeijer
et al., 2011). It can be observed that all individuals
with 75% preventive actions were non-reactive. In
this scenario, it was only highlighted that the major
issues for individuals who were not employed at the
beginning of the pandemic are different compared to
employed individuals analyzed in the previous scenar-
The objective of this study was to demonstrate the
potential of triadic analysis for extracting association
rules within the context of longitudinal studies for
psychological records, focusing on people’s reactions
to stress conditions such as the COVID-19 pandemic.
The rules can contribute to a better understanding of
individuals’ psychological reactions under stressful
It is important to emphasize that the approach re-
quires prior definition of thresholds for discretization
and determining whether an incidence is marked or
not in the triadic context. The difficulty in accessing
information about the tests on the applied scale, due
to restricted data, can hinder threshold definition to
characterize individuals as healthy or not, and to bet-
ter understand the topic being addressed. Although
threshold definition requires expert knowledge, the
approach allows for the adjustment of various sce-
narios to describe the results of a longitudinal study.
Among the positive aspects, the applicability and ease
of application to various contexts can be highlighted.
As future work, there are several implementations
that can be carried out in the considered longitudinal
study. Implementations can be performed in different
scenarios, and different attributes from the database
can be used in each of these chosen scenarios. Fur-
thermore, with the input of researchers from the field
of psychology, the data could be better analyzed to
understand the implications of a pandemic on peo-
ple’s mental health. Our intention was to demonstrate
the potential use of triadic rules to analyze the psy-
chological effects of a pandemic.
The authors would like to thank: The National
Council for Scientific and Technological Develop-
ment of Brazil (CNPQ), The Coordination for the Im-
provement of Higher Education Personnel - Brazil
(CAPES) (Grant PROAP 88887.842889/2023-00
PUC/MG, Grant PDPG 88887.708960/2022-00
PUC/MG - INFORMATICA and Finance Code 001),
Minas Gerais State Research Support Foundation
(FAPEMIG) under grant number APQ-01929-22, and
the Pontifical Catholic University of Minas Gerais,
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Longitudinal Data Analysis Based on Triadic Rules to Describe of the Psychological Reactions During COVID 19 Pandemic