Triadic Rules for Analysis of Productive and Well-Being Social in

Activity-Based Working Environments

Thiago H. C. Oliveira

, Mark A. J. Song

and Luis E. Z

arate

Applied Computational Intelligence Laboratory – LICAP, Computer Science Department,

Pontiﬁcal Catholic University of Minas Gerais, Brazil

Keywords:

Activity Based Working Environments, Data Mining, Longitudinal Data Mining, Triadic Concept Analysis,

Triadic Rules.

Abstract:

A longitudinal database records data and its variations over a period of time. The objective of this article

is to use this resource, together with the Triadic Concept Analysis theory, to analyze and characterize how

employees adapted and felt before, during and after the implementation of an activity-based work environment

which is deﬁned as a ﬂexible work setting where employees have the autonomy to choose where they perform

their tasks, seeking locations that offer optimal solutions in terms of social interaction, communication, and

collaboration. The results seek to support the implementation of this concept, verifying how, and under what

conditions, key points of employee experiences vary over time.

1 INTRODUCTION

Longitudinal studies involve the collection and anal-

ysis of data from the same sample of objects or indi-

viduals over consecutive time periods referred to as

waves. These studies can be applied to various ar-

eas of interest, such as health, social studies, ecology,

among others. For example, in the social work con-

text, these studies allow for the analysis of an indi-

vidual’s behavior before, during, and after a speciﬁc

organizational change, whether related to the individ-

uals themselves or inﬂuenced by the environment in

which they interact. Playing an essential role in ver-

ifying and identifying temporal behavioral patterns,

longitudinal studies become a valuable source for val-

idating and describing appropriate procedures to en-

sure the well-being of individuals in work environ-

ments.

An Activity-Based Working Environment (ABW)

is characterized by being a ﬂexible work environment

where employees have autonomy to choose where to

perform their tasks, seeking locations that offer the

best solutions related to social, communication, col-

laborative, and well-being aspects.

With the constant advancement of information

https://orcid.org/0009-0009-2028-3726

https://orcid.org/0000-0001-7315-3874

https://orcid.org/0000-0001-7063-1658

technology and the increasing connectivity of work

environments, the ABW concept has stood out, aim-

ing to optimize usable spaces, increase productivity,

foster information exchange, and enhance the well-

being and mental health of employees.

This study considers a longitudinal study regard-

ing the implementation of an activity-based working

environment (ABW) (Halldorsson et al., 2022) to ex-

tract information related to the ﬂuctuation of satis-

faction and productivity metrics: a) before the im-

plementation of ABW, b) during the implementation

of ABW; and c) after the implementation of ABW;

and establish the relationship between these changes

considering the temporal aspect. The goal is to assist

decision-making regarding the adoption or not of this

type of work environment in a business ofﬁce. The

longitudinal study considered in this work contains 11

variables tracking 100 employees before, during, and

after the application of the Activity-Based Working

Environment concept in their workplace.

For the description of employee behavior patterns

subjected to the ABW concept, this work is based on

Formal Concept Analysis (FCA), which is a branch

of applied mathematics related to the theory of con-

ceptual lattices, constructed from a dataset composed

of objects, attributes, and their incidence relationships

(Ganter et al., 1999). Through Triadic Concept Anal-

ysis (TCA), an extension of FCA that allows intro-

ducing a third condition, such as time, it is possible

Oliveira, T., Song, M. and Zárate, L.

Triadic Rules for Analysis of Productive and Well-Being Social in Activity-Based Working Environments.

DOI: 10.5220/0012309800003657

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 293-299

ISBN: 978-989-758-688-0; ISSN: 2184-4305

293

to identify temporal relationships for changes in vari-

ables of interest over time, such as aspects of satis-

faction, stress, psychological factors, etc. These rela-

tionships can also be characterized using association

rules for speciﬁc contexts, such as the relationship be-

tween variables before and during the implementation

of ABW, the relationship between variables during

and after its implementation, and the relationship be-

tween variables before and after the implementation

of ABW.

In this study, triadic rules are extracted to char-

acterize and evaluate the efﬁciency and satisfaction

of the work ofﬁce over time. The results obtained

highlight the potential of Triadic Concept Analysis

(Konecny and Osicka, 2010) in investigating longi-

tudinal databases. Overall, observing the implemen-

tation of an Activity-Based Working Environment

(ABW) through a longitudinal study enables an un-

derstanding of the impacts of this transition both on

the work environment itself and on the employees in-

volved.

This article is organized as follows: in Section

2, the theoretical framework covering Formal Con-

cept Analysis and Longitudinal Data Analysis is pre-

sented. In Section 3, related works are discussed.

Section 4 describes the adopted methodology, in-

cluding the materials and methods used. Section 5

presents the results and discussions based on the eval-

uation metrics. Finally, Section 6 provides the con-

cluding remarks, including potential future work.

2 BACKGROUND

2.1 Formal Concept Analysis

Formal Concept Analysis (FCA) is a branch of ap-

plied mathematics related to the formal conceptual

hierarchization, based on a set of objects, attributes,

and incidence relations between them (Ganter et al.,

1999), with the aim of identifying properties and ex-

tracting relevant knowledge from data.

In FCA, a formal dyadic context corresponds to a

tuple of the form K := (G, M, I), where G corresponds

to a set of objects (extension), M to a set of attributes

(intension), and I corresponds to the incidence rela-

tion (I ⊆ G ×M) between objects and their properties

(attributes). From this formal context, it is possible to

extract formal concepts, from which association rules

can be derived. Table 1 shows an example of a dyadic

context.

Considering the formal dyadic context K :=

(G, M, I), it is possible to obtain formal concepts de-

ﬁned by a pair (A, B) where A ⊆ G, and B ⊆ M. The

Table 1: Dyadic Context.

G/M a

× ×

formation of the pair (A, B) follows the following con-

dition: A = B’ and B = A’, where the derivation oper-

ator (

′

) is deﬁned by Equations 1 and 2:

′

= {m ∈ M|(g, m) ⊆ I∀g ∈ A} (1)

′

= {g ∈ G|(g, m) ⊆ I∀m ∈ B} (2)

From the formal context, it is possible to extract

implication rules of the form P → Q, where P and

Q are subsets of attributes with P

′

⊆ Q

′

. This means

that a given object that has attributes in P also has at-

tributes in Q. An implication rule P → Q is valid if

and only if every object that possesses the attributes

in P also possesses the attributes in Q. These implica-

tions are dependencies between elements of sets ob-

tained from a formal context.

For each rule, evaluation metrics can be associ-

ated, such as Support and Con f idence. Formally,

Support corresponds to the proportion of objects in

the subset g ∈ G that satisfy the implication P → Q,

relative to the total number of objects |G| in the for-

mal context K (Equation 3) where (

′

) corresponds to

the derivation operator.

Suporte(P → Q) =

|(P ∪ {Q})

′

|G|

(3)

Conﬁdence corresponds to the proportion of ob-

jects g ∈ G that contain P and also contain Q, relative

to the total number of objects |G| (Equation 4).

Con f (P → Q) =

|(P ∪ {Q})

′

Suporte(P → Q)

Suporte(P)

(4)

2.2 Triadic Concept Analysis (TCA)

In some applications, it becomes essential to associate

a condition related to the temporal aspect. TCA ex-

tends the classical FCA theory by introducing a new

dimension. In this case, the formal context is deﬁned

by a quadruple K = (K1, K2, K3, Y ), where K1, K2,

and K3 are sets of objects, attributes, and conditions,

respectively, and Y corresponds to a ternary relation

among them (I ⊆ K1 × K2 × K3). Table 2 shows an

example of a triadic context.

Although originating from FCA, the triadic ap-

proach has more complex deﬁnitions of concepts, im-

plication rules, and derivation than the dyadic ap-

proach. For example, a triadic formal concept is now

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294

deﬁned by a triple (A

, A

), such that A

⊆ K

, and A

⊆ K

, and A

× A

⊆ Y.

The sets A

, A

are called objects, attributes, and

mode, respectively. The set of all concepts in a par-

tially ordered triadic context forms a complete lattice,

also called a conceptual lattice.

From triadic contexts, it is possible to obtain asso-

ciation rules of the Biedermann Conditional Attribute

Association Rule (BCAAR) and Biedermann Attri-

butional Condition Association Rule (BACAR) types

(Biedermann, 1999):

1. BCAAR: (A1 → A2)B(sup, con f ), where A1 and

A2 are subsets of attributes, (A1, A2 ⊆ K2), and B

is a condition, (B ⊆ K3). If the subset of attributes

A1 occurs with the condition B, then A2 will also

occur, with support (sup) and conﬁdence (con f ).

2. BACAR: (B1 → B2)A(sup, con f ). Here, B1 and

B2 are conditions, (B1, B2 ⊆ K3), and A is a sub-

set of attributes, (A ⊆ K2). If B1 occurs for the

attributes A, then the condition B2 will also occur,

with support (sup) and conﬁdence (con f ).

2.3 Longitudinal Database

Longitudinal studies in health typically record obser-

vations related to clinical, symptomatic, psychologi-

cal, emotional, environmental, among other data. De-

pending on the type of study, the database may in-

clude the addition of new individuals from the study

population and even add new variables of interest to

the study. Longitudinal databases are sets of records

where the time period (wave) is a parameter of analy-

sis. In these databases, one can observe the variation

of attributes and characteristics, monitoring their up-

dates during the waves. This opens up possibilities

to explore cause-and-effect relationships, making this

area of study relevant.

Table 3 shows part of the database considered in

this work. It presents the variation of attributes (P1,

P2, and P3) for an employee (Object) over two waves

(t1 and t2), making it possible to observe how the

data behaves between these time periods. For exam-

ple, attribute P1 changed from a satisfaction level of

6 (high) to 3 (intermediate) between the ﬁrst and sec-

ond waves. In this work, we extract association rules

that allow evaluating changes in satisfaction and well-

being relationships among employees in a company

after the implementation of the ABW approach.

3 RELATED WORKS

The articles (Lana et al., 2022) and (Noronha et al.,

2022) are likely the ﬁrst works to explore triadic anal-

ysis in describing longitudinal studies in the ﬁeld of

health. The ﬁrst article focuses on analyzing the effec-

tiveness of prevention methods against COVID-19 in-

fection, while the second work delves into pattern dis-

covery related to human aging by observing the clin-

ical and environmental evolution of individuals over

time.

In the realm of TCA-related work, there is the

study by (Zhuk et al., 2014), where a series of ex-

periments compared the results and performance of

algorithms for triadic context analysis. Additionally,

one can mention the work by (Missaoui and Emami-

rad, 2017), where the Lattice Miner tool is proposed

to generate triadic association rules, including impli-

cations.

In the context of ABW, numerous studies propose

various methodologies to assess its impact. The ma-

jority of these studies beneﬁt from longitudinal re-

search, utilizing the variation of performance metrics

over time as an analytical tool. The works by (Rolf

et al., 2018) and (Blok et al., 2012), both longitudinal

in nature, provide a good introductory understanding

of the theme and detail case studies of implementing

this type of approach in work environments, as well

as the adoption of more ﬂexible practices. In these

studies, employees are subjected to questionnaires,

and the responses are used to deﬁne comparison met-

rics. The obtained results offer values and references

for comparison and composition of the triadic context

presented in this article.

The present work differs from previous studies

such as (Arundell et al., 2018) and (Haapakangas

et al., 2019), which utilized Linear Mixed Mod-

els (LMM), and (Haapakangas et al., 2018) and

acklander and Richter, 2022), which used Linear

Regression models, by addressing Formal Concept

Theory. Although all of them are longitudinal studies

and share similar data collection methods (question-

naires), the study proposed in this article differs in its

utilization of FCA (Formal Concept Analysis) as the

foundation of the methodology.

4 METHODOLOGY

The methodology proposed in this work aims to de-

scribe temporal associations between questionnaire

variables concerning the level of satisfaction with the

implementation of ABW and the new type of work-

place organization.

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295

Table 2: Triadic Context.

-K

× × × ×

× × ×

Table 3: An example of a longitudinal database.

Object P1-t1 P2-t1 P3-t1 P1-t2 P2-t2 P3-t2

1 6 6 6 3 4 3

4.1 Materials

The longitudinal database used for this study is avail-

able in (Halldorsson et al., 2022). The database con-

tains records of 100 employees working for a state-

owned company implementing ABW. This database

comprises 43 questionnaire variables, including re-

sponses from different perspectives of interest. Ta-

ble 4 shows the attributes that make up the database,

segmented according to the area related to each ques-

tionnaire item. The longitudinal study spans 3 waves:

the ﬁrst wave representing 2 months before the ABW

implementation, the second for 4 months after imple-

mentation, and the last for 9 months after adopting

this approach. However, upon exploring the database,

it is evident that not all employees responded to the

entire questionnaire, resulting in response rates of

87%, 75%, and 69%, respectively, across the waves.

4.2 Methods

4.2.1 Preprocessing

Before effectively starting the extraction of triadic

rules from the database, a preprocessing stage was ap-

plied. Firstly, as discussed earlier, the database does

not have 100% adherence in responses during the 3

waves. Therefore, employees with many missing data

in more than one wave were disregarded, reducing the

database size from 100 to 83 records.

Furthermore, since the database still contains

empty values in some attributes, an imputation strat-

egy was applied, ﬁlling these ﬁelds with the mean

value of the responses for the same attribute within

the same wave. For example, if an employee did not

answer a question in the ﬁrst wave (t1), this data was

ﬁlled with the average of this attribute for the t1 wave.

This is a common procedure in Machine Learning, al-

though other strategies can be applied. In general, any

sort of data imputation creates a distortion in reality.

Due to the large amount of information available

in the dataset, it was decided to segment the database

limited to the relationships between the following se-

lected topics: ”Productivity,” ”Job Satisfaction,” and

”Workload”. This segmentation resulted in a dataset

with 83 samples and 7 attributes.

4.2.2 Discretization

After the preprocessing stage, reference values, such

as thresholds, were deﬁned to determine when the to-

tal value of the questionnaire would correspond to a

negative or positive satisfaction. For this purpose, the

mean value of the scale was used as the threshold, i.e.,

on a scale from 1 to 7, the threshold deﬁned for posi-

tivity is any value above 4. Table 5 shows an example

of the triadic context, representing positive satisfac-

tions with an X.

After obtaining the triadic context, it was con-

verted into a suitable format for input into the Lattice

Miner software ((Missaoui and Emamirad, 2017)) for

the extraction of triadic rules. To do this, a JSON ﬁle

was created containing the relationships between ob-

jects, attributes, and conditions in the speciﬁc format

described in the tool’s documentation, specifying the

minimum support and conﬁdence values for generat-

ing BCAAR and BACAR rules.

For the analysis of satisfaction levels in the ABW

implementation, the following cases were considered

relevant, taking into account A and B as subsets

of questionnaire variables, and the waves of the

longitudinal study a - before, b - during, and c - after:

Case 1: Relationship Between Attributes Before

and During the ABW Implementation.

1. ( A → B ) ab

2. ( a → b ) A

3. ( b → a ) A

Case 2: Relationship Between Attributes During

and After the ABW Implementation.

1. ( A → B ) bc

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Table 4: Variables available in the database.

Questionnaire variables

Productivity Three items related to the impact on productivity.

Privacy Six items related to the impact on privacy, whether focused on the task

or on communication.

Feeling of Psychologi-

cal Ownership

Four items related to the feeling of ownership in the workplace.

Satisfaction Two items related to job satisfaction.

ABW A single item related to liking or not ABW.

Workload Four items related to workload.

Stress Four items related to stress caused by work.

Change of environment A single item that questions the frequency of changing the work envi-

ronment.

Effects on performance Personal estimation of the effect of the work environment on perfor-

mance.

Gender The employee’s gender.

Conditions

t1 Wave before ABW implantation - 2 months before.

t2 Wave after ABW implantation - 4 months later.

t3 Wave after ABW implementation - 9 months later.

Table 5: Example of table after processing.

ID P1-t1 P3-t1 P1-t2 P3-t2 P1-t3 P3-t4

1 X X X

2 X X X X X X

2. ( b → c ) A

3. ( c → b ) A

Case 3: Relationship Between Attributes Before

and After the ABW Implementation.

1. ( A → B ) ac

2. ( a → c ) A

3. ( c → a ) A

Considering, for example, rule (1) in case 1, we

have: ”Employees who positively assessed the vari-

able(s) in set A of the questionnaire in the ﬁrst wave

also did so in the second wave.” This rule allows eval-

uating the initial impact of ABW implementation and

can later serve as a way to assess employee adaptation

to the new concept over the longitudinal study. An-

other example is rule (1) in case 3, where we under-

stand: ”Employees who positively assessed the ABW

implementation in A also did so for B before and after

ABW implementation.”

5 EXPERIMENTS AND

ANALYSIS OF RESULTS

After applying LatticeMiner, it was possible to ex-

tract BACARs and BCAARs for the cases described

in the previous section, enabling the analysis of the

impact of ABW implementation in the company.

Case 1 (Before and During):

1. BACARs

(a) ( t1 → t2 ) Productivity2 [support = 96,4% conﬁ-

dence = 98,8%]

(b) ( t1 → t2 ) Productivity1 [support = 92,8% conﬁ-

dence = 95,1%]

dence = 78,1%]

2. BCAARs

(a) ( Productivity2 → Satisfaction1 ) t1 [support =

89,2% conﬁdence = 90,2%]

(b) ( Productivity2 → Satisfaction1 ) t2 [support =

85,5% conﬁdence = 87,7%]

[support = 86,7% conﬁdence = 90,0%]

(d) ( Productivity1, Productivity3 → Satisfaction1 ) t2

[support = 78,3% conﬁdence = 90,3%]

Triadic Rules for Analysis of Productive and Well-Being Social in Activity-Based Working Environments

297

(e) ( Satisfaction2 → Satisfaction1 ) t1 [support = 85,5%

conﬁdence = 97,3%]

(f) ( Satisfaction2 → Satisfaction1 ) t2 [support =

67,5% conﬁdence = 77,8%]

Case 2 (During and After):

1. BACARs

(a) ( t2 → t3 ) Productivity1 [support = 92,8% conﬁ-

dence = 95,1%]

(b) ( t2 → t3 ) Productivity1 [support = 92,8% conﬁ-

dence = 97,5%]

2. BCAARs

(a) ( Productivity1 → Satisfaction2 ) t2 [support =

72,3% conﬁdence = 75,9%]

(b) ( Satisfaction2→ Productivity1 ) t3 [support = 62,7%

conﬁdence = 98,1%]

conﬁdence = 77,8%]

(d) ( Satisfaction1 → Satisfaction2 ) t3 [support =

60,2% conﬁdence = 96,2%]

Case 3 (Before and After):

1. BACARs

(a) ( t1 → t3 ) Productivity1 [support = 95,2% conﬁ-

dence = 97,5%]

(b) (t3 → t1 ) Satisfaction2 [support = 62,7% conﬁdence

= 98,1%]

2. BCAARs

(a) ( Satisfaction2 → Satisfaction1 ) t1 [support = 85,5%

conﬁdence = 97,3%]

(b) ( Satisfaction1 → Satisfaction2 ) t3 [support =

60,2% conﬁdence = 96,2%]

With these rules, it is possible to describe and ob-

tain information about the ABW implementation pro-

cess from the longitudinal study. For example, ana-

lyzing the BACARs (c) rules from Case 1 and the (b)

rule from Case 3, it can be observed that job satis-

faction decreased, as employees who responded pos-

itively to Satisfaction2 (”I am satisﬁed with my job”)

did so less frequently between the waves (before →

during) and (before → after), with the support drop-

ping from 68.7

BCAARs rules (a) and (b) from Case 3 also indi-

cates a drop in general satisfaction, pointing that the

support of Satisfaction 1 (”My department/agency is

a good place to work”) and Satisfaction 2 (”I am sat-

isﬁed with my job”) decreased from 85.5% to 60.2%

between the ﬁrst and third wave.

Another interesting example would be BACAR

rule (b) from Case 1 in conjunction with BACAR rule

(a) from Case 3. In this context, it can be inferred that

overall efﬁciency decreased, as evidenced by the sup-

port between the ﬁrst and third wave, where the sup-

port dropped to 95.2%. This indicates that employees

who felt efﬁcient no longer do so. However, this sup-

port grows compared to the result in the second wave,

at 92.8%, showing that some efﬁciency was recovered

by the end of the study, highlighting a possible adap-

tation of employees to the new way of working.

BACAR rule (a) from Case 1, together with

BACAR rule (a) from Case 2, indicates that efﬁciency

decreased for collaborations, as employees who re-

sponded positively to Productivity2 (”I feel efﬁcient

when collaborating with my colleagues”) did so less

frequently between the waves (before → during) and

(during → after), with the support dropping from

96.4% to 92.8

6 CONCLUSIONS AND FUTURE

WORK

In this work, we showed the potential of applying tri-

adic rules to describe longitudinal study databases in

social contexts, where changes in the way of working,

as described in this article, result in various implica-

tions. In this context, rules were generated that enable

a better understanding of employee behavior before,

during, and after the implementation of ABW.

It is important to highlight that Triadic Concept

Analysis can become relevant in decision-making and

the overall analysis of longitudinal databases. Its ap-

plication to higher-dimensional databases will pro-

vide greater precision and description of the data,

leading to even more meaningful conclusions.

As future work, it would be interesting to con-

duct studies involving time intervals that allow for

a greater number of waves to observe whether em-

ployees become accustomed to and adapt to the new

way of working. This could mitigate the negative ef-

fects on performance and job satisfaction caused by

the shock of the work change.

Furthermore, the analysis could be extended to

various companies, making it possible to evaluate the

contribution of the internal culture of each company

and its employees to the negative or positive impact

of ABW implementation, given that the nature of the

topic has gaps due to the possibility of personal inter-

pretation of the changes by the participants.

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ACKNOWLEDGEMENTS

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,

Brazil.

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