Exploratory Data Analysis in Cloud Computing Environments for Server

Consolidation via Fuzzy Classiﬁcation Models

Rafael R. Bastos

1 a

, Vagner A. Seibert

1 b

, Giovani P. Maia

, Bruno M. P. de Moura

3 c

Giancarlo Lucca

2 d

, Adenauer C. Yamin

1 e

and Renata H. S. Reiser

1 f

Federal University of Pelotas (UFPel/PPGC), Pelotas, Brazil

Catholic University of Pelotas (UCPel), Pelotas, Brazil

Federal University of Pampa (Unipampa), Bag

e, Brazil

Keywords:

Fuzzy Logic, Server Consolidation, Feature Selection, Fuzzy Rule Learning.

Abstract:

The present work addresses the challenges of ﬂexible resource management in Cloud Computing, empha-

sizing the critical need for efﬁcient resource utilization. Precisely, we tackle the problem of dynamic server

consolidation, supported by the capacity of Fuzzy Logic to deal with uncertainties and imprecisions inherent

in cloud environments. In the preprocessing step, we employ a feature selection strategy to perform attribute

selection and, better understand the problem. Data classiﬁcation was performed by fuzzy rule learning ap-

proaches. Comparative evaluations of algorithm classiﬁcation highlight the remarkable accuracy of FURIA,

with IVTURS as a close alternative. While FURIA generates 41 rules, indicating a comprehensive model,

IVTURS produces only six, introducing an abstract level to model uncertainties as interval-valued fuzzy mem-

bership degrees. The study underscores the relevance of parameter adaptation in mapping feature selection

and membership functions to achieve optimal performance for ﬂexible algorithms in the Cloud Computing

environment. Our results underlie the structure of a fuzzy system adapted to CloudSim, integrating energy

optimization and Service Level Agreements assurance through different server consolidation strategies. This

research contributes valuable perspectives to decision-making processes in the Cloud Computing environment.

1 INTRODUCTION

The worldwide public Cloud Computing (CC) market

is expected to reach an estimated US$ 679 billion in

2024. This estimate encompasses business processes,

platforms, infrastructure, software, management, se-

curity, and advertising services delivered by public

CC services, as storage, bandwidth, or CPU cycles.

In such scenario, one of the main demands of

the CC environment is the efﬁcient management of

resources. In this point, the energy efﬁciency is

an interesting issue due its importance on differ-

ent fronts. Additionally, it keep satisfactory Ser-

vice Level Agreements (SLA) and Quality of Ser-

https://orcid.org/0009-0005-7494-3495

https://orcid.org/0009-0005-2128-6639

https://orcid.org/0000-0002-3960-8377

https://orcid.org/0000-0002-3776-0260

https://orcid.org/0000-0002-7333-244X

https://orcid.org/0000-0001-9934-3115

vice (QoS) (Beloglazov and Buyya, 2013; He and

Buyya, 2023). Minimizing energy consumption sat-

isfying QoS constraints is complex and is part of the

research into dynamic Virtual Machine (VM) consol-

idation, characterized as an NP-Hard problem (Fer-

daus et al., 2014).

VM consolidation involves the identiﬁcation of

underloaded and overloaded hosts, selection of VMs

for migration, and their allocation to alternative

hosts (Mittal et al., 2019). However, this strategy is

a complex task as detecting excessive workload and

initiating migration cannot quickly respond to sudden

and dynamic changes in the environment (Sowrirajan,

2022).

Fuzzy Logic (FL) (Zadeh, 1965) is frequently em-

ployed to assist in decision-making processes, ad-

dressing uncertainties and inaccuracies in the vari-

ables involved in VM consolidation.

In 1975 Sambuc (Sambuc, 1975) presented the

concept of an Interval-valued Fuzzy Set (IvFS), and

636

Bastos, R., Seibert, V., Maia, G., P. de Moura, B., Lucca, G., Yamin, A. and Reiser, R.

Exploratory Data Analysis in Cloud Computing Environments for Server Consolidation via Fuzzy Classiﬁcation Models.

DOI: 10.5220/0012615900003690

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 26th International Conference on Enterprise Information Systems (ICEIS 2024) - Volume 1, pages 636-643

ISBN: 978-989-758-692-7; ISSN: 2184-4992

other studies were established, taking into account

the uncertainty linked to the construction of a precise

interval-valued membership function (Bustince et al.,

2016).

The ability to make decisions under uncertainties

and the tolerance for imprecision of control systems

provide the seminal motivation for development of

IvFS. More recently, this logical approach has con-

tributed to solutions for complex problems, reason-

ing models, deduction, and calculation with imper-

fect information, also integrating techniques from Ar-

tiﬁcial Intelligence (AI), such as Machine Learning

(ML) and Neural Networks (Lughofer, 2022).

In this context, the integration of Computa-

tional Intelligence methodologies, especially Ma-

chine Learning, becomes opportune to enhance per-

formance in resource allocation and mitigate energy

consumption within Cloud Computing.

By integrating concepts of CC and FL, the objec-

tive of this work is to stimulate a discussion focused

on ﬂexible approaches to model uncertainties associ-

ated with data analysis related to relevant attributes

of CC environments. These attributes include CPU

usage, memory occupancy, bandwidth, and available

storage.

This paper is structured as follows. The ﬁrst

section deals with the contextual foundations of the

work. Section 2 introduces Cloud Computing chal-

lenge and basic concepts of Interval-valued Fuzzy

Logic (IvFL) and some Fuzzy Rule-Based Classiﬁ-

cation Systems (FRBCS). Related work is presented

in Section 3. In Section 4, we discuss the details

of Exploratory Data Analysis, including obtaining

the dataset, feature selection, and the deﬁnition of

membership functions and rule base. Section 5 de-

scribes the experimental evaluation. Finally, section 6

presents conclusions and future work.

2 MAIN CONCEPTS

In this section, we initiates our exploration by ad-

dressing the challenges in CC and presenting foun-

dational concepts in IvFL. Additionally, we introduce

various FRBCS.

2.1 Cloud Computing

The operational model of Cloud Computing (CC) al-

lows dynamic resource allocation based on demand

(Gourisaria et al., 2020). This elasticity facilitates

the provision of high-performance computational en-

vironments with optimized equipment investments for

the end user, aligning costs with resource requests

(Nathani et al., 2012)

In 2014, US data centers consumed an estimated

70 billion kilowatt-hours (kWh), constituting about

1.8% of the total electricity consumption in the USA,

according to a report by the Natural Resources De-

fense Council (NRDC)

(Shehabi et al., 2016).

Energy consumption is expected to rise by approx-

imately 4% from 2014 to 2023, reaching an estimated

73 billion kWh in 2023 for US data centers. Com-

panies like Google, Microsoft, and Amazon work to-

wards this goal by using renewable energy and invest-

ing in on-site green energy generation.

Efﬁcient resource management in CC requires dy-

namic consolidation of VMs, structured by identify-

ing overloaded and underutilized physical machines,

selecting VMs for migration, and allocating them to

other physical machines. However, VM migration,

aiming to optimize resource usage, is a complex task

as it may not promptly respond to sudden dynamic

changes in the CC environment.

2.1.1 CloudSim Architecture

The assessment of strategies and algorithms in cloud

computing environments requires effective simulation

tools. In this context, CloudSim (Calheiros et al.,

2011) emerges as a widely employed and esteemed

simulation framework, providing researchers with a

modular platform for analyzing policies, algorithms,

and strategies (Arshad et al., 2022).

The CloudSim architecture is designed to enable

a comprehensive and adaptable simulation of CC en-

vironments. Key entities include DatacenterBroker,

Cloudlet, VM, Host, and Datacenter. It operates

across abstraction layers, including hardware, mid-

dleware, and user/broker. The CloudSim architecture

is shown in Figure 1.

This architecture encompasses crucial modules,

such as resource provisioning and scheduling poli-

cies. Extensibility is inherent to CloudSim, allow-

ing the addition of modules and policies to meet spe-

ciﬁc research or simulation requirements. The modu-

lar and scalable nature of CloudSim facilitates its ap-

plication in diverse scenarios, contributing to detailed

simulations in cloud computing environments.

Moreover, compared to physical environments,

the possibility of experiment repetitions in a con-

trolled manner is one of the main advantages of sim-

ulation tools, as CloudSim, integrating the synergis-

tic variation of the different conditions in the system

evaluation.

https://www.nrdc.org

Exploratory Data Analysis in Cloud Computing Environments for Server Consolidation via Fuzzy Classiﬁcation Models

637

Events

Handling

CloudSim core simulation engine

Dat a Center

Clo ud

Resources

Provisioning

CPU

Allocation

Memory

Allocation

Storage

Allocation

Bandwidth

Allocation

Clo ud

Services

Cloudlet

Execution

Services

User

Interface

Structures

CloudSim

User code

User or Data Center Broker

Scheduling

Policy

Cloud

Scenario

Application

Configuration

User

Requirements

…

Simulation

Specification

Management

Network

Topology

Message delay

Calculation

Network

Cloud

Coordinator

Sensor

Cloudlet

Virtual

Machine

Figure 1: CloudSim architecture (Calheiros et al., 2011).

2.2 Fuzzy Rule-Based Classiﬁcation

Systems

Fuzzy Rule-Based Classiﬁcation Systems (FRBCSs)

represent a potent tool commonly employed to ad-

dress classiﬁcation problems. These fuzzy classi-

ﬁers are renowned for their high classiﬁcation accu-

racy and their ability to provide interpretable mod-

els through the utilization of linguistic labels (Lucca

et al., 2020; Sanz et al., 2021).

The FRBCS consists of two integral components:

the Knowledge Base, comprising a specialized Rule

Base and Data Base adapted to a speciﬁc classiﬁ-

cation problem, and the Fuzzy Reasoning Method,

which is responsible for applying fuzzy logic to the

Rule Base and Data Base, managing data uncertainty

to effectively assign class labels (Cord

on et al., 1998).

The FRBCS design entails a meticulous process

involving supervised learning, initiated with a set of

correctly classiﬁed training examples. The primary

objective is to formulate a Classiﬁcation System ca-

pable of minimizing errors in assigning class labels to

novel instances. The system’s performance is subse-

quently evaluated comprehensively on test data, pro-

viding an approximation of the FRBCS real error.

This structured approach underscores the systematic

construction and performance assessment intrinsic to

FRBCS, substantiating its utility in intricate classiﬁ-

cation scenarios. Figure 2 shows this process.

This characteristic allows FRBCSs to be applied

effectively in various real-world scenarios, span-

ning industries (Samantaray et al., 2010), health-

care (Czmil, 2023), the economy (Campisi et al.,

2022), and numerous other domains. Their wide-

ranging application is attributed to their capacity to

yield accurate results while ensuring interpretability

in the generated models.

The following are examples of FRBCSs employed

in this study.

Training Data

Testing Data

Testing

Results

Fuzzy Reasoning Method

Data Base

Fuzzy Rule Base

Knowledge Base

Fuzzy Rule Based

Classification System

Learning

Process

Classification

Process

Figure 2: Fuzzy rule-based classiﬁcation process from

training to testing (Cord

on et al., 1998).

The FARC-HD (Alcal

a-Fdez et al., 2011) algo-

rithm is a computationally efﬁcient solution tailored

for high-dimensional challenges, leveraging fuzzy

rules and integrating genetic rule selection and pa-

rameter tuning to optimize performance. The FARC-

HD uses a three-phase strategy that involves acquiring

fuzzy association rules through a structured tree ap-

proach, meticulous ﬁltering to penalize redundancy,

and the integration of a genetic algorithm for rigor-

ous rule reﬁnement. This comprehensive methodol-

ogy enhances the algorithm’s efﬁcacy, making it par-

ticularly adept at addressing the nuanced demands in-

herent in high-dimensional problem spaces.

The Chi-RW algorithm (Cord

on et al., 1999) is

a classiﬁcation algorithm discerning the relationship

among variables, establishing an association between

the resource space and the class space. This algo-

rithm deﬁnes linguistic partitions, formulates a fuzzy

rule for each example, and assigs the fuzzy region to

the highest membership degree. So, linking the label

class of an application to the consequence of the rule.

The FURIA (Fuzzy Unordered Rule Induction Al-

gorithm) algorithm is a classiﬁcation algorithm pro-

posed by (H

uhn and H

ullermeier, 2009). In con-

trast to conventional approaches, this algorithm relies

on fuzzy rules to model more ﬂexible classiﬁcation

boundaries. Rules generated by replacing fuzzy in-

tervals use a trapezoidal membership function and a

rule induction technique. FURIA generates sets of

unordered rules, providing a more ﬂexible represen-

tation of patterns in the data.

The IVTURS algorithm (Sanz et al., 2013)

(Interval-Valued Fuzzy Reasoning Method with Tun-

ing and Rule Selection) is a FARC-HD extension, in-

corporating interval-valued fuzzy rules. It employs a

parameterized Fuzzy reasoning method and an evolu-

tionary algorithm for optimization, allowing ﬂexible

handling of uncertainty in data and effective adapta-

tion to classiﬁcation problems. IVTURS features a

rule selection mechanism to identify the most rele-

vant and signiﬁcant rules, enhancing computational

ICEIS 2024 - 26th International Conference on Enterprise Information Systems

638

efﬁciency and model interpretability.

3 RELATED WORK

This section reports the main projects proposing fuzzy

strategies in the stages of dynamic server consolida-

tion in Cloud Computing. The selected papers re-

sulted from a Systematic Literature Review (SLR) re-

alized in (Bastos et al., 2023).

The SLR analysis reveals the dynamic VM con-

solidation, emerging as an effective strategy to en-

hance efﬁciency energy in CC, based on four steps: (i)

Overloaded PM Identiﬁcation; (ii) VM Selection; (iii)

Detection of Underutilized PMs; and (iv) Optimized

VM Allocation. The underlying goal is to achieve dy-

namic consolidation of VMs, aiming to optimize the

trade-off between performance and energy efﬁciency.

Table 1 presents an analysis of proposals for re-

source management in CC, applying techniques on

dynamic server consolidation, and highlighting their

signiﬁcance. The description emphasized objectives,

logical approach, variables, and prospected tools.

This analysis reveals a pronounced focus on the

optimization and minimization of energy consump-

tion in CC environments as a crucial theme to meet

the demand for consumption reduction.

Two works stand out for the integration of FL with

ML. In (Negi et al., 2021), ML is used to cluster

VMs based on resource load. Meanwhile, in (Jumnal

and Kumar, 2021), FL is combined with RL to opti-

mize the allocation and/or relocation of VMs. The

integration with ML techniques allows FL systems

to learn from data, adapting automatically to changes

and complexities in the problem. This enables the im-

provement of fuzzy rules based on the characteristics

and relationships present in the data. The other works

do not address ML techniques.

Regarding the considered logical approach, only

in (Moura et al., 2022) and (Negi et al., 2021) is

the multivalued extension of FL considered, speciﬁ-

cally IvFL and T2FL, respectively. In (Rozehkhani

and Mahan, 2022), Granular Computing is consid-

ered. The other works adopt Type-1 Fuzzy Logic.

Regarding the variables considered by Fuzzy sys-

tems, it is observed that the assessment of computa-

tional power and memory usage is a consensus among

the works. In (Negi et al., 2021), (Jumnal and Ku-

mar, 2021), (Braiki and Youssef, 2020), (Mongia and

Sharma, 2021), and (Rozehkhani and Mahan, 2022),

the authors aim to optimize the allocation or minimize

the migration time of VMs. However, they do not

account for communication costs, which can lead to

bottlenecks in the system when congested, and con-

sequently may lead to unsatisfactory performance.

Another convergence among the works is the use

of CloudSim

as a simulation tools for CC environ-

ments. Thus, our proposed feature selection also con-

siders variables available by CloudSim.

4 METHODOLOGY

In this section, we provide a comprehensive analy-

sis of the considered dataset. The dataset initially

comprises variables provided by CloudSim, with the

Virtual Machine allocation policy set to Interquartile

Range (IQR), and the VM selection policy using Ran-

dom Selection (RS).

The dataset’s foundation lies in workloads sourced

from PlanetLab

. The collected variables represent

the state of each host every 300 seconds, including

memory occupancy, CPU usage, bandwidth, available

storage, power consumption, and MIPS, along with

an indication of the host’s utilization level (underuti-

lized, regular, and overutilized).

Regarding the dataset, a feature selection was

performed using the Sequential Forward Selection

(SFS) (Pudil et al., 1994) technique to eliminate

highly correlated variables. The aim is twofold: to

enhance overall classiﬁcation performance and re-

duce computational efforts involved in processing

data. The selection process involves iteratively com-

bining variables to achieve optimal subset conﬁgura-

tions based on evaluation criteria.

For this study, we chose the Area Under the ROC

Curve (AUC) (Bradley, 1997) as evaluation criteria.

This metric was selected strategically to enhance the

assessment of the classiﬁcation performance, provid-

ing a comprehensive measure of the trade-off between

true positive rates and false positive rates across dif-

ferent classiﬁcation thresholds. The AUC metric is

particularly well-suited for our objectives, as it of-

fers a holistic evaluation of the model’s discrimina-

tory capacity, considering various decision thresholds

and encompassing a broader understanding of its pre-

dictive capabilities.

Thus, in the ﬁrst iteration of SFS, an individ-

ual analysis of variables is conducted, selecting the

one with the best classiﬁcation performance. In the

next iteration, this variable is combined with others in

search of the combination with the best performance.

This process is repeated until there is no further im-

provement in classiﬁcation performance.

In this study, the application of SFS considers

http://www.cloudbus.org/cloudsim/

https://planetlab.cs.princeton.edu/

Exploratory Data Analysis in Cloud Computing Environments for Server Consolidation via Fuzzy Classiﬁcation Models

639

Table 1: Summarized analysis of selected papers in the SRL process.

Strategy Goal LA Variables Tools

Int-FLBCC Optimizing energy consumption, reducing SLA viola-

tions, and minimizing the number of VM migrations

IvFL Computational Power; Communication

Cost; Memory

■ □

CMODLB Improving resource utilization, load balancing and energy

consumption, reducing task and transmission times

T2FL

CPU; Memory; Load Balance in PM ■

FSRL Reduction of energy usage and resource wastage FRL CPU; Memory ■ ▲

Fuzzy-EPO Minimizing VM migration time and reducing energy con-

sumption

FL CPU; Memory; Storage; Bandwidth ■

fuzzyBFD Improving energy consumption and resource utilization FL CPU; Memory; Energy; Storage ■

PRSF Optimizing VM migration for SLA assurance FL CPU; Memory ■

GRC model: Minimizing energy consumption and maximizing QoS

stability

GC CPU; Core Number; Memory; Storage;

Service Time; Request Number

■

Logic Approach FL: Fuzzy Logic; IvFL: Interval-valued Fuzzy Logic; ML: Machine Learning; T2FL: Type-2 Fuzzy Logic; FRL: Fuzzy

Reinforcement Learning; GC: Granular Computing; ■ CloudSim; □ Juzzy; ▲ Matlab

the KEEL software tool (Triguero et al., 2017), ex-

ecuted with the FARC-HD, FURIA, and IVTURS al-

gorithms.

After feature selection, the resulting combinations

were employed as inputs for classiﬁcation experi-

ments utilizing the FARC-HD, Chi-RW, FURIA, and

IVTURS algorithms within the KEEL environment.

These experiments also provided parameters, deﬁn-

ing the membership function limits and the fuzzy rule

base system, and facilitating future adaptations of the

fuzzy module on CloudSim.

Details of these experiments, including member-

ship functions and rule bases generated by algorithms,

are further elaborated in Section 5.

5 EXPERIMENTAL RESULTS

Comprehending the results of our experiments is cru-

cial for evaluating the effectiveness of the proposed

methodology.

In this section, we explore the evolving process

of feature selection, evaluate the classiﬁcation perfor-

mance of different algorithms, and examine the com-

plexities of their rule generation mechanisms.

5.1 Feature Selection Dynamics

The dynamics of feature selection are presented in

Figure 3, illustrating the stepwise contribution of vari-

ables in conjunction with the AUC metric for FARC-

HD, FURIA, and IVTURS.

5.2 Classiﬁcation Performance Review

Further insights into the classiﬁcation performance

and optimal variable combinations for each algorithm

are detailed in Table 2.

Figure 3: Variables selected by the algorithms: (a) FARC-

HD, (b) FURIA, (c) IVTURS, (d) AUC metric evaluation.

The presented results include the mean classiﬁca-

tion value and standard deviation (stddev) for FARC-

HD, Chi-RW, FURIA, and IVTURS.

Table 2: Global Results of Feature Selection Simulation.

Algorithm Variables Classiﬁcation stddev

FARC-HD CPU, Memory, Bandwidth, Storage 0.9576 0.0059

Chi-RW CPU, Memory, Bandwidth, Storage 0.9288 0.0011

FURIA CPU, Energy, Storage, Bandwidth 0.9970 0.0007

IVTURS CPU, Energy, Storage, Bandwidth 0.9583 0.0180

5.3 Algorithmic Details

It’s worth noting that the FARC-HD, Chi-RW, and

FURIA algorithms adopt Type-1 Fuzzy Logic, while

IVTURS utilizes interval fuzzy sets, enabling it to

handle more complex uncertainties in server consoli-

dation scenarios.

The membership functions corresponding to the

optimal variable combinations for each algorithm are

outlined in Table 3. Triangular membership functions

are predominantly used, with the exception of FU-

RIA, which adopts a trapezoidal format for model-

ICEIS 2024 - 26th International Conference on Enterprise Information Systems

640

ing membership relations. Each variable represents

an input of fuzzy system, and is categorized into three

linguistic terms: low, medium, and high.

These membership functions are essential for in-

terpreting the output of each algorithm and under-

standing how variables contribute to the classiﬁcation

process. They provide a linguistic representation of

the input variables, allowing for more intuitive and

human-understandable analysis.

5.4 Rule Interpretability

The generated rule bases for FARC-HD, Chi-RW, FU-

RIA, and IVTURS consist of 9, 7, 41, and 6 rules,

respectively.

We observed a substantial difference in the num-

ber of fuzzy rules generated by the algorithms. No-

tably, FURIA demonstrated a higher complexity, pro-

ducing an extensive set of 41 rules. While a greater

number of rules may imply a more intricate and de-

tailed model, it necessitates careful consideration of

the associated computational demands during imple-

mentation.

In contrast, IVTURS adopted a more parsimo-

nious approach in fuzzy rule generation, generating

a modest total of only 6 rules for data classiﬁcation.

This difference underscores the inherent trade-off be-

tween achieving a detailed model and ensuring com-

putational efﬁciency. Balancing these parameters is

essential to optimize the algorithm’s application and

performance.

The format of rules generated by FARC-HD is

based on natural language, where each attribute is as-

sociated with a set of linguistic terms describing its

characteristics: L

, L

, and L

represent low, medium,

and high, respectively. Each rule consists of a series

of antecedent conditions (if-clauses), specifying the

relationships between attributes and their respective

linguistic terms. The result or predicted class is deter-

mined by the conclusion of the rule (then-clause). Ad-

ditionally, each rule may have a certainty factor (CF),

indicating the conﬁdence or certainty in the classiﬁ-

cation made by the rule.

[(i)] FARC-HD Sample Rules

bw IS L_0(3): normal CF: 1.0

cpu IS L_1(3) AND mem IS L_1(3) AND storage

IS L_1(3): under CF: 0.5347

Rules generated by Chi-RW follow a similar for-

mat to FARC-HD (if-then rules). However, instead

of a certainty factor (CF), Chi-RW rules are accom-

panied by a rule weight, indicating the importance or

contribution of the rule to the classiﬁcation.

[(ii)] Chi-RW Sample Rules

cpu IS L_0 AND mem IS L_0 AND bw IS L_0 AND

storage IS L_0:normal with Rule Weight: 1.0

cpu IS L_1 AND mem IS L_2 AND bw IS L_2 AND

storage IS L_normal with Rule Weight: 0.5910

Rules generated by FURIA follow a different for-

mat, where antecedent conditions are expressed as

scalar values for each attribute that lead to the pre-

dicted class. The classiﬁcation result is indicated in

the rule conclusion, along with a certainty factor (CF).

[(iii)] FURIA Sample Rules

(cpu >= 0.1637(-> 0.1599)) and (cpu <= 0.1637

(-> 0.1637)) => class=normal (CF = 1.0)

(cpu >= 0.0021(-> 0)) and (storage <= 0.0025

(-> 0.0050)) and (energy <= 0(->253.7326))

and (cpu <= 0.0077(-> 0.0083))=>class=under

(CF = 0.99)

Rules generated by IVTURS also follow a for-

mat based on natural language, where attributes are

associated with linguistic terms. However, IVTURS

adopts an interval approach for the certainty factor

(CF), instead of associating a single value with each

rule. The antecedent conditions of the rules also spec-

ify intervals of values for attributes.

[(iv)] IVTURS Sample Rules

bw IS L_0(3): normal CF: [1.0, 1.0]

energy IS L_0(3) AND storage IS L_0(3) AND bw

IS L_2(3): under CF: [0.4182, 0.4238]

6 CONCLUSIONS

In this study, we focused on the dynamic consolida-

tion of servers, a complex activity that involves vari-

ous aspects such as CPU usage, memory occupancy,

bandwidth, storage, and energy consumption. The

speciﬁc characteristics of CC environment and the de-

ﬁned performance requirements guided the choice of

classiﬁcation algorithms, particularly those based on

fuzzy logic.

The Feature Selection highlighted the most rele-

vant variables for server consolidation, resulting in

simple fuzzy rule sets and a more direct interpreta-

tion. Moreover, this optimized approach simpliﬁes

the fuzzy system implementation and may lead to sav-

ing computational resources. Feature Selection is a

valuable practice to enhance the efﬁciency and in-

terpretability of fuzzy models, especially in complex

scenarios, as addressed in this study.

The comparative evaluation of classiﬁcation al-

gorithms revealed differences in their performances

and approaches. FURIA stood out, demonstrating re-

markable precision with a high AUC value of 0.9970,

consolidating its effectiveness in classiﬁcation. IV-

TURS showed a performance very close, with an

AUC of 0.9583, positioning it as a potential alterna-

tive.

Exploratory Data Analysis in Cloud Computing Environments for Server Consolidation via Fuzzy Classiﬁcation Models

641

Table 3: Membership Functions.

Variable Linguistic Term

Chi-RW FARC-HD FURIA IVTURS

Triangular MF Triangular MF Trapezoidal MF Triangular MF

Bandwidth

Low -0.0500 0.0000 0.0500 -0.0725, -0.0225, 0.0275 - - - - [-0.05, 0.05] [-0.075, 0.075] [-0.075, 0.075]

Medium 0.0000 0.0500 0.1000 -0.0139, 0.0312, 0.0812 - - - - [0.0, 0.1] [-0.025, 0.125] [-0.025, 0.125]

High 0.0500 0.1000 0.1500 0.0723, 0.1217, 0.1717 - - - - [0.05, 0.15] [0.025, 0.175] [0.025, 0.175]

CPU

Low -0.4994 0.0000 0.4994 -0.4616, 0.0704, 0.5698 -∞ 0 0.1250 0.2987 [-0.4994, 0.4994] [-0.7492, 0.7492] [-0.7492, 0.7492]

Medium 0.0000 0.4994 0.9989 0.0303, 0.494, 0.9934 0.1637 0.3480 0.6432 0.8540 [0.0, 0.9989] [-0.2497, 1.2486] [-0.2497, 1.2486]

High 0.4994 0.9989 1.4983 0.6425, 1.1419, 1.6414 0.5659 0.8705 1 ∞ [0.4994, 1.4983] [0.2497, 1.7481] [0.2497, 1.7481]

Energy

Low -∞ -∞ 0 253.7326 [-23999.55, 23999.55] [-35999.33, 35999.33] [-35999.33, 35999.33]

Medium 0 253.7326 697.0520 1 [0.0, 47999.10] [-11999.78, 59998.88] [-11999.78, 59998.88]

High 697.0520 1 ∞ ∞ [23999.55, 71998.66] [11999.78, 83998.43] [11999.78, 83998.43]

Memory

Low -0.2026 0.0000 0.2026 -0.2850, -0.0067, 0.1959

Medium 0.0000 0.2026 0.4052 -0.0237, 0.1789, 0.3815

High 0.2026 0.4052 0.6078 0.1966, 0.3992, 0.6018

Storage

Low -0.0571 0.0000 0.0571 -0.0736, -0.0165, 0.1892 -∞ 0 0.2506 0.5025 [-0.0571, 0.0571] [-0.0857, 0.0857] [-0.0857, 0.0857]

Medium 0.0000 0.0571 0.1142 -0.0046, 0.0501, 0.1072 0.2506 0.5025 0.5541 0.5820 [0.0, 0.1142] [-0.0286, 0.1428] [-0.0286, 0.1428]

High 0.0571 0.1142 0.1713 0.0750, 0.1321, 0.1892 0.0554 0.0582 1 ∞ [0.0571, 0.1713] [0.0286, 0.1999] [0.0286, 0.1999]

Along with the algorithms FARC-HD and Chi-

RW, FURIA adopts Type-1 Fuzzy Logic. Introducing

an abstract level, IVTURS extends the multi-valued

fuzzy approach by incorporating IvFS, enhancing the

capability to deal with more complex uncertainties in

the server consolidation case studies.

The servers’ dynamic consolidation is a complex

activity that involves various aspects and considera-

tions. Thus, the speciﬁc characteristics of the environ-

ment and the well-deﬁned performance requirements

guide the choice of the ideal algorithm. And, the de-

scribed results in this work provide a valuable per-

spective to support decisions regarding resource opti-

mization in CC environments, highlighting the role in

modeling uncertainties and inherent imprecise data.

In conclusion, our work provides a valuable per-

spective for supporting decisions regarding resource

optimization in CC environments, emphasizing the

role of Fuzzy Logic in modeling uncertainties and

inherent imprecise data. The complexities of server

consolidation in CC environments necessitate ongo-

ing research and innovation to address emerging chal-

lenges and ensure sustainable and efﬁcient cloud ser-

vices.

6.1 Future Research Directions

While our study contributes into server consolidation

using fuzzy logic, several promising avenues for fu-

ture research emerge. We propose the development of

an interval-valued fuzzy system for dynamic server

consolidation, aimed at optimizing energy consump-

tion in cloud environments while maintaining a satis-

factory SLA.

To achieve this, we will explore a distinct set of

variables, deviating from those employed in IvFL-

based systems (Moura et al., 2022; Negi et al., 2021).

Leveraging the outcomes of our feature selection pro-

cess, we intend to reﬁne inference modeling, adjust

membership functions, and establish rule bases using

the computational intelligence provided by FRBCS.

Our intention is to enhance the approximate rea-

soning of this approach by integrating ML techniques.

This involves formulating a strategy for dynamic rule

generation, operating in conjunction with the infer-

ence stage of the fuzzy system. Additionally, we

aim to introduce new conﬁgurations for the boundary

points deﬁning the membership functions and uncer-

tainty region.

ACKNOWLEDGEMENTS

This research was partially funded by Brazilian

funding agencies CAPES, CNPq (309160/2019-7;

311429/2020-3, 3305805/2021-5, 150160/2023-

2), PqG/FAPERGS (21/2551-0002057-1) and

FAPERGS/CNPq (23/2551-0000126-8), PRONEX

(16/2551-0000488-9).

REFERENCES

Alcal

a-Fdez, J., Alcala, R., and Herrera, F. (2011). A fuzzy

association rule-based classiﬁcation model for high-

dimensional problems with genetic rule selection and

lateral tuning. IEEE Transactions on Fuzzy systems,

19(5):857–872.

Arshad, U., Aleem, M., Srivastava, G., and Lin, J. C.-W.

(2022). Utilizing power consumption and sla viola-

tions using dynamic vm consolidation in cloud data

centers. Renewable and Sustainable Energy Reviews,

167:112782.

Bastos, R., Seibert, V., Silva, G., Moura, B., Lucca, G.,

Yamin, A., and Reiser, R. (2023). Uma revis

ao sis-

tem

atica sobre consolidac¸

ao de servidores em am-

bientes de computac¸

ao em nuvem via l

ogica fuzzy.

In Anais do VII Workshop-Escola de Inform

atica

orica, pages 120–128, Porto Alegre, RS, Brasil.

SBC.

Beloglazov, A. and Buyya, R. (2013). Managing overloaded

hosts for dynamic consolidation of virtual machines in

cloud data centers under quality of service constraints.

IEEE Transactions on Parallel and Distributed Sys-

tems, 24(7):1366–1379.

Bradley, A. P. (1997). The use of the area under the

ICEIS 2024 - 26th International Conference on Enterprise Information Systems

642

roc curve in the evaluation of machine learning algo-

rithms. Pattern Recognition, 30(7):1145–1159.

Braiki, K. and Youssef, H. (2020). Fuzzy-logic-based multi-

objective best-ﬁt-decreasing virtual machine realloca-

tion. The Journal of Supercomputing, 76:427–454.

Bustince, H., Barrenechea, E., Pagola, M., Fernandez, J.,

Xu, Z., Bedregal, B., Montero, J., Hagras, H., Her-

rera, F., and Baets, B. D. (2016). A historical account

of types of fuzzy sets and their relationships. IEEE

Transactions on Fuzzy Systems, 24(1).

Calheiros, R. N., Ranjan, R., Beloglazov, A., De Rose,

C. A., and Buyya, R. (2011). Cloudsim: a toolkit for

modeling and simulation of cloud computing environ-

ments and evaluation of resource provisioning algo-

rithms. Software: Practice and experience, 41(1):23–

50.

Campisi, G., De Baets, B., Gambarelli, L., Muzzioli, S.,

et al. (2022). Forecasting returns in the us mar-

ket through fuzzy rule-based classiﬁcation systems.

DEMB WORKING PAPER SERIES.

Cord

on, O., del Jes

us, M. J., and Herrera, F. (1998). Ana-

lyzing the reasoning mechanisms in fuzzy rule based

classiﬁcation systems. Mathware and Soft Computing,

5(2-3):321–332.

Cord

on, O., Del Jesus, M. J., and Herrera, F. (1999). A pro-

posal on reasoning methods in fuzzy rule-based clas-

siﬁcation systems. International Journal of Approxi-

mate Reasoning, 20(1):21–45.

Czmil, A. (2023). Comparative study of fuzzy rule-based

classiﬁers for medical applications. Sensors, 23(2).

Ferdaus, M. H., Murshed, M., Calheiros, R. N., and Buyya,

R. (2014). Virtual machine consolidation in cloud data

centers using aco metaheuristic. In European confer-

ence on parallel processing, pages 306–317. Springer.

Gourisaria, M. K., Samanta, A., Saha, A., Patra, S. S., and

Khilar, P. M. (2020). An extensive review on cloud

computing. Data Engineering and Communication

Technology, pages 53–78.

He, T. and Buyya, R. (2023). A taxonomy of live migra-

tion management in cloud computing. ACM Comput.

Surv., 56(3).

uhn, J. and H

ullermeier, E. (2009). Furia: an algorithm

for unordered fuzzy rule induction. Data Mining and

Knowledge Discovery, 19:293–319.

Jumnal, A. and Kumar, S. D. (2021). Optimal vm placement

approach using fuzzy reinforcement learning for cloud

data centers. In 2021 Third International Conference

on Intelligent Communication Technologies and Vir-

tual Mobile Networks (ICICV). IEEE.

Lucca, G., Sanz, J. A., Dimuro, G. P., Bedregal, B., and

Bustince, H. (2020). A proposal for tuning the α

parameter in c α c-integrals for application in fuzzy

rule-based classiﬁcation systems. Natural Computing,

19(3):533–546.

Lughofer, E. (2022). Evolving fuzzy and neuro-fuzzy sys-

tems: Fundamentals, stability, explainability, useabil-

ity, and applications. In Handbook on Computer

Learning and Intelligence: Volume 2: Deep Learn-

ing, Intelligent Control and Evolutionary Computa-

tion, pages 133–234. World Scientiﬁc.

Mittal, M., Balas, V. E., Goyal, L. M., and Kumar, R.

(2019). Big data processing using spark in cloud.

Springer.

Mongia, V. and Sharma, A. (2021). Performance and

resource-aware virtual machine selection using fuzzy

in cloud environment. In Progress in Advanced Com-

puting and Intelligent Engineering: Proceedings of

ICACIE 2020, pages 413–426. Springer.

Moura, B. M., Schneider, G. B., Yamin, A. C., Santos, H.,

Reiser, R. H., and Bedregal, B. (2022). Interval-valued

fuzzy logic approach for overloaded hosts in consoli-

dation of virtual machines in cloud computing. Fuzzy

Sets and Systems, 446:144–166.

Nathani, A., Chaudhary, S., and Somani, G. (2012). Policy

based resource allocation in iaas cloud. Future Gen-

eration Computer Systems, 28(1):94–103.

Negi, S., Rauthan, M. M. S., Vaisla, K. S., and Panwar, N.

(2021). Cmodlb: an efﬁcient load balancing approach

in cloud computing environment. The Journal of Su-

percomputing, 77.

Pudil, P., Novovi

cov

a, J., and Kittler, J. (1994). Floating

search methods in feature selection. Pattern Recogni-

tion Letters, 15(11):1119–1125.

Rozehkhani, S. M. and Mahan, F. (2022). Vm consolida-

tion improvement approach using heuristics granular

rules in cloud computing environment. Information

Sciences, 596.

Samantaray, S., El-Arroudi, K., Joos, G., and Kamwa, I.

(2010). A fuzzy rule-based approach for islanding de-

tection in distributed generation. IEEE transactions

on power delivery, 25(3):1427–1433.

Sambuc, R. (1975). Function φ-ﬂous, application a laiide

au diagnostic en pathologie thyroidienne. These de

Doctorat en Medicine, Univ. Marseille.

Sanz, J., Sesma-Sara, M., and Bustince, H. (2021). A fuzzy

association rule-based classiﬁer for imbalanced clas-

siﬁcation problems. Information Sciences, 577:265–

279.

Sanz, J. A., Fern

andez, A., Bustince, H., and Herrera, F.

(2013). Ivturs: A linguistic fuzzy rule-based classiﬁ-

cation system based on a new interval-valued fuzzy

reasoning method with tuning and rule selection.

IEEE Transactions on Fuzzy Systems, 21(3):399–411.

Shehabi, A., Smith, S., Sartor, D., Brown, R., Herrlin, M.,

Koomey, J., Masanet, E., Horner, N., Azevedo, I., and

Lintner, W. (2016). United states data center energy

usage report.

Sowrirajan, R. (2022). A literature based study on cyber

security vulnerabilities. International Journal of In-

novative Technology and Research, 10:10138–10141.

Triguero, I., Gonz

alez, S., Moyano, J. M., Garc

ıa L

opez,

S., Alcal

a Fern

andez, J., Luengo Mart

ın, J.,

Fern

andez Hilario, A. L., Jes

us D

ıaz, M. J. d.,

anchez, L., Herrera Triguero, F., et al. (2017). Keel

3.0: an open source software for multi-stage analysis

in data mining. International Journal of Computa-

tional Intelligence Systems, 10:1238–1249.

Zadeh, L. A. (1965). Fuzzy sets. Information and control,

8(3):338–353.

Exploratory Data Analysis in Cloud Computing Environments for Server Consolidation via Fuzzy Classiﬁcation Models

643