Advances in Intelligent Systems and Computing 942

Ana Maria MadureiraAjith AbrahamNiketa GandhiCatarina SilvaMário Antunes Editors

Proceedings of the Tenth International Conference on Soft Computing and Pattern Recognition (SoCPaR 2018)

Advances in Intelligent Systems and Computing

Volume 942

Series Editor

Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences,Warsaw, Poland

Advisory Editors

Nikhil R. Pal, Indian Statistical Institute, Kolkata, IndiaRafael Bello Perez, Faculty of Mathematics, Physics and Computing,Universidad Central de Las Villas, Santa Clara, CubaEmilio S. Corchado, University of Salamanca, Salamanca, SpainHani Hagras, Electronic Engineering, University of Essex, Colchester, UKLászló T. Kóczy, Department of Automation, Széchenyi István University,Gyor, HungaryVladik Kreinovich, Department of Computer Science, University of Texasat El Paso, El Paso, TX, USAChin-Teng Lin, Department of Electrical Engineering, National ChiaoTung University, Hsinchu, TaiwanJie Lu, Faculty of Engineering and Information Technology,University of Technology Sydney, Sydney, NSW, AustraliaPatricia Melin, Graduate Program of Computer Science, Tijuana Instituteof Technology, Tijuana, MexicoNadia Nedjah, Department of Electronics Engineering, University of Rio de Janeiro,Rio de Janeiro, BrazilNgoc Thanh Nguyen, Faculty of Computer Science and Management,Wrocław University of Technology, Wrocław, PolandJun Wang, Department of Mechanical and Automation Engineering,The Chinese University of Hong Kong, Shatin, Hong Kong

The series “Advances in Intelligent Systems and Computing” contains publicationson theory, applications, and design methods of Intelligent Systems and IntelligentComputing. Virtually all disciplines such as engineering, natural sciences, computerand information science, ICT, economics, business, e-commerce, environment,healthcare, life science are covered. The list of topics spans all the areas of modernintelligent systems and computing such as: computational intelligence, soft comput-ing including neural networks, fuzzy systems, evolutionary computing and the fusionof these paradigms, social intelligence, ambient intelligence, computational neuro-science, artificial life, virtual worlds and society, cognitive science and systems,Perception and Vision, DNA and immune based systems, self-organizing andadaptive systems, e-Learning and teaching, human-centered and human-centriccomputing, recommender systems, intelligent control, robotics and mechatronicsincluding human-machine teaming, knowledge-based paradigms, learning para-digms, machine ethics, intelligent data analysis, knowledge management, intelligentagents, intelligent decision making and support, intelligent network security, trustmanagement, interactive entertainment, Web intelligence and multimedia.

The publications within “Advances in Intelligent Systems and Computing” areprimarily proceedings of important conferences, symposia and congresses. Theycover significant recent developments in the field, both of a foundational andapplicable character. An important characteristic feature of the series is the shortpublication time and world-wide distribution. This permits a rapid and broaddissemination of research results.

** Indexing: The books of this series are submitted to ISI Proceedings,EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink **

More information about this series at http://www.springer.com/series/11156

Ana Maria Madureira • Ajith Abraham •

Niketa Gandhi • Catarina Silva •

Mário AntunesEditors

Proceedings of the TenthInternational Conferenceon Soft Computingand Pattern Recognition(SoCPaR 2018)

123

EditorsAna Maria MadureiraSchool of EngineeringInstituto Superior de Engenharia (ISEP/IPP)Porto, Portugal

Ajith AbrahamMachine Intelligence Research Labs (MIR)Auburn, WA, USA

Niketa GandhiMachine Intelligence Research Labs (MIRLabs)Auburn, WA, USA

Catarina SilvaPolitécnico de LeiriaLeiria, Portugal

Mário AntunesPolitécnico de LeiriaLeiria, Portugal

ISSN 2194-5357 ISSN 2194-5365 (electronic)Advances in Intelligent Systems and ComputingISBN 978-3-030-17064-6 ISBN 978-3-030-17065-3 (eBook)https://doi.org/10.1007/978-3-030-17065-3

Library of Congress Control Number: 2019936516

© Springer Nature Switzerland AG 2020This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exempt fromthe relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, expressed or implied, with respect to the material containedherein or for any errors or omissions that may have been made. The publisher remains neutral with regardto jurisdictional claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AGThe registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Welcome to Porto, Portugal, and to the tenth International Conference on SoftComputing and Pattern Recognition (SoCPaR 2018) and the fourteenthInternational Conference on Information Assurance and Security (IAS 2018) held atInstituto Superior de Engenharia do Porto (ISEP) during December 13–15, 2018.

SoCPaR 2018 is organized to bring together worldwide leading researchers andpractitioners interested in advancing the state of the art in soft computing andpattern recognition, for exchanging knowledge that encompasses a broad range ofdisciplines among various distinct communities. The themes for this conference arethus focused on “Innovating and Inspiring Soft Computing and Intelligent PatternRecognition.” The conference is expected to provide an opportunity for theresearchers to meet and discuss the latest solutions, scientific results, and methodsin solving intriguing problems in the fields of soft computing and pattern recog-nition. SoCPaR 2018 received submissions from 16 countries, and each paper wasreviewed by at least five reviewers in a standard peer-review process. Based on therecommendation by five independent referees, finally 22 papers were accepted forthe conference (acceptance rate of 47%).

Information assurance and security have become an important research issue inthe networked and distributed information sharing environments. Finding effectiveways to protect information systems, networks and sensitive data within the criticalinformation infrastructure is challenging even with the most advanced technologyand trained professionals. IAS 2018 aims to bring together researchers, practi-tioners, developers, and policy makers involved in multiple disciplines of infor-mation security and assurance to exchange ideas and to learn the latest developmentin this important field. The conference provided an opportunity for the researchersto meet and discuss the latest solutions, scientific results, and methods in solvingintriguing problems in the fields of IAS. IAS 2018 received submissions from 12countries, and each paper was reviewed by at least five reviewers in a standardpeer-review process. Based on the recommendation by five independent referees,finally 16 papers were accepted for the conference (acceptance rate of 45%).

v

Conference proceedings are published by Springer Verlag, Advances inIntelligent Systems and Computing Series. Many people have collaborated andworked hard to produce this year successful SoCPaR-IAS 2018 conference. Firstand foremost, we would like to thank all the authors for submitting their papers tothe conference, for their presentations and discussions during the conference. Ourthanks to program committee members and reviewers, who carried out the mostdifficult work by carefully evaluating the submitted papers. We are grateful to ourthree plenary speakers:

* Petia Georgieva, University of Aveiro, Portugal* J. A. Tenreiro Machado, Polytechnic of Porto, Portugal* Henrique M. Dinis Santos, University of Minho, Portugal

Our special thanks to the Springer Publication team for the wonderful supportfor the publication of these proceedings. Enjoy reading!

Ana Maria MadureiraAjith AbrahamGeneral Chairs

Catarina SilvaMário AntunesOscar Castillo

Simone LudwigProgram Chairs

vi Preface

Organization

General Chairs

Ana Maria Madureira Instituto Superior de Engenharia do Porto,Portugal

Ajith Abraham Machine Intelligence Research Labs (MIR Labs),USA

Program Chairs

Catarina Silva Politécnico de Leiria, PortugalMário Antunes Politécnico de Leiria, PortugalOscar Castillo Tijuana Institute Technology, MexicoSimone Ludwig North Dakota State University, USA

Advisory Board Members

Albert Zomaya University of Sydney, AustraliaAndre Ponce de Leon F.

de CarvalhoUniversity of Sao Paulo at Sao Carlos, Brazil

Bruno Apolloni University of Milan, ItalyImre J. Rudas Óbuda University, HungaryJanusz Kacprzyk Polish Academy of Sciences, PolandMarina Gavrilova University of Calgary, CanadaPatrick Siarry Université Paris-Est Créteil, FranceRonald Yager Iona College, USASalah Al-Sharhan Gulf University for Science and Technology,

Kuwait

vii

Sebastian Ventura University of Cordoba, SpainVincenzo Piuri Universita’ degli Studi di Milano, ItalyFrancisco Herrera University of Granada, SpainSankar Kumar Pal ISI, Kolkota, India

Publication Chairs

Niketa Gandhi Machine Intelligence Research Labs (MIR Labs),USA

Azah Kamilah Muda Universiti Teknikal Malaysia Melaka, Malaysia

Web Services

Kun Ma Jinan University, China

Publicity Committee

Bruno Cunha Instituto Superior de Engenharia do Porto,Portugal

Diogo Braga Instituto Superior de Engenharia do Porto,Portugal

Santoso Wibowo CQUniversity Melbourne, AustraliaNesrine Baklouti University of Sfax, TunisiaIsabel Jesus Institute of Engineering of Porto, PortugalMarjana Prifti Skenduli University of New York, Tirana

Local Organizing Committee

Ana Maria Madureira Instituto Superior de Engenharia do Porto,Portugal

Diogo Braga Instituto Superior de Engenharia do Porto,Portugal

Duarte Coelho Instituto Superior de Engenharia do Porto,Portugal

André Santos Instituto Superior de Engenharia do Porto,Portugal

viii Organization

Judite Ferreira Instituto Superior de Engenharia do Porto,Portugal

Luis Coelho Instituto Superior de Engenharia do Porto,Portugal

Isabel Sampaio Instituto Superior de Engenharia do Porto,Portugal

Ricardo Almeida Instituto Superior de Engenharia do Porto,Portugal

Marina Sousa Instituto Superior de Engenharia do Porto,Portugal

Technical Program Committee

Ahmad Samer Wazan Paul Sabatier University, FranceA. Galicia Pablo de Olavide University, SpainAkira Asano Kansai University, JapanAlessio Merlo DIBRIS, University of Genoa, ItalyAlberto Cano University of Córdoba, SpainAlberto Fernández University of Granada, SpainAlicia Troncoso Universidad Pablo de Olavide, SpainAmparo Fuster-Sabater Institute of Physical and Information

Technologies (CSIC), SpainAna Madureira Instituto Superior de Engenharia do Porto,

PortugalAngel Arroyo UBU, SpainArash Habibi Lashkari University of New Brunswick (UNB), CanadaAndries Engelbrecht University of Pretoria, South AfricaAntonio Bahamonde Universidad de Oviedo, Gijón, Asturias, SpainArun Kumar Sangaiah Vellore Institute of Technology, IndiaAswani Kumar Cherukuri Vellore Institute of Technology, IndiaAtta Rahman University of Dammam, Dammam, Saudi ArabiaAzah Muda UTeM, MalaysiaCandelaria Hernández-Goya Universidad de La Laguna, SpainCarlos Pereira ISEC, PortugalChian C. Ho National Yunlin University of Science

and Technology, TaiwanClay Palmeira Francois Rabelais University of Tours, FranceConstantino Malagón Nebrija University, SpainChristian Veenhuis HELLA Aglaia Mobile Vision GmbH, GermanyCorrado Mencar University of Bari “A. Moro,” ItalyDaniela Zaharie West University of Timisoara, RomaniaDonato Impedovo Dipartimento di Informatica, UNIBA, Italy

Organization ix

Dilip Pratihar Federal University of Rio Grande do Norte,Brazil

Eiji Uchino Yamaguchi University, JapanElizabeth Goldbarg Federal University of Rio Grande do Norte,

BrazilFernando Tricas Universidad de Zaragoza, SpainFicco Massimo Second University of Naples (SUN), ItalyFrancisco Valera Universidad Carlos III de Madrid, SpainFrancisco Chicano Universidad de Málaga, SpainGabriel López University of Murcia, SpainGustavo Isaza University of Caldas, ColombiaGregorio Sainz-Palmero Universidad de Valladolid, SpainIlkka Havukkala IPONZ, New ZealandIntan Ermahani A. Jalil Universiti Teknikal Malaysia Melaka (UTeM),

MalaysiaIsaac Chairez Instituto Politécnico Nacional, MexicoIsabel S. Jesus Institute of Engineering of Porto, PortugalJoan Borrell Universitat Autònoma de Barcelona, SpainJoão Paulo Magalhaes ESTGF, Porto Polytechnic Institute, PortugalJose Luis Imana Universidad Politécnica de Madrid, SpainJose M. Molina Universidad Carlos III de Madrid, SpainJose Vicent Universidad de Alicante, SpainJose-Luis Ferrer-Gomila University of the Balearic Islands, SpainJuan Jesús Barbarán University of Granada, SpainJuan Pedro Hecht University of Buenos Aires - FCE/FCEyN/FI,

ArgentinaJung-San Lee Feng Chia University, TaiwanJerry Chun-Wei Lin Western Norway University of Applied Sciences

(HVL), Bergen, NorwayJerzy Grzymala-Busse University of Kansas, USAJoana Costa CISUC, IPLeiria, PortugalJosé Everardo Bessa Maia State University of Ceará, BrazilJosé F. Torres Pablo de Olavide University, SpainJosé Raúl Romero University of Cordoba, SpainJose Santos University of A Coruña, SpainJose Tenreiro Machado ISEP, PortugalJoseph Alexander Brown Innopolis University, CanadaJuan A. Nepomuceno University of Seville, SpainKazumi Nakamatsu University of Hyogo, JapanKin Keung Lai International Business School, Shaanxi Normal

University, Xian, ChinaLeandro Maciel Almeida Federal University of Pernambuco, BrazilLin Wang Jinan University, ChinaLeocadio G. Casado University of Almeria, SpainManuel Grana University of the Basque Country, Spain

x Organization

Miguel Frade Politécnico de Leiria, PortugalMohd Faizal Abdollah University Technical Malaysia Melaka, MalaysiaM. C. Nicoletti FACCAMP and UFSCar, BrazilM. J. Ramírez Universitat Politècnica de València, SpainManuel Grana University of the Basque Country, SpainMaria Ganzha Warsaw University of Technology, PolandMario Giovanni C. A. Cimino University of Pisa, ItalyMartin Lukac Nazarbayev University, KazakhstanMichal Wozniak Wroclaw University of Technology, PolandMohammad Shojafar Sapienza University of Rome, ItalyNiketa Gandhi Machine Intelligence Research Labs (MIR Labs),

USAOscar Gabriel Reyes Pupo UCO, SpainPatrick Siarry Université Paris-Est Créteil, FrancePedro Gago Politécnico de Leiria, PortugalPedro Gonzalez Universidad de Jaén, SpainPrabukumar Manoharan Vellore Institute of Technology, IndiaRamon Rizo Universidad de Alicante, SpainRolf Oppliger eSECURITY Technologies, SwitzerlandRomain Laborde IRIT/SIERA, FranceRosaura Palma-Orozco CINVESTAV - IPN, MexicoRadu-Emil Precup Politehnica University of Timisoara, RomaniaRicardo Tanscheit PUC-Rio, BrazilSalvador Alcaraz Miguel Hernandez University, SpainSalvatore Venticinque Seconda Università di Napoli, ItalySorin Stratulat Université de Lorraine, Metz, FranceSye Loong Keoh University of Glasgow, SingaporeSabri Pllana Linnaeus University, SwedenSimone Ludwig North Dakota State University, USAStefano Cagnoni University of Parma, ItalySylvain Piechowiak LAMIH, University of Valenciennes, FranceThomas Hanne University of Applied Sciences Northwestern

Switzerland, SwitzerlandUmberto Villano University of Sannio, ItalyVarun Ojha Swiss Federal Institute of Technology,

SwitzerlandVictor Manuel Rivas Santos University of Jaen, SpainWenjian Luo University of Science and Technology of China,

China

Organization xi

Contents

Shaping the Music Perception of an Automatic Music Composition:An Empirical Approach for Modelling Music Expressiveness . . . . . . . . 1Michele Della Ventura

Diverse Ranking Approach in MCDM Based on TrapezoidalIntuitionistic Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Zamali Tarmudi and Norzanah Abd Rahman

Decision Tree and MCDA Under Fuzziness to Support E-CustomerSatisfaction Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Houda Zaim, Mohammed Ramdani, and Adil Haddi

Search Convenience and Access Convenience: The Difference BetweenWebsite Shopping and Mobile Shopping . . . . . . . . . . . . . . . . . . . . . . . . 33Ibrahim Almarashdeh, Kamal Eldin Eldaw, Mutasem AlSmadi,Usama Badawi, Firas Haddad, Osama Ahmed Abdelkader, Ghaith Jaradat,Ayman Alkhaldi, and Yousef Qawqzeh

Automatic Classification and Segmentation of Low-Grade Gliomasin Magnetic Resonance Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Marta Barbosa, Pedro Moreira, Rogério Ribeiro, and Luis Coelho

Enhancing Ensemble Prediction Accuracy of Breast CancerSurvivability and Diabetes Diagnostic Using Optimized EKF-RBFNTrained Prototypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Vincent Adegoke, Daqing Chen, Ebad Banissi, and Safia Barsikzai

Improving Audiovisual Content Annotation Througha Semi-automated Process Based on Deep Learning . . . . . . . . . . . . . . . 66Luís Vilaça, Paula Viana, Pedro Carvalho, and Teresa Andrade

xiii

Subject Identification Based on Gait Using a RGB-D Camera . . . . . . . . 76Ana Patrícia Rocha, José Maria Fernandes,Hugo Miguel Pereira Choupina, Maria do Carmo Vilas-Boas,and João Paulo Silva Cunha

Leakage Detection of a Boiler Tube Using a Genetic Algorithm-likeMethod and Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . . . 86Young-Hun Kim, Jaeyoung Kim, and Jong-Myon Kim

Sentiment Analysis on Tweets for Trains Using Machine Learning . . . . 94Sachin Kumar and Marina I. Nezhurina

A Genetic Algorithm for Superior Solution Set Search Problem . . . . . . 105Ryu Fukushima, Kenichi Tamura, Junichi Tsuchiya,and Keiichiro Yasuda

An Intelligent Tool for Detection of Phishing Messages . . . . . . . . . . . . . 116Marcos Pires and Petia Georgieva

Discrete Wavelet Transform Application in Variable DisplacementPumps Condition Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Molham Chikhalsouk, Balasubramanian Esakki, Khalid Zhouri,and Yassin Nmir

Characterizing Parkinson’s Disease from Speech SamplesUsing Deep Structured Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137Lígia Sousa, Diogo Braga, Ana Madureira, Luis Coelho,and Francesco Renna

Combinatorial Optimization Method Considering Distancein Scheduling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147Yuta Obinata, Kenichi Tamura, Junichi Tsuchiya, and Keiichiro Yasuda

An Improved Gas Classification Technique Using New Featuresand Support Vector Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Se-Jong Kang, Jae-Young Kim, In-Kyu Jeong, M. M. Manjurul Islam,Kichang Im, and Jong-Myon Kim

Superior Relation Based Firefly Algorithm in SuperiorSolution Set Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Hongran Wang, Kenichi Tamura, Junichi Tsuchiya,and Keiichiro Yasuda

Learning in Twitter Streams with 280 Character Tweets . . . . . . . . . . . . 177Joana Costa, Catarina Silva, and Bernardete Ribeiro

Retweet Predictive Model for Predicting the Popularity of Tweets . . . . . 185Nelson Oliveira, Joana Costa, Catarina Silva, and Bernardete Ribeiro

xiv Contents

Handcrafted Descriptors-Based Effective Framework for Off-lineText-Independent Writer Identification . . . . . . . . . . . . . . . . . . . . . . . . . 194Abderrazak Chahi, Youssef El Merabet, Yassine Ruichek,and Raja Touahni

Server Load Prediction on Wikipedia Traffic: Influenceof Granularity and Time Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207Cláudio A. D. Silva, Carlos Grilo, and Catarina Silva

Evolutionary Genes Algorithm to Path Planning Problems . . . . . . . . . . 217Paulo Salgado and Paulo Afonso

An Efficient and Secure Forward Error Correcting Schemefor DNA Data Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226Anouar Yatribi, Mostafa Belkasmi, and Fouad Ayoub

A Blockchain-Based Scheme for Access Controlin e-Health Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238João Pedro Dias, Hugo Sereno Ferreira, and Ângelo Martins

Blockchain-Based PKI for Crowdsourced IoT Sensor Information . . . . 248Guilherme Vieira Pinto, João Pedro Dias, and Hugo Sereno Ferreira

The Design of a Cloud Forensics Middleware System Baseon Memory Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258Shumian Yang, Lianhai Wang, Dawei Zhao, Guangqi Liu,and Shuhui Zhang

Privacy Enhancement of Telecom Processes Interactingwith Charging Data Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268Siham Arfaoui, Abdelhamid Belmekki, and Abdellatif Mezrioui

Warning of Affected Users About an Identity Leak . . . . . . . . . . . . . . . . 278Timo Malderle, Matthias Wübbeling, Sven Knauer, and Michael Meier

Network Security Evaluation and Training Based on Real WorldScenarios of Vulnerabilities Detected in Portuguese Municipalities’Network Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288Daniel José Franco, Rui Miguel Silva, Abdullah Muhammed,Omar Khasro Akram, and Andreia Graça

A Novel Concept of Firewall-Filtering Service Based on RulesTrust-Risk Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298Faouzi Jaïdi

A Survey of Blockchain Frameworks and Applications . . . . . . . . . . . . . 308Bruno Tavares, Filipe Figueiredo Correia, André Restivo,João Pascoal Faria, and Ademar Aguiar

Contents xv

Filtering Email Addresses, Credit Card Numbers and Searchingfor Bitcoin Artifacts with the Autopsy Digital Forensics Software . . . . . 318Patricio Domingues, Miguel Frade, and João Mota Parreira

A Survey on the Use of Data Points in IDS Research . . . . . . . . . . . . . . 329Heini Ahde, Sampsa Rauti, and Ville Leppanen

Cybersecurity and Digital Forensics – Course Developmentin a Higher Education Institution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338Mário Antunes and Carlos Rabadão

Model Driven Architectural Design of Information Security System . . . 349Ivan Gaidarski, Zlatogor Minchev, and Rumen Andreev

An Automated System for Criminal Police Reports Analysis . . . . . . . . . 360Gonçalo Carnaz, Vitor Beires Nogueira, Mário Antunes, and Nuno Ferreira

Detecting Internet-Scale Traffic Redirection AttacksUsing Latent Class Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370Ana Subtil, M. Rosário Oliveira, Rui Valadas, Antonio Pacheco,and Paulo Salvador

Passive Video Forgery Detection ConsideringSpatio-Temporal Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381Kazuhiro Kono, Takaaki Yoshida, Shoken Ohshiro,and Noboru Babaguchi

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

xvi Contents

Shaping the Music Perception of an AutomaticMusic Composition: An Empirical Approach

for Modelling Music Expressiveness

Michele Della Ventura(&)

Department of Technology, Music Academy “Studio Musica”,Via Andrea Gritti, 25, 31100 Treviso, Italymichele.dellaventura@tin.it

Abstract. Expressiveness is an important aspect of a music composition. Itbecomes fundamental in an automatic music composition process, a domainwhere the Artificial Intelligent Systems have shown great potential and interest.The research presented in this paper describes an empirical approach to giveexpressiveness to a tonal melody generated by computers, considering both thesymbolic music text and the relationships among the sounds of the musical text.The method adapts the musical expressive character to the musical text on thebase of the “harmonic function” carried by every single musical chord. Thearticle is intended to demonstrate the effectiveness of the method by applying itto some (tonal) musical pieces written in the 18th and 19th century. Futureimprovements of the method are discussed briefly at the end of the paper.

Keywords: Automatic music composition � Functional harmony �Music expressiveness

1 Introduction

Everyday many people listening to (live or recorded) music. But while listening tomusic, sounds have the ability to foster communication that goes beyond the use oflanguage, promoting the expression of emotions [1, 2]. The ways of musical imagi-nation are endless and it is in the process of interaction between imagination and soundevent that the expression takes shape losing its apparent “arbitrariness” and givingmeaning to the things heard. The expressivity is an important part of the music andwithout it the music would not attract people [3].

Artificial Intelligence (AI) is now present in many areas, but among these, the fieldof music is the area that has always attracted researchers and composers. As early as1950, composer Iannis Xenakis designed a system (GENDY: GENeral DYnamic) tocompose a piece of music using a computer [4].

In the past 20 years, some interesting papers have been published on the differentaspects of automatic music composition research. Consequently, the AI research areahas developed on other aspects of music such as “musical expressivity”. Approaches tothis problem were based on:

• probabilistic method [5],• statistical analysis [6, 7],

© Springer Nature Switzerland AG 2020A. M. Madureira et al. (Eds.): SoCPaR 2018, AISC 942, pp. 1–10, 2020.https://doi.org/10.1007/978-3-030-17065-3_1

• mathematical models [8],• analysis by synthesis [9, 10, 11].

They are usually empirical methods, which allow obtaining results expressed bynumbers, therefore easy to analyze. All these approaches have an algorithm created bya person who conceived a mathematical model able to seize the musical expressivenesselements of a performance.

Another interesting approach is the one based on the theory according to whichpeople acquire the affective aspects implicit in music, through a process of observationand imitation [12], that means based on inductive learning of the rules [9, 10, 11, 13]:instead of manually creating a model for the recognition of the elements related tomusical expressiveness, the computer must automatically discover these elementsthrough certain learning rules.

This research focuses on the problem of how to manage the absence of indicationsin the domain of music expressiveness. It has been created an algorithm able toinvestigate the musical expressiveness of a musical piece, by reading the score on itssymbolic level. Unlike the aforementioned studies that are based on the analysis of anexecution, the algorithm tries to define the musical expressiveness on the basis of amusical grammar which is reflected in the functional harmony. The algorithm createdfor such purpose has the task of reading a certain melody on its symbolic level (this iswhy scores in MIDI format were used, without any indication on dynamics); to identifythe harmonic structures (through a melody segmentation process) and the corre-sponding harmonic functions (see paragraph 3); finally, to render in graphic format adiagram related to the musical dynamics to apply to the melody.

The effectiveness of the method was tested by analysing tonal piano pieces, theresults of which were compared with the scores reviewed by important musicians.These results allow applying this method to the algorithms for the automatic generationof a tonal melody so as to render it pleasant and interesting.

This paper is structured as follows. Section 2 describes the theory of FunctionalHarmony. Section 3 describes the approach to consider the music score to model themusical expressiveness. We discuss the methods and initial results in Sect. 4. Finally,Sect. 5 presents some conclusions and indicates some future improvements of themethod.

2 Functional Harmony

Functional Harmony Theory tends to go beyond the sound event as it occurs, tointerpret what lies behind to what appears in a certain instant, to seize the meaning or“role” that it covers in relation to other events which precede it or follow it [14, 15, 16],i.e. the “function” that it performs within the context where it is inserted. With respectto the chord, functional theory tries to identify its harmonic function and the rela-tionship that it establishes with the preceding and with the following one [14]. When itcomes to an individual, isolated chord, we may define its structure (that is its

2 M. Della Ventura

disposition and the type of intervals1 starting from the bottom) (see Fig. 1) and identifyits inversion state (see Fig. 2) [15]; but we may not fully understand its meaning, whichessentially derives from the musical context where it is found.

Such context is temporally oriented [14, 16], in fact, except for the first and the lastsound, all the sounds are between other sounds which represent, respectively, theirpast and their future. Reference is made to sounds, before mentioning chords, in orderto underline that the latter are none other than temporary aggregates of notes on alinear motion, or rather a contrapuntal motion, and that to sign/write down/note a chord(see Fig. 3) actually corresponds to taking a snapshot in a directed flow [14, 15].

Fig. 1. Chord structure.

Fig. 2. State of a chord: (a) fundamental state, (b) first inversion, (c) second inversion.

Fig. 3. Contrapuntal motion and functional motion.

1 The interval between the various sounds is the distance separating a sound from another. Theclassification of an interval consists in the denomination (generic indication) and in the qualification(specific indication). The denomination corresponds to the number of degrees that the intervalincludes, calculated from the low one to the high one; it may be of a 2nd, a 3rd, 4th, 5th, and so on.; thequalification is deduced from the number of tones and semi-tones that the interval contains; it maybe: perfect (G), major (M), minor (m), augmented (A), diminished (d), more than augmented (A+),more than diminished (d+), exceeding (E), deficient (df).

Shaping the Music Perception of an Automatic Music Composition 3

According to functional theory, there are three harmonic functions, the tonic (T),the subdominant (S) and the dominant (D). Only two of these act dynamically “pushingforward” the musical discourse: the dominant and the subdominant [14]. These twofunctions express respectively the conduction of tension towards the tonic T andthe preparation of such conduction. The tonic, being a “static” function, is a mere restpoint, the end of the movement (Fig. 4).

The three harmonic functions of I, IV and V degree are called main because theyare linked by a relation based on the interval of the perfect 5th that separates thekeynotes of the three corresponding chords; the chords relating to the rest of degrees onthe scale are considered “representatives” of the I, IV and V degree (with which there isan affinity of the third - two sounds in common - because the 3rd is actually the intervalthat regulates the distance between the respective keynotes) and secondary harmonicfunctions rest with it (see Fig. 4) [14].

The identification of these harmonic functions allows the executant to have animage of the character of the piece so as to better define the field of dynamics.

This latter concept is represented by a sort of musical crescendo, understood not onlyin terms of intensity (i.e. an increase of the sound volume), but also as a change of timbre(i.e. a change of sound register, from low-pitch to high-pitch and the other way around).

3 Music Score Analysis

The identification of the harmonic functions, indispensable to describe the dynamics ofa score, is performed by an algorithm realized for the occasion.

Initially the algorithm has to read a score from a MIDI file (Musical InstrumentsDigital Interface). The MIDI protocol is a symbolic language of event-based messagesused to represent music. It permits to divide into levels the various voices of a melody,considering the pitch and the duration of each sound of the melody in numerical form.A monodic score may therefore be represented as a sequence Sm of N notes ni indexedon the basis of the appearance order i:

Sm ¼ ðniÞi2 0;N�1½ �

Fig. 4. Resolution tendency of the chords based on the harmonic function.

4 M. Della Ventura

A polyphonic score may be considered as the overlapping of two or more monodicsequences Sm1, Sm2, … which may be represented by a matrix Px,y

PðkÞ ¼

p1;1ðk) p1;2ðk) . . . p1;yðk)p2;1ðk) p2;2ðk) . . . p2;yðk)p3;1ðk) p3;2ðk) . . . p3;yðk)p4;1ðk) p4;2ðk) . . . p4;yðk). . . . . . . . . . . .px;1ðk) px;2ðk) . . . px;yðk)

0BBBBBB@

1CCCCCCA

where x represents the number of voices (or levels) and y the number of rhythmicmovements existing in the musical piece [17]. Figure 5 shows a polyphonic musicalsegment (4 voices or levels) and the corresponding matrix.

Every sound is identified by a number: the MIDI protocol takes into considerationthe piano keyboard and it assigns to the lowest note the value 1 and to every subsequentsound an increasing value (Fig. 6).

Every sound has its own duration which is defined considering the shortest durationexisting in the piece and calculating the other durations proportionally [18]. In theexample shown in Fig. 4 the shortest duration is represented by the eighth (�) whichassumes the value 1 and therefore the quarter (�) assumes the value 2.

Fig. 5. Score representation matrix.

Fig. 6. MIDI piano keyboard representation.

Shaping the Music Perception of an Automatic Music Composition 5

After reading the musical score, the algorithm proceeds with the recognition of thetonal system and therefore of the chords. At this point, for every single rhythmicmovement, the sounds that make up a chord are identified (keeping in mind that thesounds must be distant from each other by a third interval) and the sounds which areextraneous to the harmony must be eliminated (Fig. 7) [19].

Finally, the algorithm identifies for each chord the harmonic function (T, S, D)associated to it, so as to have for each movement a functional indication to be used forthe definition of the dynamics.

4 Obtained Results

Based on the above considerations, an algorithm was designed and developed. It is aprototype of a desktop computer application aimed at monitoring and supporting theanalysis of a musical text. The algorithm reads the initial musical notes to identify thetonal system; after that, it identifies the musical chords and defines the harmonicfunction for each one of them. Input parameters are not necessary for the elaboration.

The method may be applied only to tonal musical pieces. The initial tests werecarried out on a set of musical segments of various lengths, specifically selected, inorder to verify the ‘‘validity’’ of the analysis. Then, each analysis was compared withscores already reviewed by important musicians, in order to verify the validity of themethod.

The results of the analysis are indicated in an isometric graphic which compares theharmonic function of every single chord with the harmonic function of rest, expressedby T, which represents the chord of the reference tonal system and with respect towhich the comparisons and classifications may be made: otherwise, every single chordmay not provide any information. In an isometric graphic, if two musical chords havethe same functional harmony, the diagram will contain a column having only the colorof the corresponding information bracket. If the two functional harmonies are different,the color of the column changes, passing from the color of the preceding functional

Fig. 7. Simplification of the score by eliminating the notes which are extraneous to a harmony.

6 M. Della Ventura

harmony to the color of the current functional harmony. In this regard, Table 1 showsthe color associated with the three main functional harmonies (T, S and D), based onwhat is shown in Fig. 4. Every harmonic function gathers the various degrees together:(a) I, III and VI, (b) II and IV, (c) V and VII. At the same time, each degree wasidentified by a numeric value, which depends on the number of degrees contained in it:function T contains the degrees I, III and VI (therefore the values 1, 2 and 3), functionS contains the degrees IV and II (values 4 and 5) and, finally, function D contains thedegrees V and VII (values 6 and 7).

In Fig. 8 it is possible to see an example of analysis made up by the algorithm, withthe corresponding graphic analysis. In the upper part of the isometric graphic coloursare used to represent the harmonic functions of the single chords, while the lower partof the diagram shows only the colour of the functional chord of the Tonic chord (towhich the comparison is made).

Following the gradualness of the colour fad-out it is possible to create:

• a “crescendo”, in case the transition is from green (T) to orange (S) or to red (D);this effect is represented by the graphic symbol ˂ the length of which varies basedon the fade-out duration;

• a “diminuendo”, in case the transition goes from red (D) or orange (S) to green (T);this effect is represented by the graphic symbol > the length of which varies basedon the fade-out duration;

• an “accento” or “appoggiato”, in case a transition occurs in succession from T–D–T(green-red-green): the “accento” or “appoggiato” would be on the harmonic func-tion D (see Fig. 7, bar 3, second movement); this effect is represented by the graphicsymbol “-”.

On the basis of this information the algorithm then proposes a dynamic to apply tothe piece (see Fig. 8).

Table 1. Information value of every single chord.

T S D1 2 3 4 5 6 7I III VI II IV V VII

Shaping the Music Perception of an Automatic Music Composition 7

5 Conclusions and Discussion

This article presented an empirical method for shaping the music perception of anautomatic tonal music composition generated by computer. The model defined theexpressive musical terms analysing the harmonic structure of the musical piece. Theproposed features in terms of dynamics, derived from the functional harmony, gave agood performance compared with a human performance. Furthermore, the proposed

T T S S T S D T

T D T D T S S D T

Fig. 8. Brahms “Valzer” n.3 op.39: functional analysis.

8 M. Della Ventura

method observed both the musical grammar related to the succession of harmonies andthe musical phrase syntax. The computer played a growing role in the entire process,both in extracting the harmonic function from the symbolic music text, and in analysingand modelling the expressiveness of the musical piece.

Intelligent computational methods find many applications in music education,supporting teachers and students. These methods are able to support a learning processhelping students (with disability) advance their understanding of a complex phe-nomenon such as the expressive interpretation of a musical piece.

In other words, the method presented in this paper represents a tool to stimulate therecovery of not-fully-acquired abilities or as simple tool of consultation and support tothe explanation of the teacher.

A future study could concern the possibility of uniting the Harmonic FunctionalTheory and the Information Theory to quantify the information content of eachdetected harmonic function. On the basis of these values it would be possible to modifythe musical expressivity analysing the events that precede and follow a certain musicalchord (or harmonic function).

References

1. Scruton, R.: The Aestheics of Music, pp. 80–170. Clarendon Press, Oxford (1997)2. Bigand, E., Vieillard, S., Madurell, F., Marozeau, J., Dacquet, A.: Multidimensional scaling

of emotional responses to music: the effect of musical expertise and excerpts’ duration.Cogn. Emot. 19(8), 1113–1139 (2005)

3. Blood, A.J., Zatorre, R.J., Bermudez, P., Evans, A.C.: Emotional responses to pleasant andunpleasant music correlate with activity in paralimbic brain regions. Nat. Neurosci. 2(4),382–387 (1999)

4. Serra, M.: Stochastic composition and stochastic timbre: GENDY3 by Iannis Xenakis.Perspect. New Music 31(1), 236–257 (1993)

5. Moorer, J.A.: iMusic and computer composition. In: Schwanauer, S.M., Levitt, D.A. (eds.)Machine Models of Music, pp. 167–186. The MIT Press, Cambridge (1993)

6. Amatriain, X., Bonada, J., Loscos, A., Arcos, J., Verfaille, V.: Content-based transformation.J. New Music Res. 32(1), 95–114 (2003)

7. Bresin, R., Battel, G.U.: Articulation strategies in expressive piano performance analysis oflegato, staccato, and repeated notes in performances of the andante movement of Mozart’ssonata in g major (k 545). J. New Music Res. 29(3), 211–224 (2000)

8. Todd, N.: The dynamics of dynamics: a model of musical expression. J. Acoust. Soc. Am.91, 3540–3550 (1992)

9. Friberg, A.: A quantitative rule system for musical performance, Ph.D. thesis, KTH, Sweden(1995)

10. Grachten, M., Widmer, G.: Linear basis models for prediction and analysis of musicalexpression. J. New Music Res. 41(4), 311–322 (2012)

11. Rodà, A., Canazza, S., De Poli, G.: Clustering affective qualities of classical music: beyondthe valence arousal plane. IEEE Trans. Affect. Comput. 5(4), 364–376 (2014)

12. Dowling, W.J., Harwood, D.L.: Music Cognition. Academic, San Diego (1986)13. Lindgren, T., Bostrom, H.: Classification with intersecting rules. In: Proceedings of 13th

International Conference on Algorithmic Learning Theory. Springer (2002)14. de la Motte, D.: Manuale di armonia. Bärenreiter (1976)

Shaping the Music Perception of an Automatic Music Composition 9

15. Coltro, B.: Lezioni di armonia complementare. Zanibon (1979)16. Schonber, A.: Theory of Harmony. University of California Press, Berkeley (1983)17. Della Ventura, M.: Toward an analysis of polyphonic music in the textual symbolic

segmentation. In: Proceedings of the 2nd International Conference on Computer, DigitalCommunications and Computing (ICDCC 2013), Brasov, Romania (2013)

18. Della Ventura, M.: Rhythm analysis of the “Sonorous Continuum” and conjoint evaluationof the musical entropy. In: Proceedings of the 13th International Conference on Acoustics &Music: Theory & Applications (AMTA 2012), Iasi (Romania) (2012)

19. Della Ventura, M.: Automatic tonal music composition using functional harmony. In: SocialComputing, Behavioral - Cultural Modeling and Prediction. Springer (2015)

10 M. Della Ventura

Diverse Ranking Approach in MCDM Basedon Trapezoidal Intuitionistic Fuzzy Numbers

Zamali Tarmudi1(&) and Norzanah Abd Rahman2

1 Faculty of Computer and Mathematical Sciences,Universiti Teknologi MARA (Johor Branch),

KM12, Jalan Muar, 85000 Segamat, Johor, Malaysiazamalihj@sabah.uitm.edu.my

2 Faculty of Computer and Mathematical Sciences,Universiti Teknologi MARA (Sabah Branch),

Locked Bag 71, 88997 Kota Kinabalu, Sabah, Malaysia

Abstract. Intuitionistic fuzzy set (IFS) is a generalization of the fuzzy set thatis characterized by the membership and non-membership function. It is proventhat IFS improves the drawbacks in fuzzy set since it is designed to deal with theuncertainty aspects. In spite of this advantage, the selection of the rankingapproach is still one of the fundamental issues in IFS operations. Thus, thispaper intends to compare three ranking approaches of the trapezoidal intu-itionistic fuzzy numbers (TrIFN). The ranking approaches involved are;expected value-based approach, centroid-based approach, and score function-based approach. To achieve the objective, one numerical example in prioritizingthe alternatives using intuitionistic fuzzy multi-criteria decision making (IF-MCDM) are provided to illustrate the comparison of these ranking approaches.Based on the comparison, it was found that the alternatives MCDM problemscan be ranked easily in efficient and accurate manner.

Keywords: Intuitionistic fuzzy set � Trapezoidal intuitionistic fuzzy numbers �Multi-criteria decision-making � Ranking approach

1 Introduction

Intuitionistic fuzzy set (IFS) is one of the fuzzy set generalizations introduced byAtanassov in 1986. This IFS claims to be more precise in dealing with the uncertaintyaspects since it considers both membership and non-membership function. Ever sincethe introduction of Intuitionistic fuzzy numbers (IFN), a number of other types of IFNhave as well been introduced such as triangular IFN (TIFN), trapezoidal IFN (TrIFN),and interval-valued trapezoidal IFN. The development of the arithmetic operation ofand the ranking approach of the IFN has become one of the fundamental issues in fuzzyenvironment. For instance, Mitchell [1] adopted a statistical viewpoint and interpretedeach IFN as an ensemble of ordinary fuzzy numbers to define a fuzzy rank and acharacteristic vagueness factor of each IFN. Nayagam, Venkateshwari and Sivaraman[2] proposed new method of IF scoring that involved a hesitation for both membershipand non-membership function. This method was further developed and applied by

© Springer Nature Switzerland AG 2020A. M. Madureira et al. (Eds.): SoCPaR 2018, AISC 942, pp. 11–21, 2020.https://doi.org/10.1007/978-3-030-17065-3_2

Kakarontzas and Gerogiannis [3] to rank the web services. In 2010, Shen, Wang andFeng [4] introduced two ranking processes (i.e. based on probabilities and based onhesitation-probabilities) of IFN in MCDM. Biswas and De [5] continued by proposinga ranking technique based on probability function of the membership and non-membership function and applied it in solving linear bilevel programming.

Meanwhile, the studies on both TIFN and TrIFN’s ranking approach had receivedworldwide attention. Li, Nan and Zhang [6] introduced new ranking approach based onratio and ambiguity for TIFN. Their ranking approach was improved by Das and De [7,8] in terms of using the sum of value and ambiguity index to satisfy linear property. Byfocusing on the -cut and -cut of the membership and non-membership function, Rez-vani [9] also proposed similar approach. Likewise, Kumar and Kaur [10] claimed thattheir proposed ranking approach based on comparisons of fuzzy numbers and IFnumbers could produce IF optimal solution. Ranking approach based on magnitudeof membership and non-membership functions was introduced by Roseline andAmirtharaj [11]. As opposed to Nehi’s ranking approach based on characteristic valuesof membership and non-membership function for trapezoidal (triangular) IFN [12] andGrzegorzewski’s expected value for TrIFN [13], their method produced similar resultsto Nehi’s approach. In the same year, they also proposed a new ranking method basedon circumcenter of centroid of membership and non-membership function for TrIFN.This method was proven to provide the exact ordering and ranking of IFN in solvingdifferent fuzzy optimization problems.

In recent times, the ranking approach for TrIFN has been developed to producebetter solution. For instance, Zeng, Li and Yu [14] stated their proposed method to rankthe TrIFN using values and ambiguity was effective since it produced similar resultswith the existing method. Li and Yang [15] also proposed a ranking method based ondifference index of value-index to the ambiguity-index for TrIFN to satisfy the lin-earity. They extended this method to solve the MADM problems. Their proposedmethod was not dependent on the form or shape of its membership and non-membership functions, natural appealing interpretation, and possessed some goodlinearity properties. Keikha and Nehi [16] improved the arithmetic operation andranking based on centroid points of IFN since the outcomes were closer to the IFNreality. Prakash, Suresh, and Vengataasalam [17] also took advantage on centroidconcept to develop ranking approach of TIFN and TrIFN that claimed to be time-consuming, suitable for both TrIFN and TIFN, and flexible in ranking index of theirattitudinal analysis. Das and Guha [18] proposed a centroid point as a ranking methodfor TrIFN that showed some advantages such as reasonableness with human intuitionand consistent with other approach and ranking results, as well as flexible algorithmwhen incorporated into decision making process. Most recently, Velu et al. [19] pro-posed new ranking approach for TrIFN using eights different scores function namelyimprecise score, non-vague score, incomplete score, accuracy score, spread score, non-accuracy score, left area score and right area score. This proposed method improved theresults in MADM problems, fuzzy information systems, and artificial intelligence. Itwas also easy to understand and operationally easy to use.

Based on the literature, it shows that there are several improvements in selecting thesuitable ranking approach for IFN that can produce the best solutions. Thus, we intendto compare the ranking approaches of the trapezoidal intuitionistic fuzzy numbers

12 Z. Tarmudi and N. Abd Rahman

(TrIFN). The ranking approaches are; expected value-based approach, centroid-basedapproach, and score function-based approach. In order to achieve the objective, onenumerical example in prioritizing the alternatives using intuitionistic fuzzy multi-criteria decision making (MCDM) is provided to illustrate the comparison of theseranking approaches. The rest of this paper is organized as follows; following theintroduction in the first section, preliminaries of the IFS, IFN, and the rankingapproaches will be presented. Then, the weighted values of ranking approaches (i.e.centroid and score function) will be proposed according to the Ye’s weighted expectedvalue [20]. Based on these weighted values, one illustrative example is provided inSect. 4. Finally, conclusion on the comparison of these ranking approaches based onthe alternative ranking of trapezoidal IF-MCDM is presented.

2 Preliminaries

In this section, some basic definition and concept are introduced. These include IFS,IFN, and the ranking approaches.

2.1 Intuitionistic Fuzzy Set

An IF is a generalization of the fuzzy set that is characterized by both the degree ofmembership and non-membership.

Definition 2.1.1 [21]: Let a set X be fixed. An IFS, A in X is defined as an object ofthe A ¼ x; lAðxÞ; vAðxÞh ijx 2 Xf g, where the functions: lA : X ! ½0; 1� and vA : X !½0; 1� is the degree of membership and the degree of non-membership of the elementx 2 X, respectively, and for every x 2 X; 0� lAðxÞþ vAðxÞ� 1; x 2 X.

2.2 Intuitionistic Fuzzy Numbers

Definition 2.2.1 [22]: A trapezoidal Intuitionistic Fuzzy Number (TrIFN), A withparameters b1 � a1 � b2 � a2 � a3 � b3 � a4 � b4 is represented as A ¼a1; a2; a3; a4; b1; b2; b3; b4ð Þ in a real set of X. The membership and non-membershipare defined as follows:

lAðxÞ ¼

0 if x\a1x� a1a2 � a1

if a1 � x� a21 if a2 � x� a3x� a4a3 � a4

if a3 � x� a40 if a4\x

8>>>><>>>>:

vAðxÞ ¼

0 if x\b1x� b2b1 � b2

if b1 � x� b21 if b2 � x� b3x� b3b4 � b3

if b3 � x� b40 if b4\x

8>>>><>>>>:

ð1Þ

When a2 ¼ a3, it will change into triangular IFN.

Diverse Ranking Approach in MCDM Based on TrIFN 13

2.3 Expected Value-Based Approach

Definition 2.3.1 [13]: Let A ¼ a1; a2; a3; a4; b1; b2; b3; b4ð Þ be a TrIFN in X; X 2 <.Thus, when x� a1

a2 � a1; x� a4a3 � a4

; x� b2b1 � b2

; x� b3b4 � b3

; a1; a2; a3; a4; b1; b2; b3; b4 2 <The expected value can be calculated using the following formula:

EVðAÞ ¼ 18

a1 þ a2 þ a3 þ a4 þ b1 þ b2 þ b3 þ b4ð Þ ð2Þ

Theorem 2.3.1: Let �L and �U denote the quasi-order with respect to the lowerand upper horizon, respectively, based on the metric d1 (i.e. dp for p = 1). Then, thefollowing order of two TrIFNs, A;B 2 X can be derived:

i. A �L B , EVðAÞ�EVðBÞii. A �U B , EVðAÞ�EVðBÞ

2.4 Centroid-Based Approach

Definition 2.4.1 [17]: The centroid of a symmetric TrIFN, A ¼ a1; a2; a3; a4; b1;ðb2; b3; b4Þ are defined as follows:

~xlðAÞ ¼ 12

a23 þ a24 � a21 � a22 � a1a2 þ a3a4a4 þ a3 � a2 � a1

� �

~xvðAÞ ¼ 13

2b24 � 2b21 þ 2b22 þ 2b23 þ b1b2 � b3b4b3 þ b4 � b1 � b2

� �

~ylðAÞ ¼ 13

a1 þ 2a2 � 2a3 � a4a1 þ a2 � a3 � a4

� �

~yvðAÞ ¼ 13

2b1 þ b2 � b3 � 2b4b1 þ b2 � b3 � b4

� �

Definition 2.4.2: The ranking function of TrIFN, A ¼ a1; a2; a3; a4; b1; b2; b3; b4ð Þ formembership and non-membership function are defined as follows:

RðAÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12

~xlðAÞ � ~ylðAÞ� �2 þ ~xmðAÞ � ~ymðAÞ½ �2

� ��rð3Þ

Consider that there are two TrIFNs, A;B 2 X; X 2 < can be defined as follows:

i. R Al

[R Bl

iff A\Bii. R Al

\R Bl

iff A � B

iii. R Al ¼ R Bl

and R Avð Þ ¼ R Bvð Þ iff A B

iv. R Al

¼ R Bl

and � R Amð Þ[ � R Bvð Þ iff A\B

v. R Al ¼ R Bl

and � R Avð Þ\� R BVð Þ iff A\B

14 Z. Tarmudi and N. Abd Rahman