Table Of ContentCOMPUTATIONAL MATHEMATICS AND ANALYSIS
D -M
ECISION AKING WITH
N S
EUTROSOPHIC ET
T A
HEORY AND PPLICATIONS IN
K M
NOWLEDGE ANAGEMENT
No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or
by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no
expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No
liability is assumed for incidental or consequential damages in connection with or arising out of information
contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in
rendering legal, medical or any other professional services.
C M
OMPUTATIONAL ATHEMATICS
A
AND NALYSIS
Additional books and e-books in this series can be found on Nova’s website
under the Series tab.
COMPUTATIONAL MATHEMATICS AND ANALYSIS
D -M
ECISION AKING WITH
N S
EUTROSOPHIC ET
T A
HEORY AND PPLICATIONS IN
K M
NOWLEDGE ANAGEMENT
HARISH GARG
EDITOR
Copyright © 2021 by Nova Science Publishers, Inc.
All rights reserved. No part of this book may be reproduced, stored in a retrieval system or
transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical
photocopying, recording or otherwise without the written permission of the Publisher.
We have partnered with Copyright Clearance Center to make it easy for you to obtain permissions
to reuse content from this publication. Simply navigate to this publication’s page on Nova’s
website and locate the “Get Permission” button below the title description. This button is linked
directly to the title’s permission page on copyright.com. Alternatively, you can visit
copyright.com and search by title, ISBN, or ISSN.
For further questions about using the service on copyright.com, please contact:
Copyright Clearance Center
Phone: +1-(978) 750-8400 Fax: +1-(978) 750-4470 E-mail: [email protected].
NOTICE TO THE READER
The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or
implied warranty of any kind and assumes no responsibility for any errors or omissions. No
liability is assumed for incidental or consequential damages in connection with or arising out of
information contained in this book. The Publisher shall not be liable for any special,
consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or
reliance upon, this material. Any parts of this book based on government reports are so indicated
and copyright is claimed for those parts to the extent applicable to compilations of such works.
Independent verification should be sought for any data, advice or recommendations contained in
this book. In addition, no responsibility is assumed by the Publisher for any injury and/or damage
to persons or property arising from any methods, products, instructions, ideas or otherwise
contained in this publication.
This publication is designed to provide accurate and authoritative information with regard to the
subject matter covered herein. It is sold with the clear understanding that the Publisher is not
engaged in rendering legal or any other professional services. If legal or any other expert
assistance is required, the services of a competent person should be sought. FROM A
DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE
AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS.
Additional color graphics may be available in the e-book version of this book.
Library of Congress Cataloging-in-Publication Data
ISBN: (cid:28)(cid:26)(cid:27)(cid:16)(cid:20)(cid:16)(cid:24)(cid:22)(cid:25)(cid:20)(cid:28)(cid:16)(cid:24)(cid:21)(cid:21)(cid:16)(cid:23)(cid:3)(cid:11)(cid:72)(cid:37)(cid:82)(cid:82)(cid:78)(cid:12)
Published by Nova Science Publishers, Inc. † New York
CONTENTS
Preface vii
Section I: Mathematical Aspects of Neutrosophic Set 1
Chapter 1 Neutrosophic Set Theory and Engineering Applications: A Study 3
K. Bhargavi and B. Sathish Babu
Chapter 2 A New Type of Quasi Open Functions in
Neutrosophic Topological Environment 27
M. Parimala, C. Ozel, F. Smarandache and M. Karthika
Chapter 3 Accordance with Neutrosophic Logic?
A Multimoora Approach for Countries Worldwide 37
Willem K. M. Brauers
Chapter 4 Evaluation of Online Education Software under
Neutrosophic Environment 69
Fatma Kutlu Gündoğdu and Serhat Aydın
Chapter 5 A New Attribute Sampling Plan for
Assuring Weibull Distributed Lifetime using
Neutrosophic Statistical Interval Method 91
P. Jeyadurga and S. Balamurali
Section II: Decision Making Problems with Neutrosophic Set 111
Chapter 6 On Some Propositions of Boundary in
Interval Valued Neutrosophic Bitopological Space 113
Bhimraj Basumatary
vi Contents
Chapter 7 An Expected Value-Based Novel Similarity Measure for
Multi-Attribute Decision-Making Problems with
Single-Valued Trapezoidal Neutrosophic Numbers 133
Palash Dutta and Gourangajit Borah
Chapter 8 TrNN-ARAS Strategy for Multi-Attribute Group
Decision-Making (MAGDM) in Trapezoidal Neutrosophic
Number Environment with Unknown Weight 163
Rama Mallick and Surapati Pramanik
Chapter 9 An Application of Reduced Interval Neutrosophic Soft Matrix in
Medical Diagnosis 195
Somen Debnath
Chapter 10 Interval-Valued Neutrosophic N Soft Set and Intertemporal
Interval-Valued Neutrosophic N Soft Set to Assess the
Resilience of the Workers Amidst Covid-19 219
V. Chinnadurai and A. Bobin
Section III. Extension of the Neutrosophic Set 257
Chapter 11 2-Additive Choquet Cosine Similarity Measures for Simplified
Neutrosophic Sets and Applications to Medical Diagnosis 259
Ezgi Türkarslan, Murat Olgun, Mehmet Ünver
and Şeyhmus Yardimci
Chapter 12 Multi-Attribute Group Decision-Making Based on Uncertain
Linguistic Neutrosophic Sets and Power Hamy Mean Operator 283
Yuan Xu, Xiaopu Shang and Jun Wang
Chapter 13 An n-Dimensional Neutrosophic Linguistic Approach to
Poverty Analysis with an Empirical Study 331
D. Ajay, J. Aldring and S. Nivetha
Chapter 14 Multi-Granulation Single-Valued Neutrosophic Hesitant
Fuzzy Rough Sets 353
Tahir Mahmood and Zeeshan Ali
About the Editor 377
Contributors 379
Index 387
PREFACE
With the complexity of the socio-economic environment, today's decision-making is
one of the most notable ventures, whose mission is to decide the best alternative under
the numerous known or unknown criteria. In cognition of things, people may not possess
a precise or sufficient level of knowledge of the problem domain and hence they usually
have some sort of uncertainties in their preferences over the objects. This will make the
performance of the cognitive in terms of three-ways model namely acceptation, rejection,
indeterminacy which is falls under the neutrosophic set theory, an extension of the fuzzy
set theory. Now in days, many new extensions of the ordinary neutrosophic set are
proposed and they are expected to be competitive with the other extensions in the future.
In this book, a new extension of the fuzzy sets, entitled as Neutrosophic sets, is
introduced by eminent researchers with several applications. In this set, the performance
of the cognitive in terms of fuzzy environment is considered with the help of degrees of
acceptation, rejection, indeterminacy.
This book consists of three parts. The first part involves five chapters presenting the
important mathematical aspects of the neutrosophic sets and its extensions. The second
part contains five chapters presenting contribution on the information measures and the
aggregation operators of neutrosophic sets and its extension which include neutrosophic
fuzzy decision-making methods and different applications to the real-life problems.
Finally, the last part contains four chapters on the theory of the interval-neutrosophic sets
and their applications to the decision-making process.
The first chapter in the first part of the book is to present a basic introduction to the
neutrosophic sets and also bring out the difference between the classical seta and
neutrosophic set. The application of the neutrosophic set over the different engineering
disciplines namely civil, aerospace and mechanical engineering are discussed. The
second chapter is to define the new type of the quasi open and closed functions in
neutrosophic topological space. The fundamental properties and its characterizations are
discussed in it. The third chapter considered the credit rating of the agencies different
from the point of view of neutrosophic theory and hence discusses the scenario with the
viii Harish Garg
help of the MULTIMOORA approach. In the fourth chapter, authors propose the
neutrosophic MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus Full
Multiplicative Form) method to evaluate online learning tools concerning some critical
factors which have an essential influence on student satisfaction. Comparative and
sensitivity analyses are also performed to show the validity of the methodology. The fifth
chapter introduces an acceptance sampling for assuring Weibull distributed lifetime of
the products using neutrosophic interval method. The probabilities corresponding to non-
failure, failure and indeterminate case are obtained under Weibull distribution.
The first chapter in the second part of the book is to present a concept on interval
valued neutrosophic bitopological space by defining an interval valued neutrosophic
interior, closure and relation between them. Also, author studied an interval valued
neutrosophic boundary and some of their propositions in interval valued bitopological
space. The second chapter presents a novel similarity measure with the single-valued
trapezoidal neutrosophic numbers (SVTNNs). The proposed measure involves
calculating the salient feature of expected value of a SVTNN, using the 𝛼− cut method.
Later on, based on this measure, a decision making algorithm is introduced to solve the
multi-attribute decision making algorithms. The third chapter extends the ARAS
(Additive Ratio Assessment) strategy to the trapezoidal neutrosophic number
environment. Based on it, it presents an approach for multi-attribute group decision-
making problems under the trapezoidal neutrosophic number environment. In addition,
entropy measures are utilized to assess to compute the experts’ importance degrees. The
fourth chapter introduces the notion of interval neutrosophic soft matrix (ivn-soft matrix)
and defined some basic algebraic operations on them. Based on these new matrices, an
algorithm has been developed to solve the decision making problems such as medical
diagnosis problems etc. In the fifth chapter, the notions of an interval-valued
neutrosophic N soft set (IVNNSS) and the quasi-hyperbolic discounting intertemporal
interval-valued neutrosophic N soft set (QHDIIVNNSS) have been proposed. The
approach is applied to determine the resilience of the workers in an organization amidst
the coronavirus (COVID-19) pandemic.
The last part of the book deals on the theory of the extension of neutrosophic sets
such as uncertain linguistic neutrosophic set, neutrosophic hesitant fuzzy rough set and
their applications to the solve the decision-making problems. In this part, the first chapter
deals with cosine similarity measures for the simplified neutrosophic sets in which rating
of each objects are treated as neutrosophic numbers. For it, six new measures are defined
by considering 2-additive Choquet integral model. The advantages of their measures is to
reduce the computational effort due to the help of 2-additivity. The utility of the measures
is tested on to the medical diagnosis problems. The second chapter in this part deals with
uncertain linguistic neutrosophic sets (ULNSs), an extension of the neutrosophic set, to
solve the decision making problems. In this chapter, the definition, basic operational
rules, comparison method and distance measure of ULNSs are presented and discussed.
