Table Of Content2022
Editors:
Prof. Dr. Florentin Smarandache,
Prof. Dr. Memet Şahin,
Assoc.Prof.Dr. Derya Bakbak,
Assoc.Prof.Dr. Vakkas Uluçay,
Dr. Abdullah Kargın
Neutrosophic Algebraic Structures
and Their Applications
Editors:
Prof. Dr. Florentin Smarandache
University of New Mexico, USA
Prof. Dr. Memet Şahin
Gaziantep University, Turkey
Assoc. Prof. Dr. Derya Bakbak
Ankara, Turkey
Assoc. Prof. Dr. Vakkas Uluçay
Kilis 7 Aralık University, Turkey
Dr. Abdullah Kargın
Gaziantep University, Turkey
NSIA Publishing House
Neutrosphic Science International Association (NSIA)
https://www.publishing-nsia.com/
University of New Mexico, Gallup, United States
Universidad Regional Autónoma de los Andes (UNIANDES),
Babahoyo, Los Rios, Ecuador
ISBN:978-1-59973-739-3
Neutrosophic Algebraic Structures and Their Applications
List of Reviewers
Said Broumi, Hassan II University, Morocco
Nasruddin Hassan, Universiti Kebangsaan Malaysia
Florentin Smarandache, University of New Mexico, USA
İsmet Yıldız, Düzce University, Turkey
İhsan Ünvar, Avrasya University, Turkey
Mohamed Abdel-Baset, Zagazig University, Egypt
Ziya Yapar, Avrasya University, Turkey
Xiaohong Zhang, Shaanxi University of Science &Technology, China
Memet Şahin, Gaziantep University, Turkey
Vakkas Uluçay, Kilis 7 Aralık University, Turkey
Necati Olgun, Gaziantep University, Turkey
Abdullah Kargın, Gaziantep University, Turkey
Neutrosophic Science International Association
President: Florentin Smarandache
3
Neutrosophic Algebraic
Structures and Their
Applications
NSIA Publishing House
Neutrosphic Science International Association (NSIA)
https://www.publishing-nsia.com/
University of New Mexico, Gallup, United States
Universidad Regional Autónoma de los Andes (UNIANDES),
Babahoyo, Los Rios, Ecuador
ISBN:978-1-59973-739-3
Aims and Scope
Neutrosophic theory and its applications have been expanding in all directions at an
astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets
and Systems”. New theories, techniques, algorithms have been rapidly developed. One of
the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set
with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The
different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough
set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed
in the literature in a short period of time. Neutrosophic set has been an important tool in the
application of various areas such as data mining, decision making, e-learning, engineering,
medicine, social science, and some more.
Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay & Abdullah Kargın
Neutrosophic Algebraic Structures and Their Applications
CONTENTS
Aims and Scope
Preface
Acknowledgment
Chapter One
History of SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra
(revisited again)…………………...………………………………………....10
Florentin Smarandache
Chapter Two
A Study on the Properties of AntiTopological Space …………………...…...16
Bhimraj Basumatary, Jeevan Krishna Khaklary
Chapter Three
Some Kinds of 𝛾-Irresolute Functions in N-Neutrosophic Crisp Topological
Spaces …………………………………………………..………………..….28
A. Vadivel, C. John Sundar
Chapter Four
On dense, rare and nowhere dense sets in anti-topological spaces………....…42
Tomasz Witczak
Chapter Fıve
Neutrosophic h-ideal in INK-Algebra……...………...………………………53
Kaviayarsu M, Jayapreethi A
Chapter Six
Neutro Ordered R-module.……………………………………………...…...63
Necati Olgun, Ahmed Hatip
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Editors: Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay & Abdullah Kargın
Chapter Seven
On Neutrosophic Double Controlled Metric-like Type Spaces……………...79
Khalil Javed, Umar Ishtiaq, Fahim Uddin and Khalil Ahmed
Chapter Eight
Bipolar Generalized Set Valued Neutrosophic Quadruple Sets and
Numbers...………………………………...……………………….…….....105
Abdullah Kargın, Memet Şahin
Chapter Nine
Interval Generalized Set Valued Neutrosophic Quadruple Sets and
Numbers…………………………………………………...……………….129
Abdullah Kargın, Memet Şahin
Chapter Ten
National Human Rights in the Protection and Promotion of Human Rights
Influence of Institutions: Fuzzy Method……………………………….......152
Enver Bozkurt, Necmiye Merve Şahin and Abdullah Kargın
Chapter Eleven
VIKOR Method-based on Entropy Measure for Decision-Making Method with
N-valued Neutrosophic Trapezoidal Numbers: Application of
Architucture………...…………………………………………………...….167
Derya Bakbak, Vakkas Uluçay
Chapter Twelve
In Determining the Level of Teachers' Commitment to the Teaching Profession
Using Classical and Fuzzy Logic…………………………………………..183
Sevilay Şahin, Merve Kısaoğlu and Abdullah Kargın
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Neutrosophic Algebraic Structures and Their Applications
Chapter Thirteen
A Comparative Analysis for Multi-Criteria Decision-Making Methods:
TOPSIS and VIKOR methods using NVTN-numbers for Application of
Circular Economy……………………………………….……….…….…...201
Nuh Okumuş, Vakkas Uluçay
Chapter Fourteen
Similarity Measures on N-Valued Fuzzy Numbers and Application to Multiple
Attribute Decision Making Problem………………………………...……...221
İrfan Deli, Mehmet Ali Keleş
Chapter Fıfteen
Direct Sum of Neutrosophic submodules of an R-module….…...………....238
Binu Ra, Paul Isaacb
Chapter Sixteen
New Distance Measure for N-valued Neutrosophic Trapezoidal Numbers
Based on the Centroid Points and Their Application to Multi-Criteria Decision-
Making...…………………………………………….………….…………..246
Davut Kesen, İrfan Deli
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Editors: Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay & Abdullah Kargın
Preface
Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy.
Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent
information. Neutrosophic set approaches are suitable to modeling problems with
uncertainty, indeterminacy and inconsistent information in which human knowledge is
necessary, and human evaluation is needed.
Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also
developed the concept of single valued neutrosophic set, oriented towards real world
scientific and engineering applications. Since then, the single valued neutrosophic set theory
has been extensively studied in books and monographs introducing neutrosophic sets and its
applications, by many authors around the world. Also, an international journal -
Neutrosophic Sets and Systems started its journey in 2013.
http://fs.unm.edu/neutrosophy.htm.
This first volume collects original research and applications from different perspectives
covering different areas of neutrosophic studies, such as decision-making, neutroalgebra,
neutro metric, and some theoretical papers.
.
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Neutrosophic Algebraic Structures and Their Applications
Acknowledgment
Florentin Smarandache
University of New Mexico, USA
Memet Şahin
Gaziantep University, Turkey
Derya Bakbak
Ankara, Turkey
Vakkas Uluçay
Kilis 7 Aralık University, Turkey
Abdullah Kargın
Gaziantep University, Turkey
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