Intuitionistic Plithogenic Graph

Intuitionistic Plithogenic Graph

Author: Prem Kumar Singh

Publisher: Infinite Study

Published: 2022-04-01

Total Pages: 22

ISBN-13:

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Recently, properties of single-valued Plithogenic set is introduced for dealing with several opposite, non-opposite and neutral side of a multi-valued attribute. In this case, a problem arises due to conflict among the experts and their opinions. It is an indeed problem while dealing with single-valued Plithogenic membership. The reason is to deal with conflict or contradictions membership and non-membership values required. To deal with this problem intuitionistic Plithogenic context and its graphical structure visualization is introduced in this paper. In addition{d(a1, a2) , cb } -cut is introduced for dealing with intuitionistic degree of appurtenance and contradiction for multi-decision process.


Book Synopsis Intuitionistic Plithogenic Graph by : Prem Kumar Singh

Download or read book Intuitionistic Plithogenic Graph written by Prem Kumar Singh and published by Infinite Study. This book was released on 2022-04-01 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently, properties of single-valued Plithogenic set is introduced for dealing with several opposite, non-opposite and neutral side of a multi-valued attribute. In this case, a problem arises due to conflict among the experts and their opinions. It is an indeed problem while dealing with single-valued Plithogenic membership. The reason is to deal with conflict or contradictions membership and non-membership values required. To deal with this problem intuitionistic Plithogenic context and its graphical structure visualization is introduced in this paper. In addition{d(a1, a2) , cb } -cut is introduced for dealing with intuitionistic degree of appurtenance and contradiction for multi-decision process.


Plithogenic Graphs

Plithogenic Graphs

Author: W. B. Vasantha Kandasamy

Publisher: Infinite Study

Published:

Total Pages: 296

ISBN-13:

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The plithogenic set is a generalization of crisp, fuzzy, intuitionistic fuzzy, and Neutrosophic sets, it is a set whose elements are characterized by many attributes' values. This book gives some possible applications of plithogenic sets defined by Florentin Smarandache (2018). The authors have defined a new class of special type of graphs which can be applied for plithogenic models.


Book Synopsis Plithogenic Graphs by : W. B. Vasantha Kandasamy

Download or read book Plithogenic Graphs written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plithogenic set is a generalization of crisp, fuzzy, intuitionistic fuzzy, and Neutrosophic sets, it is a set whose elements are characterized by many attributes' values. This book gives some possible applications of plithogenic sets defined by Florentin Smarandache (2018). The authors have defined a new class of special type of graphs which can be applied for plithogenic models.


Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft sets – A Novel Outlook

Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft sets – A Novel Outlook

Author: Nivetha Martin

Publisher: Infinite Study

Published: 2020-06-01

Total Pages: 14

ISBN-13:

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Plithogenic Hypersoft sets (PHS) introduced by Smarandache are the extensions of soft sets and hypersoft sets and it was further protracted to plithogenic fuzzy whole Hypersoft set to make it more applicable to multi attribute decision making environment.


Book Synopsis Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft sets – A Novel Outlook by : Nivetha Martin

Download or read book Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft sets – A Novel Outlook written by Nivetha Martin and published by Infinite Study. This book was released on 2020-06-01 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plithogenic Hypersoft sets (PHS) introduced by Smarandache are the extensions of soft sets and hypersoft sets and it was further protracted to plithogenic fuzzy whole Hypersoft set to make it more applicable to multi attribute decision making environment.


Neutrosophic Sets and Systems, vol. 49/2022

Neutrosophic Sets and Systems, vol. 49/2022

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-04-01

Total Pages: 611

ISBN-13:

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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).


Book Synopsis Neutrosophic Sets and Systems, vol. 49/2022 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, vol. 49/2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-04-01 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).


Neutrosophic Sets and Systems, Book Series, Vol. 33, 2020. An International Book Series in Information Science and Engineering

Neutrosophic Sets and Systems, Book Series, Vol. 33, 2020. An International Book Series in Information Science and Engineering

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 341

ISBN-13:

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Contributors to current issue (listed in papers’ order): Atena Tahmasbpour Meikola, Arif Mehmood, Wadood Ullah, Said Broumi, Muhammad Imran Khan, Humera Qureshi, Muhammad Ibrar Abbas, Humaira Kalsoom, Fawad Nadeem, T. Chalapathi, L. Madhavi, R. Suresh, S. Palaniammal, Nivetha Martin, Florentin Smarandache, S. A. Edalatpanah, Rafif Alhabib, A. A. Salama, Memet Şahin, Abdullah Kargın, Murat Yücel, Dimacha Dwibrang Mwchahary, Bhimraj Basumatary, R. S. Alghamdi, N. O. Alshehri, Shigui Du, Rui Yong, Jun Ye, Vasantha Kandasamy, Ilanthenral Kandasamy, Muhammad Saeed, Muhammad Saqlain, Asad Mehmood, Khushbakht Naseer, Sonia Yaqoob, Sudipta Gayen, Sripati Jha, Manoranjan Kumar Singh, Ranjan Kumar, Huseyin Kamaci, Shawkat Alkhazaleh, Anas Al-Masarwah, Abd Ghafur Ahmad, Merve Sena Uz, Akbar Rezaei, Mohamed Grida, Rehab Mohamed, Abdelnaser H. Zaid.


Book Synopsis Neutrosophic Sets and Systems, Book Series, Vol. 33, 2020. An International Book Series in Information Science and Engineering by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Book Series, Vol. 33, 2020. An International Book Series in Information Science and Engineering written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributors to current issue (listed in papers’ order): Atena Tahmasbpour Meikola, Arif Mehmood, Wadood Ullah, Said Broumi, Muhammad Imran Khan, Humera Qureshi, Muhammad Ibrar Abbas, Humaira Kalsoom, Fawad Nadeem, T. Chalapathi, L. Madhavi, R. Suresh, S. Palaniammal, Nivetha Martin, Florentin Smarandache, S. A. Edalatpanah, Rafif Alhabib, A. A. Salama, Memet Şahin, Abdullah Kargın, Murat Yücel, Dimacha Dwibrang Mwchahary, Bhimraj Basumatary, R. S. Alghamdi, N. O. Alshehri, Shigui Du, Rui Yong, Jun Ye, Vasantha Kandasamy, Ilanthenral Kandasamy, Muhammad Saeed, Muhammad Saqlain, Asad Mehmood, Khushbakht Naseer, Sonia Yaqoob, Sudipta Gayen, Sripati Jha, Manoranjan Kumar Singh, Ranjan Kumar, Huseyin Kamaci, Shawkat Alkhazaleh, Anas Al-Masarwah, Abd Ghafur Ahmad, Merve Sena Uz, Akbar Rezaei, Mohamed Grida, Rehab Mohamed, Abdelnaser H. Zaid.


Neutrosophic Sets and Systems, Vol. 33, 2020

Neutrosophic Sets and Systems, Vol. 33, 2020

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 353

ISBN-13:

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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra, Neutrosophic Triplet Partial Bipolar Metric Spaces, The Neutrosophic Triplet of BI-algebras.


Book Synopsis Neutrosophic Sets and Systems, Vol. 33, 2020 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Vol. 33, 2020 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra, Neutrosophic Triplet Partial Bipolar Metric Spaces, The Neutrosophic Triplet of BI-algebras.


Collected Papers. Volume X

Collected Papers. Volume X

Author: Florentin Smarandache

Publisher: Infinite Study

Published: 2022-06-01

Total Pages: 1006

ISBN-13:

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This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with the following 105 co-authors (alphabetically ordered) from 26 countries: Abu Sufian, Ali Hassan, Ali Safaa Sadiq, Anirudha Ghosh, Assia Bakali, Atiqe Ur Rahman, Laura Bogdan, Willem K.M. Brauers, Erick González Caballero, Fausto Cavallaro, Gavrilă Calefariu, T. Chalapathi, Victor Christianto, Mihaela Colhon, Sergiu Boris Cononovici, Mamoni Dhar, Irfan Deli, Rebeca Escobar-Jara, Alexandru Gal, N. Gandotra, Sudipta Gayen, Vassilis C. Gerogiannis, Noel Batista Hernández, Hongnian Yu, Hongbo Wang, Mihaiela Iliescu, F. Nirmala Irudayam, Sripati Jha, Darjan Karabašević, T. Katican, Bakhtawar Ali Khan, Hina Khan, Volodymyr Krasnoholovets, R. Kiran Kumar, Manoranjan Kumar Singh, Ranjan Kumar, M. Lathamaheswari, Yasar Mahmood, Nivetha Martin, Adrian Mărgean, Octavian Melinte, Mingcong Deng, Marcel Migdalovici, Monika Moga, Sana Moin, Mohamed Abdel-Basset, Mohamed Elhoseny, Rehab Mohamed, Mohamed Talea, Kalyan Mondal, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Ihsan, Muhammad Naveed Jafar, Muhammad Rayees Ahmad, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Mujahid Abbas, Mumtaz Ali, Radu I. Munteanu, Ghulam Murtaza, Munazza Naz, Tahsin Oner, ‪Gabrijela Popović, Surapati Pramanik, R. Priya, S.P. Priyadharshini, Midha Qayyum, Quang-Thinh Bui, Shazia Rana, Akbara Rezaei, Jesús Estupiñán Ricardo, Rıdvan Sahin, Saeeda Mirvakili, Said Broumi, A. A. Salama, Flavius Aurelian Sârbu, Ganeshsree Selvachandran, Javid Shabbir, Shio Gai Quek, Son Hoang Le, Florentin Smarandache, Dragiša Stanujkić, S. Sudha, Taha Yasin Ozturk, Zaigham Tahir, The Houw Iong, Ayse Topal, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Rizha Vitania, Luige Vlădăreanu, Victor Vlădăreanu, Ștefan Vlăduțescu, J. Vimala, Dan Valeriu Voinea, Adem Yolcu, Yongfei Feng, Abd El-Nasser H. Zaied, Edmundas Kazimieras Zavadskas.


Book Synopsis Collected Papers. Volume X by : Florentin Smarandache

Download or read book Collected Papers. Volume X written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-06-01 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with the following 105 co-authors (alphabetically ordered) from 26 countries: Abu Sufian, Ali Hassan, Ali Safaa Sadiq, Anirudha Ghosh, Assia Bakali, Atiqe Ur Rahman, Laura Bogdan, Willem K.M. Brauers, Erick González Caballero, Fausto Cavallaro, Gavrilă Calefariu, T. Chalapathi, Victor Christianto, Mihaela Colhon, Sergiu Boris Cononovici, Mamoni Dhar, Irfan Deli, Rebeca Escobar-Jara, Alexandru Gal, N. Gandotra, Sudipta Gayen, Vassilis C. Gerogiannis, Noel Batista Hernández, Hongnian Yu, Hongbo Wang, Mihaiela Iliescu, F. Nirmala Irudayam, Sripati Jha, Darjan Karabašević, T. Katican, Bakhtawar Ali Khan, Hina Khan, Volodymyr Krasnoholovets, R. Kiran Kumar, Manoranjan Kumar Singh, Ranjan Kumar, M. Lathamaheswari, Yasar Mahmood, Nivetha Martin, Adrian Mărgean, Octavian Melinte, Mingcong Deng, Marcel Migdalovici, Monika Moga, Sana Moin, Mohamed Abdel-Basset, Mohamed Elhoseny, Rehab Mohamed, Mohamed Talea, Kalyan Mondal, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Ihsan, Muhammad Naveed Jafar, Muhammad Rayees Ahmad, Muhammad Saeed, Muhammad Saqlain, Muhammad Shabir, Mujahid Abbas, Mumtaz Ali, Radu I. Munteanu, Ghulam Murtaza, Munazza Naz, Tahsin Oner, ‪Gabrijela Popović, Surapati Pramanik, R. Priya, S.P. Priyadharshini, Midha Qayyum, Quang-Thinh Bui, Shazia Rana, Akbara Rezaei, Jesús Estupiñán Ricardo, Rıdvan Sahin, Saeeda Mirvakili, Said Broumi, A. A. Salama, Flavius Aurelian Sârbu, Ganeshsree Selvachandran, Javid Shabbir, Shio Gai Quek, Son Hoang Le, Florentin Smarandache, Dragiša Stanujkić, S. Sudha, Taha Yasin Ozturk, Zaigham Tahir, The Houw Iong, Ayse Topal, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Rizha Vitania, Luige Vlădăreanu, Victor Vlădăreanu, Ștefan Vlăduțescu, J. Vimala, Dan Valeriu Voinea, Adem Yolcu, Yongfei Feng, Abd El-Nasser H. Zaied, Edmundas Kazimieras Zavadskas.


A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally

A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally

Author: Fazeelat Sultana

Publisher: Infinite Study

Published: 2023-01-01

Total Pages: 21

ISBN-13:

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During the last two decades, the world has experienced three major outbreaks of Coronaviruses, namely severe acute respiratory syndrome (SARS- CoV), middle east respiratory syndrome (MERS-CoV), and the current ongoing pandemic of severe acute respiratory syndrome 2 (SARS-CoV-2). The SARS-CoV-2 caused the disease known as Coronavirus Disease 2019 (COVID-19). Since its discovery for the first time in Wuhan, China, in December 2019, the disease has spread very fast, and cases have been reported in more than 200 countries/territories. In this study, the idea of Smarandache’s pathogenic set is used to discuss the novel COVID-19 spread. We first introduced plithogenic graphs and their subclass, like plithogenic fuzzy graphs. We also established certain binary operations like union, join, Cartesian product, and composition of pathogenic fuzzy graphs, which are helpful when we discuss combining two different graphs. In the end, we investigate the spreading trend of COVID-19 by applying the pathogenic fuzzy graphs. We observe that COVID-19 is much dangerous than (MERS-CoV) and (SARS-CoV). Moreover, as the SARS-CoV and MERS-CoV outbreaks were controlled, there are greater chances to overcome the current pandemic of COVID-19 too. Our model suggests that all the countries should stop all types of traveling/movement across the borders and internally too to control the spread of COVID-19. The proposed model also predicts that in case precautionary measures have not been taken then there is a chance of severe outbreak in future.


Book Synopsis A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally by : Fazeelat Sultana

Download or read book A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally written by Fazeelat Sultana and published by Infinite Study. This book was released on 2023-01-01 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last two decades, the world has experienced three major outbreaks of Coronaviruses, namely severe acute respiratory syndrome (SARS- CoV), middle east respiratory syndrome (MERS-CoV), and the current ongoing pandemic of severe acute respiratory syndrome 2 (SARS-CoV-2). The SARS-CoV-2 caused the disease known as Coronavirus Disease 2019 (COVID-19). Since its discovery for the first time in Wuhan, China, in December 2019, the disease has spread very fast, and cases have been reported in more than 200 countries/territories. In this study, the idea of Smarandache’s pathogenic set is used to discuss the novel COVID-19 spread. We first introduced plithogenic graphs and their subclass, like plithogenic fuzzy graphs. We also established certain binary operations like union, join, Cartesian product, and composition of pathogenic fuzzy graphs, which are helpful when we discuss combining two different graphs. In the end, we investigate the spreading trend of COVID-19 by applying the pathogenic fuzzy graphs. We observe that COVID-19 is much dangerous than (MERS-CoV) and (SARS-CoV). Moreover, as the SARS-CoV and MERS-CoV outbreaks were controlled, there are greater chances to overcome the current pandemic of COVID-19 too. Our model suggests that all the countries should stop all types of traveling/movement across the borders and internally too to control the spread of COVID-19. The proposed model also predicts that in case precautionary measures have not been taken then there is a chance of severe outbreak in future.


Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited

Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 14

ISBN-13:

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In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life.


Book Synopsis Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited by : Florentin Smarandache

Download or read book Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life.


Strong Interval-valued Neutrosophic Intuitionistic Fuzzy Graph

Strong Interval-valued Neutrosophic Intuitionistic Fuzzy Graph

Author: K. Kalaiarasi

Publisher: Infinite Study

Published:

Total Pages: 22

ISBN-13:

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In this paper, the strong interval-valued neutrosophic intuitionistic fuzzy graphs are suggest. Cartesian product, composition and clamp of two strong interval-valued neutrosophic intuitionstic fuzzy graphs defined.


Book Synopsis Strong Interval-valued Neutrosophic Intuitionistic Fuzzy Graph by : K. Kalaiarasi

Download or read book Strong Interval-valued Neutrosophic Intuitionistic Fuzzy Graph written by K. Kalaiarasi and published by Infinite Study. This book was released on with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the strong interval-valued neutrosophic intuitionistic fuzzy graphs are suggest. Cartesian product, composition and clamp of two strong interval-valued neutrosophic intuitionstic fuzzy graphs defined.