Some Properties Of Pentagonal Neutrosophic Numbers And Its Applications In Transportation Problem Environment

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Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment

Author : Avishek Chakraborty
Publisher : Infinite Study
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4./5 ( download)

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Book Synopsis Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment by : Avishek Chakraborty

Download or read book Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment written by Avishek Chakraborty and published by Infinite Study. This book was released on with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this research article we actually deals with the conception of pentagonal Neutrosophic number from a different frame of reference. Recently, neutrosophic set theory and its extensive properties have given different dimensions for researchers. This paper focuses on pentagonal neutrosophic numbers and its distinct properties. At the same time, we defined the disjunctive cases of this number whenever the truthiness, falsity and hesitation portion are dependent and independent to each other. Some basic properties of pentagonal neutrosophic numbers with its logical score and accuracy function is introduced in this paper with its application in real life operation research problem which is more reliable than the other methods.

Application of Transportation Problem under Pentagonal Neutrosophic Environment

Author : Sapan Kumar Das
Publisher : Infinite Study
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4./5 ( download)

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Book Synopsis Application of Transportation Problem under Pentagonal Neutrosophic Environment by : Sapan Kumar Das

Download or read book Application of Transportation Problem under Pentagonal Neutrosophic Environment written by Sapan Kumar Das and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper talks about the pentagonal Neutrosophic sets and its operational law. The paper presents the cuts of single valued pentagonal Neutrosophic numbers and additionally introduced the arithmetic operation of single-valued pentagonal Neutrosophic numbers. Here, we consider a transportation problem with pentagonal Neutrosophic numbers where the supply, demand and transportation cost is uncertain.

De-Neutrosophication Technique of Pentagonal Neutrosophic Number and Application in Minimal Spanning Tree

Author : Avishek Chakraborty
Publisher : Infinite Study
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4./5 ( download)

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Book Synopsis De-Neutrosophication Technique of Pentagonal Neutrosophic Number and Application in Minimal Spanning Tree by : Avishek Chakraborty

Download or read book De-Neutrosophication Technique of Pentagonal Neutrosophic Number and Application in Minimal Spanning Tree written by Avishek Chakraborty and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this current era, neutrosophic set theory is a crucial topic to demonstrate the ambiguous information due to existence of three disjunctive components appears in it and it provides a wide range of applications in distinct fields for the researchers. Generally, neutrosophic sets is the extended version of crisp set, fuzzy set and intuitionistic fuzzy sets to focus on the uncertain, hesitant and ambiguous datas of a real life mathematical problem.

Neutrosophic Sets and Systems, Vol. 28, 2019

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Vol. 28, 2019 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Vol. 28, 2019 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 304 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 from this issue: Reduction of indeterminacy of gray-scale image in bipolar neutrosophic domain, Single Valued Neutrosophic Coloring, An Integrated Neutrosophic and MOORA for Selecting Machine Tool, Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique, Pi-Distance of Rough Neutrosophic Sets for Medical Diagnosis, Machine learning in Neutrosophic Environment: A Survey.

International Journal of Neutrosophic Science (IJNS) Volume 7, 2020

Author : Broumi Said
Publisher : Infinite Study
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4./5 ( download)

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Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 7, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 7, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

Neutrosophic Sets and Systems, Book Series, Vol. 28, 2019

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 302 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Book Series, Vol. 28, 2019 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Book Series, Vol. 28, 2019 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 302 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

Neutrosophic Sets and Systems, Book Series, Vol. 35, 2020. An International Book Series in Information Science and Engineering

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 594 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Book Series, Vol. 35, 2020. An International Book Series in Information Science and Engineering by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Book Series, Vol. 35, 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 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributors to current issue (listed in papers’ order): Ibrahim Yasser, Abeer Twakol, A. A. Abd El-Khalek, A. A. Salama, Ahmed Sharaf Al-Din, Issam Abu Al-Qasim, Rafif Alhabib, Magdy Badran, Remya P. B, Francina Shalini, Masoud Ghods, Zahra Rostami, A. Sahaya Sudha, Luiz Flavio Autran Monteiro Gomes, K.R. Vijayalakshmi, Prakasam Muralikrishna, Surya Manokaran, Nidhi Singh, Avishek Chakraborty, Soma Bose Biswas, Malini Majumdar, Rakhal Das, Binod Chandra Tripathy, Nidhi Singh, Avishek Chakraborty, Nilabhra Paul, Deepshikha Sarma, Akash Singh, Uttam Kumar Bera, Fatimah M. Mohammed, Sarah W. Raheem, Muhammad Riaz, Florentin Smarandache, Faruk Karaaslan, Masooma Raza Hashmi, Iqra Nawaz, Kousik Das, Sovan Samanta, Kajal De, Xavier Encarnacion, Nivetha Martin, I. Pradeepa, N. Ramila Gandhi, P. Pandiammal, Aiman Muzaffar, Md Tabrez Nafis, Shahab Saquib Sohail, Abhijit Saha, Jhulaneswar Baidya, Debjit Dutta, Irfan Deli, Said Broumi, Mohsin Khalid, Neha Andaleeb Khalid, Md. Hanif Page, Qays Hatem Imran, Shilpi Pal, S. Satham Hussain, Saeid Jafari, N. Durga, Hanieh Shambayati, Mohsen Shafiei Nikabadi, Seyed Mohammad, Ali Khatami Firouzabadi, Mohammad Rahmanimanesh, Mujahid Abbas, Ghulam Murtaza, K. Porselvi, B. Elavarasan, Y. B. Jun, Chinnadurai V, Sindhu M P, K.Radhika, K. Arun Prakash, Malayalan Lathamaheswari, Ruipu Tan, Deivanayagampillai Nagarajan, Talea Mohamed, Assia Bakali, Nivetha Martin, R. Dhavaseelan, Ali Hussein Mahmood Al-Obaidi, Suman Das, Surapati Pramanik, Madad Khan, Muhammad Zeeshan, Saima Anis, Abdul Sami Awan, M. Sarwar Sindhu, Tabasam Rashid, Agha Kashif, Rajesh Kumar Saini, Atul Sangal, Manisha.

Neutrosophic Sets and Systems, Vol. 35, 2020

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 596 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Vol. 35, 2020 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Vol. 35, 2020 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 596 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: Neutrosophic Soft Fixed Points, Selection of Alternative under the Framework of Single-Valued Neutrosophic Sets, Application of Single Valued Trapezoidal Neutrosophic Numbers in Transportation Problem.

Current Advances in Mechanical Engineering

Author : Saroj Kumar Acharya
Publisher : Springer Nature
ISBN 13 : 9813347953
Total Pages : 991 pages
Book Rating : 4.8/5 (133 download)

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Book Synopsis Current Advances in Mechanical Engineering by : Saroj Kumar Acharya

Download or read book Current Advances in Mechanical Engineering written by Saroj Kumar Acharya and published by Springer Nature. This book was released on 2021-03-18 with total page 991 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents select proceedings of the International Conference on Recent Advances in Mechanical Engineering Research and Development (ICRAMERD 2020). The contents focus on latest research and current problems in various branches of mechanical engineering. Some of the topics discussed here include fracture and failure analysis, fuels and alternative fuels, combustion and IC engines, advanced manufacturing technologies, powder metallurgy and rapid prototyping, industrial engineering and automation, supply chain management, design of mechanical systems, vibrations and control engineering, automobile engineering, fluid mechanics and machines, heat transfer, composite materials, micro and nano-engineering for energy storage and conversion, and modeling and simulations. The wide range of topics presented in this book can make it useful for beginners, researchers as well as professionals in mechanical engineering.

Neutrosophic Sets and Systems, vol. 48/2022

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, vol. 48/2022 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, vol. 48/2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-02-01 with total page 496 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, Vol. 38, 2020

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 662 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Vol. 38, 2020 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Vol. 38, 2020 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 662 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.

Neutrosophic Sets and Systems, vol. 51/2022

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 970 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, vol. 51/2022 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, vol. 51/2022 written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-09-01 with total page 970 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).

A Single-valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker’s Satisfaction Level

Author : Satyabrata Nath
Publisher : Infinite Study
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4./5 ( download)

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Book Synopsis A Single-valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker’s Satisfaction Level by : Satyabrata Nath

Download or read book A Single-valued Pentagonal Neutrosophic Geometric Programming Approach to Optimize Decision Maker’s Satisfaction Level written by Satyabrata Nath and published by Infinite Study. This book was released on 2023-01-01 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieving the desired level of satisfaction for a decision-maker in any decision-making scenario is considered a challenging endeavor because minor modifications in the process might lead to incorrect findings and inaccurate decisions. In order to maximize the decision-maker’s satisfaction, this paper proposes a Single-valued Neutrosophic Geometric Programming model based on pentagonal fuzzy numbers. The decision-maker is typically assumed to be certain of the parameters, but in reality, this is not the case, hence the parameters are presented as neutrosophic fuzzy values. The decision-maker, with this strategy, is able to achieve varying levels of satisfaction and dissatisfaction for each constraint and even complete satisfaction for certain constraints. Here the decision maker aims to achieve the maximum level of satisfaction while maintaining the level of hesitation and minimizing dissatisfaction in order to retain an optimum solution. Furthermore, transforming the objective function into a constraint adds one more layer to the N-dimensional multi-parametrizes α, β and γ. The advantages of this multi-parametrized proposed method over the existing ones are proven using numerical examples.

International Journal of Neutrosophic Science (IJNS) Volume 3, 2020

Author : Broumi Said
Publisher : Infinite Study
ISBN 13 :
Total Pages : 117 pages
Book Rating : 4./5 ( download)

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Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 3, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 3, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

International Journal of Neutrosophic Science (IJNS) Volume 8, 2020

Author : Broumi Said
Publisher : Infinite Study
ISBN 13 :
Total Pages : 127 pages
Book Rating : 4./5 ( download)

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Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 8, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 8, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

Neutrosophic Sets and Systems, Book Series, Vol. 34, 2020. An International Book Series in Information Science and Engineering. Special Issue: Social Neutrosophy in Latin America

Download Neutrosophic Sets and Systems, Book Series, Vol. 34, 2020. An International Book Series in Information Science and Engineering. Special Issue: Social Neutrosophy in Latin America PDF Online Free

Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 223 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Book Series, Vol. 34, 2020. An International Book Series in Information Science and Engineering. Special Issue: Social Neutrosophy in Latin America by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Book Series, Vol. 34, 2020. An International Book Series in Information Science and Engineering. Special Issue: Social Neutrosophy in Latin America written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributors to current issue (listed in papers’ order): Noel Batista Hernández; C.V. Valenzuela Chicaiza; O.G. Arciniegas Paspuel; P.Y. Carrera Cuesta; D.R. Álvarez Hernández, C.E. Pozo Hernández; E.T. Mejía Álvarez; E.T. Villa Shagnay; S. Guerrón Enríquez; M.A. Tello Cadena; E.M. Pinos Medina; M. Jaramillo Burgos; F. Jara Vaca; R. Aguilar Berrezueta; E.M. Sandoval; B. Villalta Jadán; D. Palma Rivera; L.E. Valencia Cruzaty; M. Reyes Tomalá; C.M. Castillo Gallo, M.R. Velázquez; M.R. Mena Peralta; L. Ricardo Domínguez; D. Andrade Santamaría; X.Cangas Oña; M. Jaramillo Burgos; G.A. Calderón Vallejo; M. Orellana Cepeda; M.F. Galarza Villalba; M.S. Serrano Viteri; I. Ramos Castro; F. Vera Díaz; N.P. Lastra Calderón; D.L. Villarruel Delgado; D. Sandoval Malquín; E. Araujo Guerrón; A.R. Pupo Kairuz; D.V. Ponce Ruiz; F. Viteri Pita; F.S. Bustillo Mena; M.E. Narváez Jaramillo; M.A. Guerrero Ayala; D.A. Flores Jurado; O.M. Alonzo Pico; A.I. Utrera Velázquez; D.A. García Coello; E. Real Garlobo; C. Escobar Vinueza; R.C. Hernández Infante; M.E. Infante Miranda; F.R. Rivadeneira Enríquez; C.J. Galeano Páez; R.M. Montalvo Pantoja; K.A. Narváez Ortiz; S. Guaytarilla Salas; A.D. Rodríguez Lara; C.P. Rendón Tello; J. Almeida Blacio; R. Hurtado Guevara; L.G. Guallpa Zatán; H.J. Paillacho Chicaiza; J. Yaguar Mariño; M. Aguilar Carrión; D.A. Viteri Intriago; L. Álvarez Gómez; D. Ponce Ruiz; L.H. Carrión Hurtado; W.R. Salas Espín; M. Benalcázar Paladines; L. Moreira Rosales; L.K. Baque Villanueva; M.A. Mendoza; R. Salcedo; A.M. Izquierdo Morán; M.A. Checa Cabrera; B.J. Ipiales Chasiguano; A.L. Sandoval Pillajo; R. Díaz Vázquez; N.P. Becerra Arévalo; M.F. Calles Carrasco; John Luis Toasa Espinoza; M. Velasteguí Córdova; V.M. Parrales Carvajal; M.T. Macías Valverde; R. Aguas Pután; N. García Arias; N. Quevedo Arnaiz; S. Gavilánez Villamarín; M. Cleonares Borbor; M.F. Galarza Villalba; R. Aguas Pután; J. Mora Romero; J.E. Espìn Oviedo; L.J. Molina Chalacán; L.O. Albarracín Zambrano; E.J. Jalón Arias; A. Zúñiga Paredes; F. Smarandache; J. Estupiñán Ricardo; E. González Caballero; M.Y. Leyva Vázquez.

Neutrosophic Operational Research

Author : Florentin Smarandache
Publisher : Springer Nature
ISBN 13 : 3030571971
Total Pages : 628 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Neutrosophic Operational Research by : Florentin Smarandache

Download or read book Neutrosophic Operational Research written by Florentin Smarandache and published by Springer Nature. This book was released on 2021-09-09 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses new concepts, methods, algorithms, modeling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, linear problems and new information related to optimization for the topic from the theoretical and applied viewpoints of neutrosophic sets and logic. The book is an innovatory of new tools and procedures, such as: Neutrosophic Statistical Tests and Dependent State Samplings, Neutrosophic Probabilistic Expert Systems, Neutrosophic HyperSoft Set, Quadripartitioned Neutrosophic Cross-Entropy, Octagonal and Spherical and Cubic Neutrosophic Numbers used in machine learning. It highlights the process of neutrosofication {which means to split the universe into three parts, two opposite ones (Truth and Falsehood), and an Indeterminate or neutral one (I) in between them}. It explains Three-Ways Decision, how the universe set is split into three different distinct areas, in regard to the decision process, representing: Acceptance, Noncommitment, and Rejection, respectively. The Three-Way Decision is used in the Neutrosophic Linguistic Rough Set, which has never been done before.