Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)

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Book Synopsis Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree by : Kanika Mandal

Download or read book Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree written by Kanika Mandal and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Minimum spanning tree finds its huge application in network designing, approximation algorithms for NP-hard problems, clustering problems and many more.

A Neutrosophic Similarity Approach to Selection of Department for Student Transiting from JSS3 to SSS 1 Class in Nigerian Education System

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4./5 ( download)

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Book Synopsis A Neutrosophic Similarity Approach to Selection of Department for Student Transiting from JSS3 to SSS 1 Class in Nigerian Education System by : Misturah Adunni Alaran

Download or read book A Neutrosophic Similarity Approach to Selection of Department for Student Transiting from JSS3 to SSS 1 Class in Nigerian Education System written by Misturah Adunni Alaran and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: Single-valued neutrosophic set has been of valued importance in multi-criteria decision making problems using sim-ilarity measure. Department selection for students moving from JSS to SSS class in Nigerian Education System is such an area where decision taking has been critical as the future career of a student depends of the choice of Department in SSS class. Neutrosophic similarity measure is proposed for this department selection.

Minimum Spanning Tree in Trapezoidal Fuzzy Neutrosophic Environment

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4./5 ( download)

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Book Synopsis Minimum Spanning Tree in Trapezoidal Fuzzy Neutrosophic Environment by : Said Broumi

Download or read book Minimum Spanning Tree in Trapezoidal Fuzzy Neutrosophic Environment written by Said Broumi and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, an algorithm for searching the minimum spanning tree (MST) in a network having trapezoidal fuzzy neutrosophic edge weight is presented.

Neutrosophic Sets and Systems, Vol. 27, 2019

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 252 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Vol. 27, 2019 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Vol. 27, 2019 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 252 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: BMBJ-neutrosophic ideals in BCK/BCI-algebras, Neutrosophic General Finite Automata, Generalized Neutrosophic Exponential map, Implementation of Neutrosophic Function Memberships Using MATLAB Program.

Collected Papers. Volume VIII

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 1002 pages
Book Rating : 4./5 ( download)

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Book Synopsis Collected Papers. Volume VIII by : Florentin Smarandache

Download or read book Collected Papers. Volume VIII written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-04-01 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with the following 102 co-authors (alphabetically ordered) from 24 countries: Mohamed Abdel-Basset, Abduallah Gamal, Firoz Ahmad, Ahmad Yusuf Adhami, Ahmed B. Al-Nafee, Ali Hassan, Mumtaz Ali, Akbar Rezaei, Assia Bakali, Ayoub Bahnasse, Azeddine Elhassouny, Durga Banerjee, Romualdas Bausys, Mircea Boșcoianu, Traian Alexandru Buda, Bui Cong Cuong, Emilia Calefariu, Ahmet Çevik, Chang Su Kim, Victor Christianto, Dae Wan Kim, Daud Ahmad, Arindam Dey, Partha Pratim Dey, Mamouni Dhar, H. A. Elagamy, Ahmed K. Essa, Sudipta Gayen, Bibhas C. Giri, Daniela Gîfu, Noel Batista Hernández, Hojjatollah Farahani, Huda E. Khalid, Irfan Deli, Saeid Jafari, Tèmítópé Gbóláhàn Jaíyéolá, Sripati Jha, Sudan Jha, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, M. Karthika, Kawther F. Alhasan, Giruta Kazakeviciute-Januskeviciene, Qaisar Khan, Kishore Kumar P K, Prem Kumar Singh, Ranjan Kumar, Maikel Leyva-Vázquez, Mahmoud Ismail, Tahir Mahmood, Hafsa Masood Malik, Mohammad Abobala, Mai Mohamed, Gunasekaran Manogaran, Seema Mehra, Kalyan Mondal, Mohamed Talea, Mullai Murugappan, Muhammad Akram, Muhammad Aslam Malik, Muhammad Khalid Mahmood, Nivetha Martin, Durga Nagarajan, Nguyen Van Dinh, Nguyen Xuan Thao, Lewis Nkenyereya, Jagan M. Obbineni, M. Parimala, S. K. Patro, Peide Liu, Pham Hong Phong, Surapati Pramanik, Gyanendra Prasad Joshi, Quek Shio Gai, R. Radha, A.A. Salama, S. Satham Hussain, Mehmet Șahin, Said Broumi, Ganeshsree Selvachandran, Selvaraj Ganesan, Shahbaz Ali, Shouzhen Zeng, Manjeet Singh, A. Stanis Arul Mary, Dragiša Stanujkić, Yusuf Șubaș, Rui-Pu Tan, Mirela Teodorescu, Selçuk Topal, Zenonas Turskis, Vakkas Uluçay, Norberto Valcárcel Izquierdo, V. Venkateswara Rao, Volkan Duran, Ying Li, Young Bae Jun, Wadei F. Al-Omeri, Jian-qiang Wang, Lihshing Leigh Wang, Edmundas Kazimieras Zavadskas.

Neutrosophic Sets and Systems, Vol. 38, 2020

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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.

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

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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.

Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets

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Publisher : Springer
ISBN 13 : 3030000451
Total Pages : 734 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets by : Cengiz Kahraman

Download or read book Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets written by Cengiz Kahraman and published by Springer. This book was released on 2018-11-03 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive guide to the use of neutrosophic sets in multiple criteria decision making problems. It shows how neutrosophic sets, which have been developed as an extension of fuzzy and paraconsistent logic, can help in dealing with certain types of uncertainty that classical methods could not cope with. The chapters, written by well-known researchers, report on cutting-edge methodologies they have been developing and testing on a variety of engineering problems. The book is unique in its kind as it reports for the first time and in a comprehensive manner on the joint use of neutrosophic sets together with existing decision making methods to solve multi-criteria decision-making problems, as well as other engineering problems that are complex, hard to model and/or include incomplete and vague data. By providing new ideas, suggestions and directions for the solution of complex problems in engineering and decision making, it represents an excellent guide for researchers, lecturers and postgraduate students pursuing research on neutrosophic decision making, and more in general in the area of industrial and management engineering.

Neutrosophic Sets and Systems, Book Series, Vol. 29, 2019

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Book Series, Vol. 29, 2019 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Book Series, Vol. 29, 2019 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 262 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. 29, 2019

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4./5 ( download)

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Book Synopsis Neutrosophic Sets and Systems, Vol. 29, 2019 by : Florentin Smarandache

Download or read book Neutrosophic Sets and Systems, Vol. 29, 2019 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 264 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.

Collected Papers. Volume VII

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 1002 pages
Book Rating : 4./5 ( download)

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Book Synopsis Collected Papers. Volume VII by : Florentin Smarandache

Download or read book Collected Papers. Volume VII written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-02-01 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: This seventh volume of Collected Papers includes 70 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2013-2021 by the author alone or in collaboration with the following 122 co-authors from 22 countries: Mohamed Abdel-Basset, Abdel-Nasser Hussian, C. Alexander, Mumtaz Ali, Yaman Akbulut, Amir Abdullah, Amira S. Ashour, Assia Bakali, Kousik Bhattacharya, Kainat Bibi, R. N. Boyd, Ümit Budak, Lulu Cai, Cenap Özel, Chang Su Kim, Victor Christianto, Chunlai Du, Chunxin Bo, Rituparna Chutia, Cu Nguyen Giap, Dao The Son, Vinayak Devvrat, Arindam Dey, Partha Pratim Dey, Fahad Alsharari, Feng Yongfei, S. Ganesan, Shivam Ghildiyal, Bibhas C. Giri, Masooma Raza Hashmi, Ahmed Refaat Hawas, Hoang Viet Long, Le Hoang Son, Hongbo Wang, Hongnian Yu, Mihaiela Iliescu, Saeid Jafari, Temitope Gbolahan Jaiyeola, Naeem Jan, R. Jeevitha, Jun Ye, Anup Khan, Madad Khan, Salma Khan, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Kifayat Ullah, Kishore Kumar P.K., Sujit Kumar De, Prasun Kumar Nayak, Malayalan Lathamaheswari, Luong Thi Hong Lan, Anam Luqman, Luu Quoc Dat, Tahir Mahmood, Hafsa M. Malik, Nivetha Martin, Mai Mohamed, Parimala Mani, Mingcong Deng, Mohammed A. Al Shumrani, Mohammad Hamidi, Mohamed Talea, Kalyan Mondal, Muhammad Akram, Muhammad Gulistan, Farshid Mofidnakhaei, Muhammad Shoaib, Muhammad Riaz, Karthika Muthusamy, Nabeela Ishfaq, Deivanayagampillai Nagarajan, Sumera Naz, Nguyen Dinh Hoa, Nguyen Tho Thong, Nguyen Xuan Thao, Noor ul Amin, Dragan Pamučar, Gabrijela Popović, S. Krishna Prabha, Surapati Pramanik, Priya R, Qiaoyan Li, Yaser Saber, Said Broumi, Saima Anis, Saleem Abdullah, Ganeshsree Selvachandran, Abdulkadir Sengür, Seyed Ahmad Edalatpanah, Shahbaz Ali, Shahzaib Ashraf, Shouzhen Zeng, Shio Gai Quek, Shuangwu Zhu, Shumaiza, Sidra Sayed, Sohail Iqbal, Songtao Shao, Sundas Shahzadi, Dragiša Stanujkić, Željko Stević, Udhayakumar Ramalingam, Zunaira Rashid, Hossein Rashmanlou, Rajkumar Verma, Luige Vlădăreanu, Victor Vlădăreanu, Desmond Jun Yi Tey, Selçuk Topal, Naveed Yaqoob, Yanhui Guo, Yee Fei Gan, Yingcang Ma, Young Bae Jun, Yuping Lai, Hafiz Abdul Wahab, Wei Yang, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Lemnaouar Zedam.

International Journal of Neutrosophic Science (IJNS) Volume 1, 2020

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 95 pages
Book Rating : 4./5 ( download)

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Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 1, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 1, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 95 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.

Collected Papers. Volume VI

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 1002 pages
Book Rating : 4./5 ( download)

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Book Synopsis Collected Papers. Volume VI by : Florentin Smarandache

Download or read book Collected Papers. Volume VI written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-01-15 with total page 1002 pages. Available in PDF, EPUB and Kindle. Book excerpt: This sixth volume of Collected Papers includes 74 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2015-2021 by the author alone or in collaboration with the following 121 co-authors from 19 countries: Mohamed Abdel-Basset, Abdel Nasser H. Zaied, Abduallah Gamal, Amir Abdullah, Firoz Ahmad, Nadeem Ahmad, Ahmad Yusuf Adhami, Ahmed Aboelfetouh, Ahmed Mostafa Khalil, Shariful Alam, W. Alharbi, Ali Hassan, Mumtaz Ali, Amira S. Ashour, Asmaa Atef, Assia Bakali, Ayoub Bahnasse, A. A. Azzam, Willem K.M. Brauers, Bui Cong Cuong, Fausto Cavallaro, Ahmet Çevik, Robby I. Chandra, Kalaivani Chandran, Victor Chang, Chang Su Kim, Jyotir Moy Chatterjee, Victor Christianto, Chunxin Bo, Mihaela Colhon, Shyamal Dalapati, Arindam Dey, Dunqian Cao, Fahad Alsharari, Faruk Karaaslan, Aleksandra Fedajev, Daniela Gîfu, Hina Gulzar, Haitham A. El-Ghareeb, Masooma Raza Hashmi, Hewayda El-Ghawalby, Hoang Viet Long, Le Hoang Son, F. Nirmala Irudayam, Branislav Ivanov, S. Jafari, Jeong Gon Lee, Milena Jevtić, Sudan Jha, Junhui Kim, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Songül Karabatak, Abdullah Kargın, M. Karthika, Ieva Meidute-Kavaliauskiene, Madad Khan, Majid Khan, Manju Khari, Kifayat Ullah, K. Kishore, Kul Hur, Santanu Kumar Patro, Prem Kumar Singh, Raghvendra Kumar, Tapan Kumar Roy, Malayalan Lathamaheswari, Luu Quoc Dat, T. Madhumathi, Tahir Mahmood, Mladjan Maksimovic, Gunasekaran Manogaran, Nivetha Martin, M. Kasi Mayan, Mai Mohamed, Mohamed Talea, Muhammad Akram, Muhammad Gulistan, Raja Muhammad Hashim, Muhammad Riaz, Muhammad Saeed, Rana Muhammad Zulqarnain, Nada A. Nabeeh, Deivanayagampillai Nagarajan, Xenia Negrea, Nguyen Xuan Thao, Jagan M. Obbineni, Angelo de Oliveira, M. Parimala, Gabrijela Popovic, Ishaani Priyadarshini, Yaser Saber, Mehmet Șahin, Said Broumi, A. A. Salama, M. Saleh, Ganeshsree Selvachandran, Dönüș Șengür, Shio Gai Quek, Songtao Shao, Dragiša Stanujkić, Surapati Pramanik, Swathi Sundari Sundaramoorthy, Mirela Teodorescu, Selçuk Topal, Muhammed Turhan, Alptekin Ulutaș, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Dan Valeriu Voinea, Volkan Duran, Navneet Yadav, Yanhui Guo, Naveed Yaqoob, Yongquan Zhou, Young Bae Jun, Xiaohong Zhang, Xiao Long Xin, Edmundas Kazimieras Zavadskas.

Neutrosophic Operational Research, 2nd volume

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Publisher : Infinite Study
ISBN 13 : 1599735377
Total Pages : 207 pages
Book Rating : 4.5/5 (997 download)

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Book Synopsis Neutrosophic Operational Research, 2nd volume by : Florentin Smarandache

Download or read book Neutrosophic Operational Research, 2nd volume written by Florentin Smarandache and published by Infinite Study. This book was released on 2017 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats all kind of data in neutrosophic environment, with real-life applications, approaching topics as linear programming problem, linear fractional programming, integer programming, triangular neutrosophic numbers, single valued triangular neutrosophic number, neutrosophic optimization, goal programming problem, Taylor series, multi-objective programming problem, neutrosophic geometric programming, neutrosophic topology, neutrosophic open set, neutrosophic semi-open set, neutrosophic continuous function, cylindrical skin plate design, neutrosophic MULTIMOORA, alternative solutions, decision matrix, ratio system, reference point method, full multiplicative form, ordinal dominance, standard error, market research, and so on. The selected papers deal with the alleviation of world changes, including changing demographics, accelerating globalization, rising environmental concerns, evolving societal relationships, growing ethical and governance concern, expanding the impact of technology; some of these changes have impacted negatively the economic growth of private firms, governments, communities, and the whole society.

Neutrosophic Sets in Decision Analysis and Operations Research

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Publisher : IGI Global
ISBN 13 : 1799825574
Total Pages : 470 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Neutrosophic Sets in Decision Analysis and Operations Research by : Abdel-Basset, Mohamed

Download or read book Neutrosophic Sets in Decision Analysis and Operations Research written by Abdel-Basset, Mohamed and published by IGI Global. This book was released on 2019-12-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: In information technology, the concepts of cost, time, delivery, space, quality, durability, and price have gained greater importance in solving managerial decision-making problems in supply chain models, transportation problems, and inventory control problems. Moreover, competition is becoming tougher in imprecise environments. Neutrosophic sets and logic are gaining significant attention in solving real-life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. Neutrosophic Sets in Decision Analysis and Operations Research is a critical, scholarly publication that examines various aspects of organizational research through mathematical equations and algorithms and presents neutrosophic theories and their applications in various optimization fields. Featuring a wide range of topics such as information retrieval, decision making, and matrices, this book is ideal for engineers, technicians, designers, mathematicians, practitioners of mathematics in economy and technology, scientists, academicians, professionals, managers, researchers, and students.

Neutrosophic Graph Theory and Algorithms

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Publisher : IGI Global
ISBN 13 : 1799813150
Total Pages : 434 pages
Book Rating : 4.7/5 (998 download)

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Book Synopsis Neutrosophic Graph Theory and Algorithms by : Smarandache, Florentin

Download or read book Neutrosophic Graph Theory and Algorithms written by Smarandache, Florentin and published by IGI Global. This book was released on 2019-10-25 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory.

On Deneutrosophication

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Publisher : Infinite Study
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4./5 ( download)

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Book Synopsis On Deneutrosophication by : Kanika Mandal

Download or read book On Deneutrosophication written by Kanika Mandal and published by Infinite Study. This book was released on 2020-12-01 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deneutrosophication is a process to evaluate real output from neutrosophic information. The paper presents on a novel deneutrosophication algorithm. The process is developed with similarity measure and probability density function (PDF). This similarity measure is newly defined to prepare a correct transformation from neutrosophic set (NS) to fuzzy set (FS). Then an approach to find PDF is formulated which relates with fuzzy set. Finally, the algorithm has been implemented in solving a critical path problem to find out the completion time of a certain project.