Table Of Content

Florentin Smarandache, Surapati Pramanik (Editors) Pons Edit ions Florentin Smarandache, Surapati Pramanik (Editors) New Trends in Neutrosophic Theory and Applications Neutrosophic Science International Association President: Florentin Smarandache Pons asbl 5, Quai du Batelage, Brussells, Belgium, European Union President: Georgiana Antonescu DTP: George Lukacs ISBN 978-1-59973-498-9 Florentin Smarandache, Surapati Pramanik (Editors) New Trends in Neutrosophic Theory and Applications Pons Editions Brussels, Belgium, EU 2016 Peer Reviewers Prof. Paul P. Wang, Department of Electrical & Computer Engineering, Pratt School of Engineering, Duke University, Durham, NC 27708, USA. Dr. Mumtaz Ali, University of Southern Queensland, Australia. Prof. Luige Vladareanu, Romanian Academy, Bucharest, Romania. Dr. Dominique Maltese, SAFRAN ELECTRONICS & DEFENSE, Paris, France. New Trends in Neutrosophic Theory and Applications TABLE OF CONTENTS Aims and Scope ................................................................................................................................................... 7 Preface ................................................................................................................................................................. 9 DATA MINING Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri Role of Neutrosophic Logic in Data Mining ....................................................................................................... 15 DECISION MAKING Pranab Biswas, Surapati Pramanik, Bibhas C. Giri Some Distance Measures of Single Valued Neutrosophic Hesitant Fuzzy Sets and Their Applications to Multiple Attribute Decision Making ........................................................................................................................... 27 Rıdvan Şahin, Peide Liu Distance and Similarity Measures for Multiple Attribute Decision Making with Single-Valued Neutrosophic Hesitant Fuzzy Information .......................................................................................................................... 35 Pranab Biswas, Surapati Pramanik, Bibhas C. Giri GRA Method of Multiple Attribute Decision Making with Single Valued Neutrosophic Hesitant Fuzzy Set Information .................................................................................................................................................. 55 Partha Pratim Dey, Surapati Pramanik, Bibhas C. Giri TOPSIS for Solving Multi-Attribute Decision Making Problems under Bi-Polar Neutrosophic Environment ..... 65 Surapati Pramanik, Durga Banerjee, B. C. Giri TOPSIS Approach for Multi Attribute Group Decision Making in Neutrosophic Environment .......................... 79 Kalyan Mondal, Surapati Pramanik, Florentin Smarandache Several Trigonometric Hamming Similarity Measures of Rough Neutrosophic Sets and their Applications in Decision Making .......................................................................................................................................... 93 Nital P. Nirmal, Mangal G. Bhatt Selection of Automated Guided Vehicle using Single Valued Neutrosophic Entropy Based Novel Multi Attribute Decision Making Technique ....................................................................................................................... 105 Florentin Smarandache, Mirela Teodorescu From Linked Data Fuzzy to Neutrosophic Data Set Decision Making in Games vs. Real Life .......................... 115 Partha Pratim Dey, Surapati Pramanik, Bibhas C. Giri Extended Projection Based Models for Solving Multiple Attribute Decision Making Problems with Interval Valued Neutrosophic Information ........................................................................................................................... 127 Kanika Mandal, Kajla Basu Multi Criteria Decision Making Method in Neutrosophic Environment Using a New Aggregation Operator, Score and Certainty Function ............................................................................................................................... 141 Surapati Pramanik, Shyamal Dalapati, Tapan Kumar Roy Logistics Center Location Selection Approach Based on Neutrosophic Multi-Criteria Decision Making .......... 161 E-LEARNING Nouran M. Radwan Neutrosophic Applications in E-learning: Outcomes, Challenges and Trends ................................................... 177 GRAPH THEORY Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache Single Valued Neutrosophic Graphs ................................................................................................................. 187 5 Florentin Smarandache, Surapati Pramanik (Editors) Said Broumi, Mohamed Talea, Assia Bakali, Florentin Smarandache On Bipolar Single Valued Neutrosophic Graphs .............................................................................................. 203 Shimaa Fathi, Hewayda ElGhawalby , A.A. Salama A Neutrosophic Graph Similarity Measures ..................................................................................................... 223 Broumi, S., Smarandache, F., Talea, M., Bakali, A. Operations on Interval Valued Neutrosophic Graphs .......................................................................... 231 MEDICAL DIAGNOSIS Deepika Koundal, Savita Gupta, Sukhwinder Singh Applications of Neutrosophic Sets in Medical Image Denoising and Segmentation .......................................... 257 NEUTROSOPHIC MODEL IN SOCIOLOGY Santanu Ku. Patro On a model of Love dynamics: A Neutrosophic analysis .................................................................................. 279 PROBABILITY THEORY A. A. Salama, Florentin Smarandache Neutrosophic Crisp Probability Theory & Decision Making Process ................................................................ 291 TOPOLOGY Francisco Gallego Lupiañez On neutrosophic sets and topology ................................................................................................................... 305 A.A. Salama, I.M.Hanafy, Hewayda Elghawalby, M.S.Dabash Some GIS Topological Concepts via Neutrosophic Crisp Set Theory ............................................................... 315 OTHER THEORETICAL PAPERS J. Martina Jency,I. Arockiarani ∗ Hausdorff Extensions in Single Valued Neutrosophic S Centered Systems ................................................... 327 Saeid Jafari, I. Arockiarani, J. Martina Jency ∗ The Alexandrov-Urysohn Compactness On Single Valued Neutrosophic S Centered Systems ........................ 345 Eman.M.El-Nakeeb, H. ElGhawalby, A.A.Salama, S.A.El-Hafeez Foundation for Neutrosophic Mathematical Morphology ................................................................................. 363 M. K. El Gayyar Smooth Neutrosophic Preuniform Spaces ........................................................................................................ 381 Hewayda ElGhawalby, A. A. Salama Ultra neutrosophic crisp sets and relations ........................................................................................................ 395 A.A.Salama, I.M.Hanafy, Hewayda Elghawalby, M.S.Dabash Neutrosophic Crisp Closed Region and Neutrosophic Crisp Continuous Functions .......................................... 403 Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa A New Order Relation on the Set of Neutrosophic Truth Values ...................................................................... 413 Fu Yuhua Expanding Comparative Literature into Comparative Sciences Clusters with Neutrosophy .............................. 415 Contributors ..................................................................................................................................................... 421 6 New Trends in Neutrosophic Theory and Applications Aims and Scope Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after 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 structure 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 a very important tool in all various areas of data mining, decision making, e-learning, engineering, medicine, social science, and some more. The Book “New Trends in Neutrosophic Theories and Applications” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic information. Some topics deal with data mining, decision making, e- learning, graph theory, medical diagnosis, probability theory, topology, and some more. Florentin Smarandache, Surapati Pramanik 7 New Trends in Neutrosophic Theory and Applications 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 was 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. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. The present book starts by proposing an approach for data mining with single valued neutrosophic information from large amounts of data and then progresses to topics in decision making in neutrosophic environment and neutrosophic hybrid environment, e-learning, graph theory, medical diagnosis, neutrosophic models in sociology, topology, and some more. The book collects thirty original research and application papers from different perspectives covering different areas of neutrosophic studies, such data mining, decision making, e-learning, graph theory, medical diagnosis, probability theory, topology, and some theoretical papers. This book shows examples applications of neutrosophic set and neutrosophic hybrid set in multiple criteria and multiple attribute decision making, medical diagnosis, etc. The first chapter presents the two essential pillars of data mining: similarity measures and machine learning in single valued neutrosophic environment. It shows that neutrosophic logic can perform an important role in data mining method. It defines single valued neutrosophic score function (SVNSF) to aggregate attribute values of each alternative. It also presents an approach of data mining with single valued neutrosophic information from large amounts of data, and furnishes a numerical example for the proposed approach. The second, third, and fourth chapter deal with decision making in neutrosophic hesitant fuzzy information. The second chapter presents a class of distance measures for single-valued neutrosophic hesitant fuzzy sets and discusses their properties with parameter changing. It also provides multi-attribute decision making (MADM), an illustrative example, and a comparison with other existing methods. 9