Zadeh introduced in 1965 the theory of fuzzy sets, in which truth values are modelled by numbers in the unit interval [0, 1], for tackling mathematically the frequently appearing in everyday life partial truths. In a second stage, when membership functions were reinterpreted as possibility distributions, fuzzy sets were extensively used to embrace uncertainty modelling. Uncertainty is defined as the shortage of precise knowledge or complete information and possibility theory is devoted to the handling of incomplete information. Zadeh articulated the relationship between possibility and probability, noticing that what is probable must preliminarily be possible. Following the Zadeh’s fuzzy set, various generalizations (intuitionistic, neutrosophic, rough, soft sets, etc.) have been introduced enabling a more effective management of all types of the existing in real world uncertainty. This book presents recent theoretical advances and applications of fuzzy sets and their extensions to Science, Humanities and Education.

This book:

Presents a qualitative assessment of big data in the education sector using linguistic Quadri partitioned single valued neutrosophic soft sets.
Showcases application of n-cylindrical fuzzy neutrosophic sets in education using neutrosophic affinity degree and neutrosophic similarity Index.
Covers scientific evaluation of student academic performance using single value neutrosophic Markov chain.
Illustrates multi-granulation single-valued neutrosophic probabilistic rough sets for teamwork assessment.
Examines estimation of distribution algorithm based on multiple attribute group decision-making to evaluate teaching quality.

It is primarily written for Senior undergraduate and graduate students and academic researchers in the fields of electrical engineering, electronics and communication engineering, computer science and engineering.

About the Author

Said Broumi is serving as an Assistant Professor at Regional Center for the Professions of Education and Training, Casablanca-Settat, Morocco. Dr. Broumi Said completed his MSc and PhD in Computer Science from University of Hassan II of Casablanca, Morocco. He is permanent member at Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco. His research interests are in the field of graph theory, extended fuzzy graphs, decision analysis and neutrosophic theory. He has diversity in his research work. He has published several works on neutrosophic graph theory, soft set theory, multi-attribute decision analysis and some alternative theories of Neutrosophic Mathematics. He has published more than 200 research articles in international peer-reviewed ISI Indexed /Impact factor journals. Some of his papers have been published in high impact journals including, Complex & Intelligent Systems, Computational and Applied Mathematics, Symmetry, and Journal of Neutrosophic Set and Systems. His work has largely been cited and total citation is more than 5992 (Scholar Google, H-index 41). He has presented his research work at some national as well as international conferences. He has been acting as a reviewer for a number of international journals. He is also an Editor in chief of the following journals:

1. International Journal of Neutrosophic Set and Systems

2. International Journal of Neutrosophic Science

Dr. D. Nagarajan is a Professor in the Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India. He received his Ph.D., from Manonmaniam Sundaranar University,2007. He has a total of twenty-three years of experience in both academia and research National as well as International Institutions. He has published 110 research articles in international reputed journals as well as serving as a reviewer for many peers reviewed journals. He has two patents on his credit.His research interests include Stochstic processes ,Fuzzy sets and system, Neutrosophic control systems and image processing. He is also associated with various educational and research societies, like IMS, ISTE, IAENG, AMTI and ISRD. He is the Guest editor of 3 Journals, also coauthor of 3 books published by different publishers like Lambert and Notion Press.He is associate editor of Franklin Open journal.

Dr. Seyyed Ahmad Edalatpanah is Associate Professor at the Ayandegan Institute of Higher Education, Tonekabon, Iran. S. A. Edalatpanah received his Ph.D. degree in Applied Mathematics from the University of Guilan, Rasht, Iran. He is currently working as the Chief of R&D at the Ayandegan Institute of Higher Education, Iran. He is also an academic member of Guilan University and the Islamic Azad University of Iran. Dr. Edalatpanah's fields of interest include numerical computations, operational research, uncertainty, fuzzy set and its extensions, numerical linear algebra, soft computing, and optimization. He has published over 150 journal and conference proceedings papers in the above research areas. He serves on the editorial boards of several international journals. He is also the Director-in-Charge of the Journal of Fuzzy Extension & Applications. Currently, he is president of "International Society of Fuzzy Set Extensions and Applications" (ISFSEA).

Michael Gr. Voskoglou (B.Sc., M.Sc., M.Phil., Ph.D. in Mathematics) is an Emeritus Professor of Mathematical Sciences at the School of Engineering of the Graduate Technological Educational Institute (T. E. I.) of Western Greece, which has recently been joined with the University of Peloponnese. He was a full Professor at the same Institute from 1987 to 2010. He was also an instructor at the Hellenic Open University, at the Mathematics Department of the University of Patras, at the Schools of Primary and Secondary In – Service Teachers’ Training in Patras and a teacher of mathematics at the Greek Public Secondary Education (1972-1987). He worked as a Visiting Researcher at the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences in Sofia for three years (1997-2000), under sabbatical. He has lectured as a Visiting Professor in postgraduate courses at the School of Management of the University of Warsaw (2009), at the Department of Operational Mathematics of the University of Applied Sciences in Berlin (2010) and at the Mathematics Department of the National Institute of Technology of Durgapur (2016) under a grand of the Indian Government. He is the author/editor of 18 books in Greek and in English language and of more than 600 papers published in international journals, book chapters and proceedings of conferences of more than 30 countries in the five continents, with more than 2000 citations from other researchers. He used to be the Editor in Chief of the “International Journal of Applications of Fuzzy Sets and Artificial Intelligence” (2011-2020) and currently he is a reviewer of the American Mathematical Society, Editor in Chief of the journal “Construction, Design, Maintenance” (www.wseas.com/journals/dcm/index.php) and member of the Editorial Board of many other international scientific journals. He has conducted five programs of technological research on applications of quantitative methods to Management (1989–1997), he has supervised many student dissertations, and he was external examiner of Ph.D. dissertations at Universities of Egypt, India and Saudi Arabia. He is the recipient of many scholarships, distinctions and honorary awards and member of many scientific associations (AMS, HMS, ICTMA, IETI, etc.). His research interests include Algebra, Fuzzy Logic, Markov Chains, Artificial Intelligence and Mathematics Education.

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