The first fuzzy set type, which was introduced to the iteration by Zadeh in 1965 and called ordinary fuzzy sets or type-1 fuzzy sets, started to expand with type-2 fuzzy sets in 1975.
Neutrosophic sets, unstable fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, spherical fuzzy sets have been the new extensions added to the fuzzy set theory up to the present day.
This book is full of introductory and educational information from type-1 fuzzy sets to the fuzzy set extensions that have been recently introduced to the literature.
Numerous numerical examples are given to facilitate the understanding of the new extensions.
In addition, various article and book sources are given at the end of each chapter in addition to the resources used.
The book is prepared in a simple language so that undergraduate and graduate students can easily learn fuzzy sets and their extensions.
University students, as well as managers involved in decision-making processes and engineers working in the field of control theory can benefit from the book.
We hope that our book will be useful to all university students and managers and engineers working in industry.
1- Ordinary Fuzzy Sets
1.1 - From Classical Logic to Fuzzy Logic
1.2-Continuous Ordinary Fuzzy Sets
1.2.1-Triangular Fuzzy Numbers
1.2.2-Agglomeration Operators on Triangular Fuzzy Numbers
1.2.3-Trapezoidal Fuzzy Numbers
1.2.3.1-Arithmetic Operations on Trapezoidal Fuzzy Numbers
1.2.3.2-Agglomeration Operators on Trapezoidal Intuitive Fuzzy Numbers
1.3-Interval Valued Ordinary Fuzzy Sets
1.4-Agglomeration Operators on Interval Valued Triangular Fuzzy Numbers
2- Type-2 Fuzzy Sets
2.1-Type-2 Fuzzy Sets in Literature
2.2-Type-1 and Type-2 Fuzzy Inference Systems
2.3-Type-2 Fuzzy Set Operations
3- Intuitive Fuzzy Sets
3.1-Single Valued Intuitive Fuzzy Sets
3.2-Interval Valued Intuitive Fuzzy Sets
3.3-Triangular Intuitive Fuzzy Numbers
3.4-Trapezoidal Intuitive Fuzzy Numbers
3.5-Circular Intuitive Fuzzy Sets
4- Unstable Fuzzy Sets
4.1-Single Valued Unstable Fuzzy Sets
4.2-Interval Valued Unstable Fuzzy Sets
4.3-Unstable Fuzzy Linguistic Term Set
5- Intuitive Fuzzy Set Extensions
5.1-Pythagorean Fuzzy Sets
5.2-Interval Valued Pythagorean Fuzzy Sets
5.3-Fermat Fuzzy Sets
5.4-Qth Degree Intuitive Fuzzy Sets
6- Image Fuzzy Sets and Extensions
6.1-Image Fuzzy Sets
6.2-Spherical Fuzzy Sets
6.3-T-Spherical Fuzzy Sets
7- Sets with Independent Degree of Membership (Neutrosophic Sets)
7.1-Single Valued Independent Degree of Membership Sets
7.2-Interval Valued Independent Degree of Membership Sets
Prof. Dr. Cengiz KAHRAMAN
He was born in Üsküdar in 1965. He graduated from Kuleli Military High School in 1983. He started his higher education at Istanbul Technical University, Department of Industrial Engineering in 1984. He started working as a research assistant in this department, where he graduated in 1988. He received his bachelor's degree in Industrial Engineering in 1988, his master's degree in Industrial Engineering in 1990 and his doctorate in Industrial Engineering in 1996 from ITU.
Prof. Kahraman received the titles of assistant associate professor in 1996, associate professor in 1998 and professor in 2003 from Istanbul Technical University. Prof. Dr. Cengiz Kahraman's main areas of study include engineering economics, quality management, multi-criteria decision making, statistical decision making and fuzzy decision making.
Prof. Kahraman has written more than 320 internationally indexed articles, more than 220 international reports, and more than 100 international book chapters.
He has edited 25 international books and guest edited special issues of numerous international journals. He currently serves on the editorial boards of more than 20 international journals, including one as editor-in-chief. Cengiz Kahraman, who has also organized many international scientific conferences, served as the Vice Dean of the ITU Faculty of Business Administration between 2004-2007 and as the Head of the ITU Department of Industrial Engineering between 2007-2010, and also held administrative positions at the university.
According to the research results published by Turkishtime magazine in 2017, Prof. Dr. Cengiz Kahraman, who was ranked 40th on the list of “The Top 100 Turks Leading the World of Science,” also won the TÜBİTAK Science Award in 2018.
Prof. Dr. Başar ÖZTAYŞİ
Prof. Dr. Sezi ÇEVİK ONAR
He completed his PhD in Industrial Engineering at ITU, and was a student at Eindhoven Technical University and Copenhagen Business School during his studies.
His research interests include intelligent systems in management, fuzzy logic, innovation management, creative thinking, strategic management, business planning and multi-criteria decision making. He has taken part in many private and publicly supported national and international projects funded by the European Union, such as intelligent system design, organization design and human resources management system design.
He worked as a visiting professor and researcher at Ecole des Ponts ParisTech, Rennes Business School, and Troyes Technical University.
His various articles have been published in high impact factor journals such as Energy, Computers & Industrial Engineering, Supply Chain Management: An International Journal and Expert Systems with Applications.
He edited the book "Intelligent Systems in Engineering Management" published by Springer and is on the editorial boards of many prestigious journals indexed by SCI.
His publications have been cited more than 4000 times and his h-index is 30. He was recognized as one of the most influential researchers in the field of artificial intelligence by Stanford University and Elsevier in 2021. He is on the editorial boards of the Journal of Engineering Applications of Artificial Intelligence, Journal of Intelligent & Fuzzy Systems and Modeling Journal, and International Journal of Computational Intelligence.