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• Chapter 1. Introduction
• Chapter 2. Normalizing Rank Aggregation-based Method
• Chapter 3. Eigenvector Method
• Chapter 4. Logarithmic Least Squares Method
• Chapter 5. A Chi-Square Method
• Chapter 6. A Least Deviation Method
• Chapter 7. Priorities from Fuzzy Best Worst Method Matrix
• Chapter 8. Weighted Least Square Method
• Chapter 9. Priorities from Incomplete Hesitant Fuzzy Reciprocal Preference Relations

As we know, multiplicative preference relations (or called pairwise comparisons in AHP) were proposed by Dr. Thomas L Saaty. One important work is to derive its priority from pairwise comparisons. It has been proposed many methods to derive priority for multiplicative preference relation. On the basis of fuzzy sets, the fuzzy reciprocal preference relation is proposed and is extended to the incomplete contexts. However, how to derive the priorities from incomplete fuzzy reciprocal preference relations is an interesting and challenging work. This book systematically presents the theories and methodologies for deriving priorities from incomplete fuzzy reciprocal preference relations. This book can be divided into three parts. In the first part, this book introduces the basic concepts of fuzzy reciprocal preference relations and incomplete fuzzy reciprocal preference relations. Then, two consistencies of complete fuzzy reciprocal preference relations are introduced: additive consistency and multiplicative consistency. Then, the relationships between the fuzzy reciprocal elements and the weights are showed. Afterward, in the second part, different priority methods are presented. The inconsistency repairing procedures are also proposed. Last, the priority method for incomplete hesitant fuzzy reciprocal preference relations is presented. This book can be used as a reference for researchers in the areas of management science, information science, systems engineering, operations research, and other relevant fields. It can also be employed as a textbook for upper-level undergraduate students and graduate students

• 1. Introduction to fuzzy sets, soft sets, mulit sets and their generations
• 2. Fuzzy soft multiset theory
• 3. Relation on fuzzy soft multisets
• 4. Topology on fuzzy soft multisets
• 5. Fuzzy soft multi points and their sequences
• 6. Fuzzy soft multi compactness and separation axioms
• 7. Fuzzy soft multiset based applications
• 8. Generalization of fuzzy soft multisets
• 9. Intuitionistic fuzzy soft multiset theory
• 10. Application of intuitionistic fuzzy soft multisets. .

This book discusses major theories and applications of fuzzy soft multisets and their generalization which help researchers get all the related information at one place. The primary objective of this book is to help bridge the gap to provide a textbook on the theories in fuzzy soft multisets and their applications in real life. It is targeted to researchers and students working in the field of fuzzy set theory, multiset theory, soft set theory and their applications. Uncertainty, vagueness and the representation of imperfect knowledge have been a problem in many fields of research, including artificial intelligence, network and communication, signal processing, machine learning, computer science, information technology, as well as medical science, economics, environments and engineering. There are many mathematical tools for dealing with uncertainties. They include fuzzy set theory, multiset theory, soft set theory and soft multiset theory.

• Part I. Preliminaries of Spherical Fuzzy Set Theory
• Properties and Arithmetic Operations of Spherical Fuzzy Sets
• Interval Valued Spherical Fuzzy Aggregation Operators and Their Application in Decision Making Problem
• Spherical Fuzzy Numbers and Multi-criteria Decision-Making
• The Generalized Dice Similarity Measures for Spherical Fuzzy Sets and Their Applications
• Spherical Fuzzy Bonferroni Mean Aggregation Operators and Their Applications to Multiple-Attribute Decision Making
• Spherical Fuzzy Soft Sets
• Decision Making Method Based on Spherical Fuzzy Graphs
• Part II. Spherical Fuzzy Multi-criteria Decision Making
• Optimal Site Selection of Electric Vehicle Charging Station by Using Spherical Fuzzy TOPSIS Method
• Spherical Fuzzy VIKOR with SWAM and SWGM Operators for MCDM
• Simple Additive Weighting and Weighted Product Methods Using Spherical Fuzzy Sets
• Prioritizing Manufacturing Challenges of a Contract Manufacturing Company for Personal Auto by Using Spherical WASPAS Method
• Assessment of Livability Indices of Suburban Places of Istanbul by Using Spherical Fuzzy CODAS Method
• Interval-Valued Spherical Fuzzy MULTIMOORA Method and Its Application to Industry 4.0
• Global Supplier Selection with Spherical Fuzzy Analytic Hierarchy Process
• Hospital Performance Assessment Using Interval-Valued Spherical Fuzzy Analytic Hierarchy Process
• Evaluating Geothermal Energy Systems Using Spherical Fuzzy PROMETHEE
• Delivery Drone Design Using Spherical Fuzzy Quality Function Deployment
• Analysis of Usability Test Parameters Affecting the Mobile Application Designs by Using Spherical Fuzzy Sets
• Part III. Mathematical Programming with Spherical Fuzzy Sets
• Spherical Fuzzy Linear Programming Problem
• Spherical Fuzzy Goal Programming Problem
• Spherical Fuzzy Geometric Programming Problem.

This book introduces readers to the novel concept of spherical fuzzy sets, showing how these sets can be applied in practice to solve various decision-making problems. It also demonstrates that these sets provide a larger preference volume in 3D space for decision-makers. Written by authoritative researchers, the various chapters cover a large amount of theoretical and practical information, allowing readers to gain an extensive understanding of both the fundamentals and applications of spherical fuzzy sets in intelligent decision-making and mathematical programming.
(source: Nielsen Book Data)

• Chapter 1: Hesitant Fuzzy Set.-
• Chapter 2: Hesitant Fuzzy Linguistic Term Set.-
• Chapter 3: Neutrosophic Hesitant Fuzzy Set.-
• Chapter 4: Pythagorean Hesitant Fuzzy Set.-
• Chapter 5: q-Rung Orthopair Hesitant Fuzzy Set.-
• Chapter 6: Probabilistic Hesitant Fuzzy Set.-
• Chapter 7: Type 2 Hesitant Fuzzy Set.-
• Chapter 8: Hesitant Bipolar Fuzzy Set.-
• Chapter 9: Cubic Hesitant Fuzzy Set.-
• Chapter 10: Complex Hesitant Fuzzy Set.-
• Chapter 11: Picture Hesitant Fuzzy Set.-
• Chapter 12: Spherical Hesitant Fuzzy Set.
• (source: Nielsen Book Data)

Covering a wide range of notions concerning hesitant fuzzy set and its extensions, this book provides a comprehensive reference to the topic. In the case where different sources of vagueness appear simultaneously, the concept of fuzzy set is not able to properly model the uncertainty, imprecise and vague information. In order to overcome such a limitation, different types of fuzzy extension have been introduced so far. Among them, hesitant fuzzy set was first introduced in 2010, and the existing extensions of hesitant fuzzy set have been encountering an increasing interest and attracting more and more attentions up to now. It is not an exaggeration to say that the recent decade has seen the blossoming of a larger set of techniques and theoretical outcomes for hesitant fuzzy set together with its extensions as well as applications.As the research has moved beyond its infancy, and now it is entering a maturing phase with increased numbers and types of extensions, this book aims to give a comprehensive review of such researches. Presenting the review of many and important types of hesitant fuzzy extensions, and including references to a large number of related publications, this book will serve as a useful reference book for researchers in this field.
(source: Nielsen Book Data)

• A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making.- A new method for Atanassov's interval-valued intuitionistic fuzzy MAGDM with incomplete attribute weight information.- Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees.- A selection method based on MAGDM with interval-valued intuitionistic fuzzy sets, Mathematical Problems in Engineering.- Aggregating decision information into interval-valued intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making.- A novel method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations.- Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making.- A three-phase method for group decision making with interval-valued intuitionistic fuzzy preference relations.- A group decision-making method considering both the group consensus and multiplicative consistency of interval-valued intuitionistic fuzzy preference relations.
• (source: Nielsen Book Data)

This is the first book to provide a comprehensive and systematic introduction to the ranking methods for interval-valued intuitionistic fuzzy sets, multi-criteria decision-making methods with interval-valued intuitionistic fuzzy sets, and group decision-making methods with interval-valued intuitionistic fuzzy preference relations. Including numerous application examples and illustrations with tables and figures and presenting the authors' latest research developments, it is a valuable resource for researchers and professionals in the fields of fuzzy mathematics, operations research, information science, management science and decision analysis.
(source: Nielsen Book Data)

• Introduction.- Classification.- Understanding OWA based fuzzy rough sets.- Fuzzy rough set based classification of semi-supervised data.- Multi-instance learning.- Multi-label learning.- Conclusions and future work.- Bibliography.
• (source: Nielsen Book Data)

This book presents novel classification algorithms for four challenging prediction tasks, namely learning from imbalanced, semi-supervised, multi-instance and multi-label data. The methods are based on fuzzy rough set theory, a mathematical framework used to model uncertainty in data. The book makes two main contributions: helping readers gain a deeper understanding of the underlying mathematical theory; and developing new, intuitive and well-performing classification approaches. The authors bridge the gap between the theoretical proposals of the mathematical model and important challenges in machine learning. The intended readership of this book includes anyone interested in learning more about fuzzy rough set theory and how to use it in practical machine learning contexts. Although the core audience chiefly consists of mathematicians, computer scientists and engineers, the content will also be interesting and accessible to students and professionals from a range of other fields. .
(source: Nielsen Book Data)

• 1. Introduction.-
• 2. The Nature of Similarity.-
• 3. Historic Assessment of Compatibility.-
• 4. Foundations of Fuzzy Set Theory.-
• 5. Compatibility in Fuzzy Inference.-
• 6. Compatibility in Approximate Reasoning.-
• 7. Set-Theoretic Measures.-
• 8. Proximity-Based Measures.-
• 9. Logic-Based Measures.-
• 10. Fuzzy-Valued Similarity Measures.-
• 11. Generic Classification Domain.-
• 12. Set-Theoretic Comparative Study.-
• 13. Proximity-Based Comparative Study.-
• 14. Logic-Based Comparative Study.-
• 15. Comparison Among the Three Classes.- Index of Notation.- References.
• (source: Nielsen Book Data)

Assessing the degree to which two objects, an object and a query, or two concepts are similar or compatible is a fundamental component of human reasoning and consequently is critical in the development of automated diagnosis, classification, information retrieval and decision systems. The assessment of similarity has played an important role in such diverse disciplines such as taxonomy, psychology, and the social sciences. Each discipline has proposed methods for quantifying similarity judgments suitable for its particular applications. This book presents a unified approach to quantifying similarity and compatibility within the framework of fuzzy set theory and examines the primary importance of these concepts in approximate reasoning. Examples of the application of similarity measures in various areas including expert systems, information retrieval, and intelligent database systems are provided.
(source: Nielsen Book Data)

• Part 1 Fundamentals of fuzzy sets: basic notions and concepts of fuzzy sets - set membership and fuzzy sets, basic definitions of a fuzzy set, types of membership functions, characteristics of a fuzzy set, basic relationships between fuzzy sets - equality and inclusion, fuzzy sets and sets - the representation theorem, the extension principles, membership function determination, generalizations of fuzzy sets, chapter summary, problems, references
• fuzzy set operations - set theory operations and their properties, triangular norms, aggregation operations on fuzzy sets, sensitivity of fuzzy sets operators, negations, comparison operations on fuzzy sets, chapter summary, problems, references
• information-based characterization of fuzzy sets -entropy measures of fuzziness, energy measures of fuzziness, specificity of a fuzzy set, frames of cognition, information encoding and decoding using linguistic landmarks, decoding mechanisms for pointwise data, decoding using membership functions of the linguistic terms of the codebook, general possibility-necessity decoding, distance between fuzzy sets based on their internal, linguistic representation, chapter summary, problems, references
• fuzzy relations and their calculus -relations and fuzzy relations, operations on fuzzy relations, compositions of fuzzy relations, projections and cylindric extensions of fuzzy relations, binary fuzzy relations, some classes of fuzzy relations, fuzzy-relational equations, estimation and inverse problem in fuzzy relational equations, solving fuzzy-relational equations with the sup-t composition, solutions to dual fuzzy-relational equations, adjoint fuzzy-relational equations, generaliations of fuzzy relational equations, approximate solutions to fuzzy-relational equations, chapter summary, problems, references
• fuzzy numbers - defining fuzzy numbers, interval analysis and fuzzy numbers, computing with fuzzy numbers, triangular fuzzy numbers and basic operations, general formulas for LR fuzzy numbers, accumulation of fuzziness in computing with fuzzy numbers, inverse problem in computation with fuzzy numbers, fuzzy numbers and approximate operations, chapter summary, problems, references
• fuzzy modelling - fuzzy models - beyond numerical computations, main phases of system modelling, fundamental design objectives in system modelling, general topology of fuzzy models, compatibility of encoding and decoding modules, classes of fuzzy models, verification and validation of fuzzy models, chapter summary, problems, references. Part 3 Problem solving with fuzzy sets: methodology -analysis and design, fuzzy controllers and fuzzy control, mathematical programming and fuzzy optimization, chapter summary, problems, references
• case studies - traffic intersection control, distributed traffic control, elevator group control, induction motor control, communication network planning, neurocomputation in fault diagnosis of dynamic systems, multicommodity transportation planning in railways.
• (source: Nielsen Book Data)

The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book aims to bridge the gap between developed theory and practice. The authors explain what fuzzy sets are, why they work, when they should be used (and when they shouldn't), and how to design systems using them. The authors take a top-down approach to the design for detailed algorithms. They begin with illustrative examples, explain the fundamental theory and design methodologies, and then present more-advanced case studies dealing with practical tasks. While they use mathematics to introduce concepts, they ground them in examples of real-world problems that can be solved through fuzzy set technology. The only mathematics prerequisites are basic knowledge of introductory calculus.
(source: Nielsen Book Data)

• 1 On the Evolution of the Mathematics of Fuzziness
• 2 Closedness and Upper Semi-Continuity of Fuzzy Multivalued Mappings
• 3 An Order-Theorethic Approach to Solving Sup-T Equations
• 4 Towards a Possibilistic Logic
• 5 Fuzzy Dynamic Programming: a New Quality Through Fuzzy Sets
• 6 On Transitivity of Fuzzy Preference Relations in Ranking Fuzzy Numbers
• 7 Information Aggregation: Ethical and Computational Issues
• 8 On the Notion State in Multistate Structure Function Theory
• 9 Fuzzy Logic And Neural Systems
• 10 Some Mathematical Problems of Fuzzy Controllers
• 11 Keep Fuzzy Controllers Fuzzy
• 12 Comparative Study of Fuzzy Control, Neural Network Control And Neurofuzzy Control.

Fuzzy Set Theory and Advanced Mathematical Applications contains contributions by many of the leading experts in the field, including coverage of the mathematical foundations of the theory, decision making and systems science, and recent developments in fuzzy neural control. The book supplies a readable, practical toolkit with a clear introduction to fuzzy set theory and its evolution in mathematics and new results on foundations of fuzzy set theory, decision making and systems science, and fuzzy control and neural systems. Each chapter is self-contained, providing up-to-date coverage of its subject. Audience: An important reference work for university students, and researchers and engineers working in both industrial and academic settings.

• Construction of a Topological Degree theory in Generalized Sobolev Spaces
• Existence of positive solutions of nonlinear fractional quadratic differential equations
• Comments on fuzzy sets, interval type-2 fuzzy sets, general type-2 fuzzy sets and intuitionistic fuzzy sets
• Quotient Rings Induced Via Intuitionistic Fuzzy Ideals
• A fourth order Runge-Kutta Gill method for the numerical solution of intuitionistic fuzzy differential equations
• Task Parameter Impacts in Fuzzy Real Time Scheduling
• Framework for Optimization of Intuitionistic and Type-2 Fuzzy Systems in Control Applications
• Approximation of Intuitionistic Fuzzy Systems for Time Series Analysis in Plant Monitoring and Diagnosis
• New fractional derivative in Colombeau algebra
• Controlled fuzzy evolution equations
• Multiplication Operation and Powers of Trapezoidal Fuzzy Numbers
• Intuitioinistic fuzzy Hilbert space
• On Intuitionistic fuzzy Laplace transforms for second order intuitionistic fuzzy differential equations
• Approximate Solution of Intuitionistic Fuzzy Differential Equations by using Picard's method
• Fuzzy Cross Language Plagiarism Detection Approach Based on Semantic Similarity and Hadoop MapReduce
• Existence results for an impulsive fractional integro-differential equations with a non-compact semigroup
• Existence results of hybrid fractional integro-differential equations
• Convergence on intuitionistic fuzzy metric space
• Graphical Representation of Intuitionistic Membership Functions for its efficient use in Intuitionistic Fuzzy Systems
• Existence of mild solutions for an impulsive fractional integro-differential equations with non-local condition
• Fixed point theory, Contractive mapping, Fuzzy metric space
• Common fixed point theorems in b-Menger spaces
• On Intuitionistic Fuzzy Vector Spaces
• Time-dependent Neutral stochastic delay partial differential equations driven by Rosenblatt process in Hilbert space.

This book aims at providing an overview of state-of-the-art in both the theory and methods of intuitionistic fuzzy logic, partial differential equations and numerical methods in informatics. It covers topics such as fuzzy intuitionistic Hilbert spaces, intuitionistic fuzzy differential equations, fuzzy intuitionistic metric spaces, and numerical methods for differential equations. It reports on applications such as fuzzy real time scheduling, intelligent control, diagnostics and time series prediction. Chapters were carefully selected among contributions presented at the second edition of the International Conference on Intuitionistic Fuzzy Sets and Mathematical Science, ICIFSMAS, held on April 11-13, 2018, at Al Akhawayn University of Ifrane, in Morocco.

• Survey of fundamental notions
• fuzzy set theory
• the model of natural language semantics and linguistic variables
• fuzzy logic
• decision and control
• fuzzy systems
• fuzzy algorithms and programming languages
• other applications
• general problems of fuzzy set theory.
• (source: Nielsen Book Data)

This volume contains a systematic account of a new branch of mathematics, fuzzy sets, which seeks to overcome the problems of applying mathematics to the real world. Fuzzy models have been used for such diverse problems as weather forecasting, predictions of water flow in rivers and flooding, and capital cost estimates in the chemical industry. This monograph provides a detailed exposition of the fuzzy set theory and some of its applications, containing many of the author's original results together with those of other Czech scientists. The first section of the book gives information on fuzzy set theory, fuzzy logic and the model of natural language semantics, which together form an integrated theory based on the unified structure of membership degrees. The second section of the text presents selected applications of fuzzy set theory, such as decision-making, fuzzy systems, algorithms and mathematical programming. The book concludes with various problems, such as determination of the membership function and mathematical foundations of the theory. This book should be of interest to postgraduates and researchers in pure and applied mathematics, and specialists in artificial intelligence, computational linguistics, systems engineering and expert systems.
(source: Nielsen Book Data)

The use of fuzzy logic has become prominent in a variety of fields and applications. By implementing these logic sets, problems and uncertainties are more effectively resolved. Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices is a pivotal reference source for the latest scholarly perspectives on the interdisciplinary use of fuzzy logic theory, focusing on the application of sets and matrices. Highlighting theoretical framework and empirical research findings, this book is ideally designed for academics, practitioners, upper-level students, and professionals interested in an innovative overview of fuzzy logic sets and matrices.
(source: Nielsen Book Data)

• Intuitionistic Fuzzy Sets as a Generalization of Fuzzy Sets
• Distances
• Similarity Measures between Intuitionistic Fuzzy Sets.

This book presents the state-of-the-art in theory and practice regarding similarity and distance measures for intuitionistic fuzzy sets. Quantifying similarity and distances is crucial for many applications, e.g. data mining, machine learning, decision making, and control. The work provides readers with a comprehensive set of theoretical concepts and practical tools for both defining and determining similarity between intuitionistic fuzzy sets. It describes an automatic algorithm for deriving intuitionistic fuzzy sets from data, which can aid in the analysis of information in large databases. The book also discusses other important applications, e.g. the use of similarity measures to evaluate the extent of agreement between experts in the context of decision making.

• Hesitant Fuzzy Aggregation Operators and Their Applications
• Distance, Similarity, Correlation, Entropy Measures and Clustering
• Algorithms for Hesitant Fuzzy Information
• Hesitant Preference Relations
• Hesitant Fuzzy MADM Models.

This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) characterized by uncertain ("hesitant") information. Because of its clarity and self contained explanations, the book can also be adopted as a textbook from graduate and advanced undergraduate students