This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.

The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.

This book mainly introduces the latest development of generalized intuitionistic multiplicative fuzzy calculus and its application. The book pursues three major objectives: (1) to introduce the calculus models with concrete mathematical expressions for generalized intuitionistic multiplicative fuzzy information; (2) to introduce new information fusion methods based on the definite integral models; and (3) to clarify the involved approaches bymilitary case. The book is especially valuable for readers to understand how the theoretical framework of generalized intuitionistic multiplicative fuzzy calculus is constructed, not only discrete or continuous but also correlative (generalized) intuitionistic (multiplicative) fuzzy information is aggregated based on the definite integral models and the theory with a military practice is integrated, which would deepen the understanding and give researchers more inspiration in practical decision analysis under uncertainties.

This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author ́s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author ́s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.

Complex problems and systems, which prevail in the real world, cannot often be tackled and solved either by traditional methods offered by mathematics or even the traditional computer science (CS) and and artificial intelligence (AI)..). What is the way out of this dilemma? Advanced methodologies, and tools and techniques, „mimicking” human reasoning or the behavior of animals, animal populations or certain parts of the living bod, based on traditional computer science science and the initial approaches of artificial intelligence are often referred to as biologically inspired methods, or often computational intelligence (CI). Computational intelligence offers effective and efficient solutions to many „unsolvable" problems problems. However, it is far from being a ready to use and complete collection of approaches, and is rather a continuously developing field without clear borders. The emerging new models and algorithms of computational intelligence are deeply rooted in the vast apparatus of traditional mathematics. Thus, the investigation of connections and synergy between mathematics and computational intelligence is an eminent goal which is periodically pursued by a group of mathematicians and computational intelligence researchers who regularly attand the annual European Symposia on Computational Intelligence and Mathematics (ESCIM). Some relevant papers from the last ESCIM-2020 are included in this volume.

This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.