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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Basic Concepts Related to Intuitionistic Fuzzy Numbers

Abstract
The concept of fuzzy set, which was proposed by Zadeh (1965), has been paid more and more attention. Zadeh tried to remind people that objective things are not always black or white. For example, dogs, horses and birds are obviously animals, and plants and rocks must not belong to the category of animals, however, for some special
Qian Lei, Zeshui Xu

Chapter 2. Derivatives and Differentials of Intuitionistic Fuzzy Functions

Abstract
Calculus, which is an important branch of classical mathematics, is the mathematical study of change. Like the calculus of real numbers and the complex numbers, the calculus of IFNs is very significant to the theory environment. Thus, this chapter aims to do work in the calculus in intuitionistic fuzzy environment.
Qian Lei, Zeshui Xu

Chapter 3. Integrals of Intuitionistic Fuzzy Functions

Abstract
Based on the derivatives of intuitionistic fuzzy functions (IFFs), this chapter first introduce its inverse operation, which is the indefinite integrals of IFFs, and then investigates the properties of the indefinite integrals of IFFs. In addition, this chapter deliberates on the definite integrals of IFFs.
Qian Lei, Zeshui Xu

Chapter 4. Aggregation Operations of Continuous Intuitionistic Fuzzy Information

Abstract
In this chapter, we focus on a problem about how to aggregate the IFNs spreading all over an area, which means that each point in a two-dimensional plane to be aggregated is an IFN that we want to aggregate.
Qian Lei, Zeshui Xu

Chapter 5. Relationships Among IFWA Operator, IFIA Operator and Definite Integrals of IFFs

Abstract
Chapter 5 first reveals the relationship between the IFIA operator introduced in Chap. 4 and the definite integrals of IFFs defined in Chap. 3, where the IFIA operator is used to aggregate continuous intuitionistic fuzzy information. Even though the motivation and the purpose of proposing the IFIA operator and the integral of IFFs are completely different, this chapter builds the bridge between the two different concepts, which manifests that the IFIA operator is actually the definite integral of a special IFF. Moreover, we will also show the relationship between the IFIA operator and the IFWA operator from another perspective, which is different from one given in Chap. 4, which declares that the IFIA operator is the continuous form of the IFWA operator.
Qian Lei, Zeshui Xu

Chapter 6. Complement Theory of Intuitionistic Fuzzy Calculus

Abstract
In this chapter, we first introduce the complement operator of IFNs, which actually interchanges the membership degree and the non-membership degree of an IFN.
Qian Lei, Zeshui Xu

Backmatter

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