Intuitionistic fuzzy calculus (Q2406168)

Intuitionistic fuzzy sets are introduced 1986 by \textit{K. T. Atanassov} [Fuzzy Sets Syst. 20, 87--96 (1986; Zbl 0631.03040)]. They are characterized not only by a membership function \(m(x)\) but also by a non-membership function \(n(x)\), and \(1-m(x)-n(x)>0\) is called the degree of indeterminacy. In this book, the authors present more or less the results of their own research on intuitionistic fuzzy calculus during the last ten years. Intuitionistic fuzzy calculus is investigated by utilizing intuitionistic fuzzy numbers (IFN) rather than real numbers in classical calculus. They firstly introduce the operational laws of IFNs (geometric and algebraic properties), next, they define the concept of intuitionistic fuzzy functions and present then their results on derivatives, differentials, infinite and definite integrals. Moreover, they discuss aggregation operations of continuous intuitionistic fuzzy information. Finally, they complete their investigations by the complement theory of intuitionistic calculus. Note, that for a given IFN its complement is obtained by changing the role of membership and non-membership values.