Abstract
In this paper, we study two new binary operations, which are addition and scalar multiplication, for intuitionistic fuzzy numbers (IFNs). Thereafter, we introduce a semi-linear space for IFNs that it is called the narrow metric semi-linear space— $$L^{*}$$ . At the same time, we present a new type of intuitionistic fuzzy functions with a real domain and propose a number of concepts and properties for these functions such as geometric difference, geometric differentiability, derivative and integral. In addition, we give a model of initial value problem for intuitionistic fuzzy differential equations and present its application to an AIDS model. Some examples are given to illustrate the theoretical results.
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