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Infinite Intuitionistic Fuzzy Series and Product

Since the Atanassov's intuitionistic fuzzy set theory was introduced, many intuitionistic fuzzy aggregation operators have been proposed for the integration of the intuitionistic fuzzy information. It is necessary to extend them to accommodate the infinite situations so that we can deal with the large amount of intuitionistic fuzzy data, and, at the same time, we must solve an important issue that whether the sum of an infinite number of intuitionistic fuzzy numbers is convergent or not. Thus, in this paper, we first put forward the infinite intuitionistic fuzzy series and product. Then, we investigate the properties and the convergences of the infinite intuitionistic fuzzy series and product, respectively. These results greatly enrich the intuitionistic fuzzy calculus theory.