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Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory, other try to handle imprecision and uncertainty in different way. In this paper, we introduce a new notion of picture fuzzy sets (PFS), which are directly extensions of fuzzy sets and of intuitonistic fuzzy sets (Atanassov). Then some operations on picture fuzzy sets are defined and some properties of these operations are considered. Here the basic preliminaries of PFS theory are presented.
Cường et al. (Sun,) studied this question.