Abstract
We consider four different generalizations of bags (alias multisets). We first discuss Yager’s fuzzy bags having different sets of operations. It is shown that one is not a generalization of fuzzy sets but a mapping of them into fuzzy bags, since operations are inconsistent between the two, while the other includes fuzzy sets as particular cases. Third type is called real-valued bags which is simpler than the former two and is a kind of the reduction of fuzzy bags. Finally, the fourth generalization called G-bags includes all three except the first type. It is a minimal extension of the second and the third generalizations. Bag relations are defined for the third type of real-valued bags, which can further be generalized for G-bags.
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