Different generalizations of bags

作者：Miyamoto Sadaaki^*

来源：Annals of Operations Research, 2012, 195(1): 221-236.

DOI：10.1007/s10479-011-0980-6

• Bags
• Fuzzy bags
• t-norms
• Bag relations

We consider four different generalizations of bags (alias multisets). We first discuss Yager%26apos;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.

• 出版日期2012-5