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Different generalizations of bags

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  • Sadaaki Miyamoto

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Sadaaki Miyamoto, 2012. "Different generalizations of bags," Annals of Operations Research, Springer, vol. 195(1), pages 221-236, May.
    • Handle: RePEc:spr:annopr:v:195:y:2012:i:1:p:221-236:10.1007/s10479-011-0980-6
    DOI: 10.1007/s10479-011-0980-6
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    References listed on IDEAS

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    1. Rebai, Abdelwaheb, 1994. "Canonical fuzzy bags and bag fuzzy measures as a basis for MADM with mixed non cardinal data," European Journal of Operational Research, Elsevier, vol. 78(1), pages 34-48, October.
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