On a characterization of fuzzy bags

Authors:
Miguel Delgado;María J. Martín-Bautista;Daniel Sánchez;María A. Vila
Affiliations:
Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain;Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain;Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain;Department of Computer Science and Artificial Intelligence, University of Granada, Granada, Spain
Venue:
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Year:
2003

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Abstract

Bags, also called multisets, were introduced by R. Yager as set-like algebraic structures where elements are allowed to be repeated. Since the original papers by Yager, different definitions of the concept of fuzzy bag, and the corresponding operators, are available in the literature, as well as some extensions of the union, intersection and difference operators of sets, and new algebraic operators. In general, the current definitions of bag pose very interesting issues related to the ontological aspects and practical use of bags. In this paper we introduce a characterization of bags viewing them as the result of a count operation on the basis of a mathematical correspondence. We also discuss on the extension of our alternative characterization of bags to the fuzzy case. On these basis we introduce some operators on bags and fuzzy bags, and we compare them to existing approaches.