Fuzzy Sets and Systems
BBTOPSIS: a bag based technique for order preference by similarity to ideal solution
Fuzzy Sets and Systems
Fuzzy Sets and Systems
On the theory of bags and lists
Information Sciences: an International Journal
Formal Concept Analysis: Mathematical Foundations
Formal Concept Analysis: Mathematical Foundations
A probabilistic definition of a nonconvex fuzzy cardinality
Fuzzy Sets and Systems
The Magic of Duplicates and Aggregates
VLDB '90 Proceedings of the 16th International Conference on Very Large Data Bases
Information clustering based on fuzzy multisets
Information Processing and Management: an International Journal - Modelling vagueness and subjectivity in information access
Multirelations: semantice and languages
VLDB '85 Proceedings of the 11th international conference on Very Large Data Bases - Volume 11
Gradual elements in a fuzzy set
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Scalar and fuzzy cardinalities of crisp and fuzzy multisets
International Journal of Intelligent Systems - Fuzzy Bags, Cardinality, and Quantification
An extended characterization of fuzzy bags
International Journal of Intelligent Systems - Fuzzy Bags, Cardinality, and Quantification
The set of fuzzy rational numbers and flexible querying
Fuzzy Sets and Systems
A framework for multiset merging
Fuzzy Sets and Systems
On a non-nested level-based representation of fuzziness
Fuzzy Sets and Systems
Gradual Numbers and Their Application to Fuzzy Interval Analysis
IEEE Transactions on Fuzzy Systems
A Possibility-Theoretic View of Formal Concept Analysis
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
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In this paper we claim that, though algebraically well-defined, bags are not well suited for representing and reasoning with real-world information, and we propose suitable alternatives. We extend the same discussion to the fuzzy case, in which membership of elements to bags is gradual, extending the proposed alternatives. There are two main ideas behind our approach. The first is that in general the elements of a bag can be identified and are distinguishable in the real world and, when this is not the case, we are facing a problem of representation of partial knowledge, i.e., we have a lack of information. Under this consideration, we discuss and criticize the usual operations for bags. The second is to manage the fuzziness by levels using a recent level-based representation approach that extends that of fuzzy sets and keeps all the properties of the crisp case. The classical notion of bag can be seen in our approach as a bag summary. We propose a new model that generalizes the existing approach, defining new operations from this new perspective. We also propose how to deal with fuzziness and incompleteness following our approach, doing a review of the existing approaches and applications concerning bags.