Fuzzy cardinals based on the generalized equality of fuzzy subsets
Fuzzy Sets and Systems
Fuzzy entropy and conditioning
Information Sciences: an International Journal
Measuring properties of fuzzy sets: a general technique and its use in fuzzy query evaluation
Fuzzy Sets and Systems - On fuzzy information and database systems
Higher order fuzzy entropy and hybrid entropy of a set
Information Sciences: an International Journal
Cardinality, quantifiers, and the aggregation of fuzzy criteria
Fuzzy Sets and Systems - Special issue on fuzzy information processing
A note on fuzzy information measures
Pattern Recognition Letters
Questions of cardinality of finite fuzzy sets
Fuzzy Sets and Systems
An axiomatic approach to scalar cardinalities of fuzzy sets
Fuzzy Sets and Systems
On the best scalar approximation of cardinality of a fuzzy set
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
An axiomatic approach to fuzzy cardinalities of finite fuzzy sets
Fuzzy Sets and Systems - Theme: Basic notions
Quantifier guided aggregation of fuzzy criteria with associated importances
Aggregation operators
Evolutionary algorithms for reasoning in fuzzy description logics with fuzzy quantifiers
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Granular Association Rules for Multiple Taxonomies: A Mass Assignment Approach
Uncertainty Reasoning for the Semantic Web I
Possibilistic information fusion using maximal coherent subsets
IEEE Transactions on Fuzzy Systems
Meta-theorems on inequalities for scalar fuzzy set cardinalities
Fuzzy Sets and Systems
The set of fuzzy rational numbers and flexible querying
Fuzzy Sets and Systems
On a characterization of fuzzy bags
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
On a non-nested level-based representation of fuzziness
Fuzzy Sets and Systems
RL-bags: A conceptual, level-based approach to fuzzy bags
Fuzzy Sets and Systems
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The existing methods to assess the cardinality of a fuzzy set with finite support are intended to preserve the properties of classical cardinality. In particular, the main objective of researchers in this area has been to ensure the convexity of fuzzy cardinalities, in order to preserve some properties based on the addition of cardinalities, such as the additivity property. We have found that in order to solve many real-world problems, such as the induction of fuzzy rules in Data Mining, convex cardinalities are not always appropriate. In this paper, we propose a possibilistic and a probabilistic cardinality of a fuzzy set with finite support. These cardinalities are not convex in general, but they are most suitable for solving problems and, contrary to the generalizing opinion, they are found to be more intuitive for humans. Their suitability relies mainly on the fact that they assume dependency among objects with respect to the property "to be in a fuzzy set". The cardinality measures are generalized to relative ones among pairs of fuzzy sets. We also introduce a definition of the entropy of a fuzzy set by using one of our probabilistic measures. Finally, a fuzzy ranking of the cardinality of fuzzy sets is proposed, and a definition of graded equipotency is introduced.