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A graded approach to cardinal theory of finite fuzzy sets, part I: Graded equipollence

Fuzzy Sets and Systems, 2016
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Michal Holčapek
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A graded approach to cardinal theory of finite fuzzy sets, part II: Fuzzy cardinality measures and their relationship to graded equipollence

Fuzzy Sets and Systems, 2020
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Michal Holčapek
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Graded equipollence and fuzzy c-measures of finite fuzzy sets

2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), 2011
In the classical set theory, there is the well known correspondence between the equipollence of finite sets and the equality of natural numbers expressing their cardinalities. In the fuzzy set theory, an equivalent correspondence between the equipollence of finite fuzzy sets and the equality of generalized cardinals has been proposed in [1]. This paper
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Graded Dominance and Cantor-Bernstein Equipollence of Fuzzy Sets

Communications in Computer and Information Science, 2016
The aim of the paper is to propose a graded dominance for fuzzy sets that assigns to each pair of fuzzy sets a degree in which one fuzzy set has less cardinality than another one or the cardinalities of both fuzzy sets are approximately equal. The graded dominance for fuzzy sets is a natural generalization of the dominance relation for sets. The graded
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