Abstract
Twofold fuzzy sets model ill-known collections of objects, where, for each element of a given domain, both necessity and possibility degrees of membership are specified. It is proved that the cardinality of a twofold fuzzy set is equivalent to possibilistic granular count when the twofold fuzzy set is derived from a possibilistic assignment table. This result sheds light on the connections between twofold fuzzy sets and granular counts: in particular, it is possible to take interactivity into account when aggregating twofold fuzzy sets derived from a possibilistic assignment table.
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Notes
- 1.
Henceforth, we assume the referential X to be finite.
- 2.
From now on, the notation used in [9] will be used, in order to facilitate cross reading.
- 3.
The conventions \(\min \emptyset =1\) and \(\max \emptyset =0\) are followed throughout the paper.
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Acknowledgments
The research is partially supported by Ministero dello Sviluppo Economico (MISE) under grant F/190030/01-03/X44 “LIFT”. C.M. is member of the INdAM Research group GNCS and CILA (Centro Interdipartimentale di Logica e Applicazioni).
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Mencar, C., Dubois, D. (2022). Connections Between Granular Counts and Twofold Fuzzy Sets. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1602. Springer, Cham. https://doi.org/10.1007/978-3-031-08974-9_41
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