Metasets, Intuitionistic Fuzzy Sets and Uncertainty

Starosta, Bartłomiej; Kosiński, Witold

doi:10.1007/978-3-642-38658-9_35

Cited by 5 publications

(3 citation statements)

References 6 publications

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“…Its scope of practical usage is similar to fuzzy sets [57], intuitionistic fuzzy sets [5], or rough sets [45]. There are close relationships between fuzzy set and metaset approaches, described in [50,55].…”

Section: Metasetsmentioning

confidence: 99%

“…We interpret it as the certainty degree for Φ (cf. [55,56]) Definition 10 Let Φ be a metaset sentence. The following element of algebra B is called the certainty degree for Φ.…”

Section: Definition 9 Let Xmentioning

confidence: 99%

“…It is possible that degrees of membership and nonmembership do not sum up to unity. The remaining part is called the hesitancy degree of membership (see [55,56]). This property has important consequences mentioned in Sect.…”

Section: Definition 11mentioning

confidence: 99%

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Two Approaches to Fuzzy Implication

Kacprzak

Starosta

2017

Theory and Applications of Ordered Fuzzy Numbers

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We discuss construction of fuzzy implication and also correlation between negation and implication operators defined on fuzzy values. Two structures for fuzzy implications are studied: the lattice of Step-Ordered Fuzzy Numbers (SOFNs) and the Boolean algebra B of membership degrees for metasets. Even though these two approaches stem from completely different areas it turned out that they lead to similar applications and results. Both of them emerged from research conducted by W. Kosiński and can be applied not only in the most popular application field which is approximate reasoning but also for designing decision-support systems, enriching methods and techniques of opinion mining, or modeling fuzzy beliefs in multiagent systems.

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Section: Metasetsmentioning

confidence: 99%

“…We interpret it as the certainty degree for Φ (cf. [55,56]) Definition 10 Let Φ be a metaset sentence. The following element of algebra B is called the certainty degree for Φ.…”

Section: Definition 9 Let Xmentioning

confidence: 99%