Implications on Ordered Fuzzy Numbers and Fuzzy Sets of Type Two

Kacprzak, Magdalena; Kosiński, Witold; Prokopowicz, Piotr

doi:10.1007/978-3-642-29347-4_29

Cited by 4 publications

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“…Thus given disjunction and complement, implication can be defined in the standard way. Such a new operator on the set N was introduced by Kacprzak and Kosiński and is called 2K-fuzzy implication [28,29,38]. The set of all OFNs is not a complete lattice, therefore the way of defining implication is still an open question.…”

Section: Fuzzy Implication On Bsofnmentioning

confidence: 99%

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: Fuzzy Implication On Bsofnmentioning

confidence: 99%