Generators of Fuzzy Logical Operations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60460709%3A41310%2F20%3A82350" target="_blank" >RIV/60460709:41310/20:82350 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/chapter/10.1007%2F978-3-030-38565-1_8" target="_blank" >https://link.springer.com/chapter/10.1007%2F978-3-030-38565-1_8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-38565-1_8" target="_blank" >10.1007/978-3-030-38565-1_8</a>

Result language
angličtina
Original language name
Generators of Fuzzy Logical Operations
Original language description
We deal with fuzzy logical operations with values in the real unit interval. Many of them can be considered equivalent up to an isomorphism (i.e., increasing bijection) of the set of values. This is the case of all involutive fuzzy negations, an elegant proof was given by Nguyen and Walker (A first course in fuzzy logic, 2nd edn., Boca Raton, 2000). The situation is more tricky for binary operations, triangular norms, triangular conorms, and fuzzy implications. For the most common classes of these operations, the existence of their (additive or multiplicative) generators is known, however, their computation can be often unfeasible. We proved that a rather general subclass allows computing the generators from partial derivatives. Here we summarize preceding results in this direction (mostly with simplified proofs) and add several new ones.
Czech name
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Czech description
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Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Book/collection name
Algebraic Techniques and Their Use in Describing and Processing Uncertainty
ISBN
978-3-030-38564-4
Number of pages of the result
24
Pages from-to
89-112
Number of pages of the book
170
Publisher name
Springer
Place of publication
Cham
UT code for WoS chapter
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