A fuzzy logic for an ordinal sum t-norm
References (11)
The LΠ and propositional and predicate logics
Fuzzy Sets and Systems
(2001)- et al.
Monoidal t-norm based logictowards a logic for left-continuous t-norms
Fuzzy Sets and Systems
(2001) Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
(1995)- et al.
A survey on different triangular norm-based fuzzy logics
Fuzzy Sets and Systems
(1999) - et al.
Basic fuzzy logic is the logic of continuous t-norms and their residua
Soft Comput
(2000)
Cited by (30)
Ordinal sums of the main classes of fuzzy negations and the natural negations of t-norms, t-conorms and fuzzy implications
2020, International Journal of Approximate ReasoningCitation Excerpt :In [28] was proved that continuous t-norms (and therefore of continuous t-conorms) can be obtained as ordinal sums of continuous Archimedean t-norms (t-conorms), i.e., ordinal sums where the summands are conjugated of the product or Łukasiewicz t-norm (for more details see [27]). This characterization theorem had important consequences in t-norm based fuzzy logics, which are axiomatic extensions of some classes of algebraic logics, as can be seen in [21,36,44]. In addition, this characterization also had been useful in a neural net approach of multi-adjoint logic programming, which are unified frameworks where uncertainty, imprecise data and incomplete information can coexist [30].
On some questions concerning the axiomatisation of WNM-algebras and their subvarieties
2016, Fuzzy Sets and SystemsCitation Excerpt :“for each element of a chain, either its monoidal square is null, or it coincides with the identity”. It turns out for instance that also NMG is axiomatisable from GHP, and hence from MTL with one-variable axioms, and that these axioms are, according to us, much more transparent in their reading with respect to the original axiomatisation found in [42]. On the other hand, extending GHP with (RDP) yields a logic properly weaker than RDP, and which is not an extension of WNM.
Hierarchical structure and applications of fuzzy logical systems
2013, International Journal of Approximate ReasoningDistinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies
2009, Annals of Pure and Applied LogicAxiomatization for 1-level universal AND operator
2008, Journal of China Universities of Posts and TelecommunicationsNormal forms and free algebras for some extensions of MTL
2008, Fuzzy Sets and Systems