A note on the ordinal sum theorem and its consequence for the construction of triangular norms

DOI10.1016/S0165-0114(01)00040-9zbMath0996.03508OpenAlexW1986180896MaRDI QIDQ1602901

Publication date: 24 June 2002

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0165-0114(01)00040-9

zbMATH Keywords

t-norms triangular norms ordinal sum

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72)

Related Items (52)

Unnamed Item ⋮ On the Relation Between Loss Functions and T-Norms ⋮ Triangular norms. Position paper II: General constructions and parameterized families ⋮ Ordinal sum construction for uninorms and generalized uninorms ⋮ On the scope of some formulas defining additive connectives in fuzzy logics ⋮ ORDINAL SUMS IN INTERVAL-VALUED FUZZY SET THEORY ⋮ Ordinal sums of triangular norms on bounded lattices ⋮ Continuous additive generators of continuous, conditionally cancellative triangular subnorms ⋮ A fuzzy logic for the revised drastic product t-norm. ⋮ The logic of the strongest and the weakest t-norms ⋮ T-norms and t-conorms continuous around diagonals ⋮ On rearrangement inequalities for triangular norms and co-norms in multi-valued logic ⋮ Convex combinations of uninorms and triangular subnorms ⋮ Ordinal sums: from triangular norms to bi- and multivariate copulas ⋮ Triangular norms which are meet-morphisms in interval-valued fuzzy set theory ⋮ On some questions concerning the axiomatisation of WNM-algebras and their subvarieties ⋮ Continuous weakly cancellative triangular subnorms. I: Their web-geometric properties ⋮ On properties of uninorms locally internal on the boundary ⋮ The cross-migrativity with respect to continuous triangular norms revisited ⋮ New construction of t-norms and t-conorms on bounded lattices ⋮ How to construct left-continuous triangular norms -- state of the art. ⋮ Residual implications and left-continuous t-norms which are ordinal sums of semigroups. ⋮ Continuous triangular subnorms. ⋮ The structure ofn-contractive t-norms ⋮ Uninorms which are neither conjunctive nor disjunctive in interval-valued fuzzy set theory ⋮ Some results of weighted quasi-arithmetic mean of continuous triangular norms ⋮ Semi-divisible triangular norms ⋮ Computational method for fuzzy arithmetic operations on triangular fuzzy numbers by extension principle ⋮ Smooth t-subnorms on finite scales ⋮ Continuous completions of triangular norms known on a subregion of the unit interval ⋮ Undefinability of min-conjunction in MTL ⋮ On ordinal sums of triangular norms on bounded lattices ⋮ On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums ⋮ Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics ⋮ On triangular norms and uninorms definable in Ł\(\Pi \frac{1}{2}\) ⋮ Unnamed Item ⋮ Generalized ordinal sums of aggregation operators on bounded lattices ⋮ Lattice-based sum of t-norms on bounded lattices ⋮ Uninorms continuous on \([0, e[^{2}\cupe, 1]^{2}\)] ⋮ Cancellativity properties for t-norms and t-subnorms ⋮ Structure of Uninorms with Continuous Diagonal Functions ⋮ A general method for constructing left-continuous t-norms ⋮ A characterization theorem on the rotation construction for triangular norms ⋮ A Note on Drastic Product Logic ⋮ A spectrum of compromise aggregation operators for multi-attribute decision making ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Representations for logics and algebras related to revised drastic product t-norm ⋮ Rotation-invariant t-norms: where triple rotation and rotation-annihilation meet ⋮ Hesitant fuzzy linguistic aggregation operators based on the Hamacher t-norm and t-conorm ⋮ Extremal Completions of Triangular Norms Known on a Subregion of the Unit Interval ⋮ Generating pseudo-t-norms and implication operators

Cites Work

This page was built for publication: A note on the ordinal sum theorem and its consequence for the construction of triangular norms