Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms
Fuzzy Sets and Systems - Special issue on triangular norms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Aggregation operators: properties, classes and construction methods
Aggregation operators
Negation and affirmation: the role of involutive negators
Soft Computing - A Fusion of Foundations, Methodologies and Applications
The self-dual core and the anti-self-dual remainder of an aggregation operator
Fuzzy Sets and Systems
On the duality of aggregation operators and k-negations
Fuzzy Sets and Systems
Aggregation functions and contradictory information
Fuzzy Sets and Systems
A generalization of the migrativity property of aggregation functions
Information Sciences: an International Journal
Associativity of triangular norms characterized by the geometry of their level sets
Fuzzy Sets and Systems
| Hi-index | 0.01 |
The mathematical expressions for the commutativity or self-duality of an increasing [0,1]^2-[0,1] function F involve the transposition of its arguments. We unite both properties in a single functional equation. The solutions of this functional equation are discussed. Special attention goes to the geometrical construction of these solutions and their characterization in terms of contour lines. Furthermore, it is shown how 'rotating' the arguments of F allows to convert the results into properties for [0,1]^2-[0,1] functions having monotone partial functions.