The theory of semirings with applications in mathematics and theoretical computer science
The theory of semirings with applications in mathematics and theoretical computer science
Fuzzy Sets and Systems
Van Melle's combining function in MYCIN is a representable uninorm: an alternative proof
Fuzzy Sets and Systems - Special issue on triangular norms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Uncertain Information Processing in Expert Systems
Uncertain Information Processing in Expert Systems
Rule Based Expert Systems: The Mycin Experiments of the Stanford Heuristic Programming Project (The Addison-Wesley series in artificial intelligence)
Rotation-invariant t-norms: The rotation invariance property revisited
Fuzzy Sets and Systems
Distributivity and conditional distributivity of a uninorm and a continuous t-conorm
IEEE Transactions on Fuzzy Systems
A generalization of the migrativity property of aggregation functions
Information Sciences: an International Journal
An extension of the migrative property for uninorms
Information Sciences: an International Journal
A class of implications related to Yager's f-implications
Information Sciences: an International Journal
On the structure of special classes of uninorms
Fuzzy Sets and Systems
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We study uninorms of which both the underlying t-norm and underlying t-conorm are strict. Such uninorms are the only candidates for being representable by an additive generator. We prove that the representability of such a uninorm depends solely on its value at a single arbitrary point in the 'remaining' open part of the unit square. More explicitly, such a uninorm turns out to be representable if and only if this single value is located strictly between the minimum and the maximum of the corresponding arguments. If this single value coincides with one of these bounds, then the value of the uninorm at any point in the 'remaining' open part is determined by the same bound.