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**On properties of uninorms with underlying t-norm and t-conorm given as ordinal sums.**
*(English)*
Zbl 1191.03039

The study is concerned with binary operations \(U: [0,1]^2\to [0,1]\) which are increasing, associative, and have a neutral element \(e\) in the unit interval. Particular cases include uninorms (where in addition to the properties listed above, we also require commutativity) and t-norms and t-conorms where the neutral element is 1 and 0, respectively.

Presented are some properties of operations for which the underlying components are given as ordinal sums. It is demonstrated that if such components are given by ordinal sums, then the Cartesian product of the union of two arbitrary intervals (each coming from a domain of different ordinal sums) is closed under the uninorm. Furthermore, a description of uninorm-like operations is provided when the underlying operations are pseudo t-norms and pseudo t-conorms and one of them is idempotent.

Presented are some properties of operations for which the underlying components are given as ordinal sums. It is demonstrated that if such components are given by ordinal sums, then the Cartesian product of the union of two arbitrary intervals (each coming from a domain of different ordinal sums) is closed under the uninorm. Furthermore, a description of uninorm-like operations is provided when the underlying operations are pseudo t-norms and pseudo t-conorms and one of them is idempotent.

Reviewer: Witold Pedrycz (Edmonton)

### Keywords:

aggregation operations; uninorm; t-norm; t-conorm; ordinal sum; associativity of operations### References:

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