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**Convex combinations in terms of triangular norms: A characterization of idempotent, bisymmetrical and self-dual compensatory operators.**
*(English)*
Zbl 0928.03063

Summary: It is observed that most of the well-known compensatory operators are defined in terms of convex transformations of the values of triangular norms and conorms or other operators. In this paper, the characterization and the applicability of parametrized operators constructed again in terms of triangular norms and conorms, but as transformations of their arguments, are studied. It turns out that these operators are closely related to the ordinary convex combination. Moreover, when idempotency is required, these operators can be characterized algebraically as bisymmetrical and self-dual operators that satisfy the cancellation law.

### MSC:

03E72 | Theory of fuzzy sets, etc. |

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

### Keywords:

bisymmetry; compensatory operators; triangular norms; convex combination; idempotency; self-dual operators; cancellation law
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\textit{B. Moser} et al., Fuzzy Sets Syst. 104, No. 1, 97--108 (1999; Zbl 0928.03063)

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### References:

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