RELAXING BOUNDARY CONDITION FOR t– NORMS

Aleksandar Pavlović

   A class O of binary operators is introduced on the interval [0,1] which includes t-norms, t- conorms, uninorms, nullnorms and t-operators. This class O is obtained by relaxing boundary conditions for t-norms with a weaker one. For C ∈ O we have only C(0,0) = 0 and C(1,1) = 1 (instead of the boundary conditions for a t-norm). This class of operators can be used for the construction of the aggregation operators. Using arbitrary t-norm T, non-decreasing function f and its quasi-inverse we will obtain a new operator in class O which is none of the mentioned ones. It will be shown that in some cases we can apply the same method to C ∈ O which is not a t-norm.

Keywords: operators, t-norm, aggregation operator, quasi-inverse

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