Pointwise construction of Lippschitz aggregation operators with specific properties

This paper describes an approach to pointwise construction of general aggregation operators, based on monotone Lipschitz approximation. The aggregation operators are constructed from a set of desired values at certain points, or from empirically collected data. It establishes tight upper and lower bounds on Lipschitz aggregation operators with a number of different properties, as well as the optimal aggregation operator, consistent with the given values. We consider conjunctive, disjunctive and idempotent n-ary aggregation operators; p-stable aggregation operators; various choices of the neutral element and annihilator; diagonal, opposite diagonal and marginal sections; bipolar and double aggregation operators. In all cases we provide either explicit formulas or deterministic numerical procedures to determine the bounds. The findings of this paper are useful for construction of aggregation operators with specified properties, especially using interpolation schemata.<br /

Pointwise construction of Lipschitz aggregation operators

This paper establishes tight upper and lower bounds on Lipschitz aggregation operators considering their diagonal, opposite diagonal and marginal sections. Also we provide explicit formulae to determine the bounds. These are useful for construction of these type of aggregation operators, especially using interpolation schemata.<br /

Construction of aggregation operators for automated decision making via optimal interpolation and global optimization

This paper examines methods of point wise construction of aggregation operators via optimal interpolation. It is shown that several types of application-specific requirements lead to interpolatory type constraints on the aggregation function. These constraints are translated into global optimization problems, which are the focus of this paper. We present several methods of reduction of the number of variables, and formulate suitable numerical algorithms based on Lipschitz optimization.<br /