Pointwise construction of Lipschitz aggregation operators
نویسندگان
چکیده
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.
منابع مشابه
Construction of Aggregation Operators for Automated Decision Making via Optimal Interpolation and Global Optimization
This paper examines methods of pointwise 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 numbe...
متن کاملOn convergence of certain nonlinear Durrmeyer operators at Lebesgue points
The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate...
متن کاملMöbius fitting aggregation operators
Standard Mobius transform evaluation formula for the Choquet integral is associated with the min-aggregation. However, several other aggregation operators replacing min operator can be applied, which leads to a new construction method for aggregation operators. All binary operators applicable in this approach are characterized by the 1-Lipschitz property. Among ternary aggregation operators all...
متن کاملT-extension as a method of construction of a generalized aggregation operator
This paper is a contribution to the theory of generalized aggregation operators (shortly gagops) introduced by Takači in [11]. The term generalized refers to the inputs of an aggregation operator (shortly agop), they are a special type of fuzzy sets. In the sequel we study a method of construction of a gagop by means of an arbitrary continuous t-norm, called T -extension. Another construction m...
متن کاملPOINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS
The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let be a non-emp...
متن کامل