Generalized deviation functions and construction of aggregation functions

Abstract

We generalize the concept of moderate deviation functions D :→R and propose a D (k) -based method for constructing idempotent aggregation functions. More, to enable to introduce weights of groups of criteria (coordinates) into our construction method, the concept of normed (k + 1)-dimensional moderate deviation functions is proposed and exemplified.

A fusion method for multi-valued data

“…It is worth mentioning that via deviation-based approaches there is possible to catch several types of mixture operators and their generalizations (more in [17], [18], [19], [20], [21]).…”

Aggregation Function Constructed from Copula

“…Another example is the transformations of aggregation functions such as flippings [14,24], polynomial transformations [3,6,10,33,40,42,41], compositions [18,31] and others [27,28,30]. Penalty-based constructions also gain interest in recent years [1,4,5,13,12,23,35,36,39,42,38].…”

New Classes of the Moderate Deviation Functions

“…Therefore, the authors in [5,6] introduced a so-called moderate deviation function, which ensures that the aggregation functions based on the moderate deviation functions meet all the properties of aggregation functions. At present, researches offer various constructions of aggregation functions, which are based on the use of the mentioned moderate deviation functions, [1,5,6,11]. To such a construction of the moderate deviation function led us discussions of papers [3] and [9].…”

“…([1],[11]) A function D : I 2 → R is called a moderate deviation function, if and only if it satisfies the following conditions:(i) for every x ∈ I, D(x, •) : I → R is increasing (not necessarily strictly); (ii) for every y ∈ I, D(•, y) : I → R is decreasing (not necessarily strictly); (iii) D(x, y) = 0 if and only if x = y, x ∈ I, y ∈ I. Definition 6.…”