Aggregation operators for linguistic variables usually assume a uniform and symmetrical distribution of the linguistic terms that define the variable. This paper defines the Induced Unbalanced Linguistic Ordered Weighted Average (IULOWA). This aggregator takes into account the fuzzy membership functions...

In this paper we analyze two classes of functions proposed in the literature to simultaneously generalize weighted means and OWA operators: WOWA operators and HWA operators. Since, in some cases, the results provided by these operators may be questionable, we introduce functions that also generalize...

This paper aims to establish the relationship between two apparent disparate problems: (i) the aggregation of uncertain information modelled by type-1 fuzzy sets via OWA mechanism, and (ii) the computation of the centroid of type-2 fuzzy sets. In order to cut down the computational complexity of the...

The paper is devoted to a concept of aggregation of binary fuzzy relations. Consider two n-ary vectors, when we know the degrees to which corresponding components are in relation we can measure the degree to which vectors are in relation. Tasks with such background justify the necessity of aggregation...

In the paper we study a method extending fuzzy measures on the set N = {1, . . ., n} to n-ary aggregation functions on the interval [0, 1]. The method is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered fuzzy measure. This approach generalizes the wellknown...

In several economic fields, such as those related to health, education or poverty, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed....

In this paper we deal with the problem of aggregating pairwise distance values in order to obtain a multi-argument distance function. After introducing the concept of functionally expressible multidistance, several essential types of multidimensional aggregation functions are considered to construct...

The paper is devoted to a general aggregation operator acting on L-fuzzy real numbers. It is defined as a t-norm based extension of an ordinary aggregation operator. The aim of our research is to analyze properties of the general aggregation operator depending on properties of the ordinary aggregation...

Two classes of aggregation functions: L-statistics and S-statistics and their generalizations called quasi-L-statistics and quasi-S-statistics are considered. Some interesting characterizations of these families of operators are given. The aforementioned functions are useful for various applications....

In this paper a method to extend discrete uninorms and nullnorms on the finite chain L = {0, . . . , n}, to uninorms and nullnorms defined on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers contained in L is presented. Some basic properties of discrete uninorms...

A new method to construct aggregation functions is introduced. These aggregation functions are called biconic aggregation functions with a given diagonal (resp. opposite diagonal) section and their construction method is based on linear interpolation on segments connecting the diagonal (resp. opposite...

The aim of this paper is to introduce, by axiomatic way, the measure of the general (i.e. without probability) aimed information for crisp sets. We traslate the problem in a system of functional equation and we present a class of solutions; in the case of independence we characterize the solution. Finally,...

In this work we introduce the definition of restricted dissimilarity functions and we link it with some other notions, such as metrics. In particular, we also show how restricted dissimilarity functions can be used to build penalty functions.

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. Two different types of aggregation functionals are introduced and investigated. We consider a target-based approach that has been studied in Decision Theory and we focus on the...