Guest editorial: foreword to the special issue on aggregation operators

The fourteen papers in this special section are devoted to aggregation operators with respect to knowledge based systems.<br /

Basic generated universal fuzzy measures

AbstractThe concept of basic generated universal fuzzy measures is introduced. Special classes and properties of basic generated universal fuzzy measures are discussed, especially the additive, the symmetric and the maxitive case. Additive (symmetric) basic universal fuzzy measures are shown to correspond to the Yager quantifier-based approach to additive (symmetric) fuzzy measures. The corresponding fuzzy integral-based aggregation operators are introduced, including the generated OWA operators

Conjunctors and their residual implicators: characterizations and construction methods

In many practical applications of fuzzy logic it seems clear that one needs more flexibility in the choice of the conjunction: in particular, the associativity and the commutativity of a conjunction may be removed. Motivated by these considerations, we present several classes of conjunctors, i.e. binary operations on $[0,1]$ that are used to extend the boolean conjunction from $\{0,1\}$ to $[0,1]$, and characterize their respective residual implicators. We establish hence a one-to-one correspondence between construction methods for conjunctors and construction methods for residual implicators. Moreover, we introduce some construction methods directly in the class of residual implicators, and, by using a deresiduation procedure, we obtain new conjunctors

2-Increasing binary aggregation operators

In this work we investigate the class of binary aggregation operators (=agops) satisfying the 2-increasing property, obtaining some characterizations for agops having other special properties (e.g., quasi-arithmetic mean, Choquet-integral based, modularity) and presenting some construction methods. In particular, the notion of P-increasing function is used in order to characterize the composition of 2-increasing agops. The lattice structure (with respect to the pointwise order) of some subclasses of 2-increasing agops is presented. Finally, a method is given for constructing copulas beginning from 2- increasing and 1-Lipschitz agops

Restricted dissimilarity functions and penalty functions

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

Copulas constructed from horizontal sections

In analogy with the study of copulas whose diagonal sections have been fixed, we study the set $\mathcal{C}_h$ of copulas for which a horizontal section $h$ has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call \textit{horizontal copula}. Then we find the copulas that bound both below and above the set $\mathcal{C}_h$. Finally we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas

Penalty functions over a cartesian product of lattices

In this work we present the concept of penalty function over a Cartesian product of lattices. To build these mappings, we make use of restricted dissimilarity functions and distances between fuzzy sets. We also present an algorithm that extends the weighted voting method for a fuzzy preference relation