Abstract - We recall and discuss some recent results and trends in the aggregation theory. In particular, we discuss several monotonicity issues, construction issues and generalization of considered scales issues.
Abstract - In this paper aggregation functions whose expressions are given by polynomial functions are investigated. A detailed study focused on binary polynomial aggregation functions of degree one and two is given not only in general, but also requiring some additional properties like idempotency, commutativity, associativity, one-side neutral (or absorbing) element and so on, leading to some families of binary polynomial aggregation functions. The results concerning polynomials of degree one are generalized to n-ary polynomial aggregation functions whereas, with respect to those of degree two, the commutative case is also generalized obtaining the characterization of all commutative n-ary polynomial aggregation functions of degree two in general and jointly with the idempotent property.
Abstract - Logic aggregators are defined as graded aggregators that aggregate degrees of truth, suitability, preference, and fuzzy membership. In this paper we present necessary and sufficient logic aggregators. In particular, we study logic aggregators that generalize classical Boolean logic and model observable properties of human reasoning in the area of soft computing evaluation logic. This paper introduces restrictive conditions that logic aggregators must satisfy.
Abstract - n-dimensional fuzzy sets are an extension of fuzzy sets where the membership values are n-truples of real numbers in the unit interval [0,1] ordered in increasing order, called n-dimensional intervals. The set of n- dimensional intervals is denoted by Ln([0,1]). In the present paper, we consider the definitions and results obtained for n-dimensional fuzzy negations, applying these studies mainly on natural n-dimensional fuzzy negations for n-dimensional triangular norms and triangular conorms. Additionally, the conjugate obtained by action of an n-dimensional automorphism on an n- dimensional natural fuzzy negations for n-dimensional triangular norms and triangular conorms, provides a method to obtain other n-dimensional strong fuzzy negations, in which its properties on Ln ([0, 1]) are preserved.
Abstract - Penalty functions are widely used to measure disagreement or consensus. On the other hand, subsethood measures have been applied in several areas. In this paper, we introduce a method for constructing penalty functions by means of QL fuzzy subsethood measures, introduced by Dimuro et al., which are built from QL-operations derived from tuples (O, G, N), for overlap functions O, grouping functions G and fuzzy negations N.