The idea of computable aggregation operators was introduced as a generalization of aggregation operators, allowing the replacement of the mathematical function usually considered for aggregation, by a program that performs the aggregation process. There are different reasons to justify this extension. One of them is the interest in exploring some computational properties not directly related to the aggregation itself but to its implementation (complexity, recursivity, parallelisation, etc). Another reason, the one driving to the present paper, is the need to define a framework where the quite common process of first sampling (over a large data set) and then aggregating the sample, could be analysed as a formal aggregation process. This process does not match with the idea of an aggregation function, due to its non-deterministic nature, but could easily be adapted to that of a (non-deterministic) computable aggregation. The idea of non-deterministic aggregation requires the extension of the concept of monotonicity (a key aspect of aggregation operators) to this new framework. The present paper will explore this kind of non-deterministic aggregation processes, first from an empirical point of view and then in terms of populations, adapting the idea of monotonicity to both of them and finally defining a common framework for its analysis.

One of the most common techniques to find the adequate weights in ordered weighted averaging (OWA) operators is based on the orness concept, where the weights are determined by maximizing the entropy (variation) for a fixed orness value. But such an entropy represents a dispersion measure for nominal variables, while weights in an OWA operator are essentially ordinal rather than nominal. Hence, in this paper, we propose a novel way to determine OWA weights based upon ordinal dispersion measures instead of an standard entropy measure. From this approach, we find an explicit formula for the weights, and we illustrate differences by means some multicriteria decision-making examples.

Inspired by the Zadeh approach to fuzzy connectives in fuzzy set theory and by some applications, we introduce and study set-based extended functions, and in particular, set-based extended aggregation functions. These functions reflect neither reordering nor repetition of input values, and, linking different arities, they introduce serious constraints for extended functions. A complete characterization of set-based extended (aggregation) functions is given, and some constructions of such functions are also proposed, including several examples.

An associative binary connective allows the evaluation of arbitrary finite sequences of items by means of a one-by-one sequential process. In this paper we develop an alternative approach for those nonassociative connectives, allowing a sequential definition by means of binary fuzzy connectives. It will be then stressed that a connective rule should be understood as a consistent sequence of binary connective operators. ©1999 John Wiley & Sons, Inc.

We will continue here the research work, the goal of which was to introduce the notion of nondeterministic aggregation operators and study their properties, even in relation to classification systems and the associated learning problem. Here we will concentrate mostly on the notion of the nondeterministic aggregation system and its relation with deterministic ones. We will also see how such a model extends a discretized version of a model of participatory learning with an arousal background mechanism. © 1998 John Wiley & Sons, Inc.13: 181–192, 1998

This article deals with hierarchies of operators. In particular, we will analyze the problem of amalgamating individual opinions into a single group opinion, based upon hierarchical intensity aggregation rules. Our main goal is to decide whether hierarchical amalgamations are supported from an ethical and rational point of view. We will consider two different hierarchical procedures: cover-based hierarchical aggregations and ordered hierarchical aggregations, focusing here our attention to ordered hierarchical aggregations of OWA operators. In particular, we will obtain that basic key properties propagate under both hierarchical amalgamation rules, in the sense that the procedure itself will verify such properties whenever they are assumed for every partial amalgamation defining such a hierarchical procedure. © 1994 John Wiley & Sons, Inc.