Aggregation theory is devoted to the fusing of several values into a unique output that summarizes the given information. Typically, the aggregation process is formalized in terms of an increasing mathematical function that maps the input values to the result, fulfilling some boundary conditions. However, this formalization can be too restrictive for some scenarios. In some cases, the inputs can be seen as observations of random variables, the aggregation result being also a random variable. In others, the aggregation process can be identified as a program that performs the aggregation rather than a mathematical function. In this direction, the concepts of aggregation of random variables and computable aggregation have been defined in the literature. This paper is devoted to the definition of computable aggregation of random variables, which are computer programs, not functions, that aggregate random variables, not numbers. Special attention is given to different possible alternatives to modelize random variables and monotonicity. The implementation of some examples is also provided.

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.

This work describes a new methodology for making easier the design process of interpretable knowledge bases. It considers both expert knowledge and knowledge extracted from data. The combination of both kinds of knowledge is likely to yield robust compact systems with a good trade-off between accuracy and interpretability. Fuzzy logic offers an integration framework where both types of knowledge are represented using the same formalism. However, as two knowledge bases may convey contradictions and/or redundancies, the integration process must be made carefully. Results obtained, in four well-known benchmark classification problems, show that our methodology leads to highly interpretable knowledge bases with a good accuracy, comparable to that achieved by other methodologies. © 2008 Wiley Periodicals, Inc.

This article analyzes the role of context in hierarchical fuzzy controllers based on the decomposition of the input space. The usual consideration in most hierarchical fuzzy systems is the reduction of dimensionality problems. This article will analyze how to profit from the qualities of context as a key question in the definition of a fuzzy controller, to reduce the design efforts by making it easier to introduce the expert knowledge in that process. The idea is to use the output of a level of the hierarchy as the method to define (or adjust) the normalization functions (considered as contextual information) applied to the variables of the following level of that hierarchy. Two different situations will be analyzed, including an application example for each case. In the first case the decomposition will affect variables placed at the same level of description (abstraction) regarding the problem to be solved. In the second case, the decomposition process works on variables placed at different levels of description of the problem (descriptions with a different level of abstraction). © 2002 Wiley Periodicals, Inc.

In recent years the use of genetic or evolutionary techniques has produced interesting results in the automatic generation of knowledge bases for fuzzy logic controllers. Three different representations of the rule base have been considered: lists of rules, relational matrices, and decision tables. The use of lists of rules reduces the size of the rule base, but presents some handicaps in crossover since it usually requires some kind of list ordering before applying the operator. A new crossover operator, working with lists (sets) of rules, is designed in such a way that maintaining the advantage of working with a reduced set of rules incorporates the characteristic of easy crossover by using the virtual structure of decision table. © 1998 John Wiley & Sons, Inc.