Among the different techniques of the Computational Intelligence, the usage of hybrid tech- niques has been extended notably in recent years. One of the most common hybridizations is obtained whit the combination of Fuzzy Systems with the Genetic Algorithms (GA), in- troducing the Evolutionary Fuzzy Sets (EFS) [Her08, CH01, CCJH01]. Basically, an EFS is a fuzzy system improved by a learning process. Having this process based on evolutionary computation e.g. GAs, genetic programming or evolutionary strategies, among others.
The design process of a FRBCS can be seen as an optimization or search problem. Due to this reason, the AGs are a satisfactory mechanism to deal with this issue. Considering that they are a global search technique with the ability to explore large search spaces requiring only a measure of performance. Thus, we can say that AGs are adequate to find almost optimal solutions in complex search spaces. Furthermore, due to its generic coding structure is easy to incorporate prior knowledge. For example, the parameters of the membership functions or the number of rules of the system. We present in Figure 10 an scheme of an evolutionary
fuzzy system.
Environment Computation with Fuzzy Rule-Based Systems Environment Fuzzy Rule-Based
Systems
Input Interface Input Interface
Knowledge Based Rule Base Data Base
Genetic Algorithm Based Learning Process
DESING PROCESS
Figure 10: The scheme of an evolutionary fuzzy system [HL09].
In FRBCSs, from a point of view of the optimization, find a good KB is equivalent to codify it as a structure of parameters and find the values of these parameters that give us the optima for a determined measure of performance. The parameters of the KB define the search space and they are adapted according to a genetic representation.
The proposals of EFSs can by divided in two ways: tuning, related to the adjustment of the components of the fuzzy system and, learning, corresponding to the learning of the fuzzy system directly. In the following, we briefly describe them:
1. Genetic Adjustment – If exists a Knowledge Base (KB), this method apply a genetic adjustment process to improve the quality of the FRBCSs without modifying the learned RB. There are different groups of techniques within this paradigm:
posteriori adjustment of the parameters of the membership functions. In this way, the RB never changes, that is, it learns a FRBCS with an initial configuration in terms of the number of labels per variable and their shape. Once the fuzzy rules are learned, the parameters that define the membership functions are optimized in order to make the fuzzy rules work better. For more information see [Kar91]. ◦ Genetic adaptive inference systems. The main objective of this proposal is to
use parametric expressions in the inference system to obtain a better coopera- tion among the fuzzy rules and more precise fuzzy models, without losing the interpretability inherent in linguistic rules. This method is often called Adaptive Inference Systems. In [AFHHP07, CABFO06, CBM07] we can find proposals in this area which are focused in classification and regression.
2. Genetic Learning –In this process we can learn the components of the knowledge base (even including an adaptive FRM). In what follows, we describe the four groups that can be found in the genetic learning:
◦ Genetic learning of the fuzzy rules. The majority of the approaches that have been proposed to automatically learn the KB, from numerical information, have focused on the rule base (RB) learning, using a predefined data base (DB). The usual way to define the DB demands to pick a number of linguistic terms for each linguistic variable and give it the value of the system parameters by means of an uniform distribution of the linguistic terms considering the universe of discourse of the variables. In [Thr91], it was proposed the first proposal in this area. ◦ Genetic selection of the fuzzy rules. Once a RB has been learned, this process can
be used to select fuzzy rules, in order to avoid including irrelevant, redundant and noisy fuzzy rules. In [AAFH07, CCdJH05], the authors present a methodology for combining the selection of the rules with the genetic adjustment of the parameters. ◦ Genetic learning of the Data Base. There is another way to generate all the KB, that is, the DB and the RB. The DB generating process allows us to learn the form of membership functions and other components of the DB such as scaling functions or granularity of the diffuse partitions, among others. This process of generating the DB can use a measure to evaluate the quality of the DB, which is called apriori genetic learning of the DB. The second possibility is to consider an embedded genetic learning process where the process of generating the DB is done together with the learning of the RB. In this manner a partitioning of the learning
problem of the KB is required. In [CHV01], we can find a proposal related to the embedded genetic learning of the DB.
◦ Simultaneous genetic learning of the components of the knowledge base. This
method intends to learn both components of the KB at the same time. In this way, the obtained KB could be of superior quality. However, the process is slower and hard. See [HM95] for more information.