Automatic synthesis of fuzzy systems: An evolutionary overview with a genetic programming perspective

Studies in Evolutionary Fuzzy Systems (EFSs) began in the 90s and have experienced a fast development since then, with applications to areas such as pattern recognition, curve‐fitting and regression, forecasting and control. An EFS results from the combination of a Fuzzy Inference System (FIS) with an Evolutionary Algorithm (EA). This relationship can be established for multiple purposes: fine‐tuning of FIS's parameters, selection of fuzzy rules, learning a rule base or membership functions from scratch, and so forth. Each facet of this relationship creates a strand in the literature, as membership function fine‐tuning, fuzzy rule‐based learning, and so forth and the purpose here is to outline some of what has been done in each aspect. Special focus is given to Genetic Programming‐based EFSs by providing a taxonomy of the main architectures available, as well as by pointing out the gaps that still prevail in the literature. The concluding remarks address some further topics of current research and trends, such as interpretability analysis, multiobjective optimization, and synthesis of a FIS through Evolving methods

A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretability of a Neuro-Fuzzy Controller

In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binary-real Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The  approach  is  tested  on  two  control examples:  a single  input  single  output (SISO) system  and  a  multivariable (MIMO) system

Multiobjective Evolutionary Optimization of Type-2 Fuzzy Rule-Based Systems for Financial Data Classification

Classification techniques are becoming essential in the financial world for reducing risks and possible disasters. Managers are interested in not only high accuracy, but in interpretability and transparency as well. It is widely accepted now that the comprehension of how inputs and outputs are related to each other is crucial for taking operative and strategic decisions. Furthermore, inputs are often affected by contextual factors and characterized by a high level of uncertainty. In addition, financial data are usually highly skewed toward the majority class. With the aim of achieving high accuracies, preserving the interpretability, and managing uncertain and unbalanced data, this paper presents a novel method to deal with financial data classification by adopting type-2 fuzzy rule-based classifiers (FRBCs) generated from data by a multiobjective evolutionary algorithm (MOEA). The classifiers employ an approach, denoted as scaled dominance, for defining rule weights in such a way to help minority classes to be correctly classified. In particular, we have extended PAES-RCS, an MOEA-based approach to learn concurrently the rule and data bases of FRBCs, for managing both interval type-2 fuzzy sets and unbalanced datasets. To the best of our knowledge, this is the first work that generates type-2 FRBCs by concurrently maximizing accuracy and minimizing the number of rules and the rule length with the objective of producing interpretable models of real-world skewed and incomplete financial datasets. The rule bases are generated by exploiting a rule and condition selection (RCS) approach, which selects a reduced number of rules from a heuristically generated rule base and a reduced number of conditions for each selected rule during the evolutionary process. The weight associated with each rule is scaled by the scaled dominance approach on the fuzzy frequency of the output class, in order to give a higher weight to the minority class. As regards the data base learning, the membership function parameters of the interval type-2 fuzzy sets used in the rules are learned concurrently to the application of RCS. Unbalanced datasets are managed by using, in addition to complexity, selectivity and specificity as objectives of the MOEA rather than only the classification rate. We tested our approach, named IT2-PAES-RCS, on 11 financial datasets and compared our results with the ones obtained by the original PAES-RCS with three objectives and with and without scaled dominance, the FRBCs, fuzzy association rule-based classification model for high-dimensional dataset (FARC-HD) and fuzzy unordered rules induction algorithm (FURIA), the classical C4.5 decision tree algorithm, and its cost-sensitive version. Using nonparametric statistical tests, we will show that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable with and complexity lower than the ones generated by the two versions of the original PAES-RCS. Further, the FRBCs generated by FARC-HD and FURIA and the decision trees computed by C4.5 and its cost-sensitive version, despite the highest complexity, result to be less accurate than the FRBCs generated by IT2-PAES-RCS. Finally, we will highlight how these FRBCs are easily interpretable by showing and discussing one of them

A Genetic Tuning to Improve the Performance of Fuzzy Rule-Based Classification Systems with Interval-Valued Fuzzy Sets: Degree of Ignorance and Lateral Position

Fuzzy Rule-Based Systems are appropriate tools to deal with classification problems due to their good properties. However, they can suffer a lack of system accuracy as a result of the uncertainty inherent in the definition of the membership functions and the limitation of the homogeneous distribution of the linguistic labels. The aim of the paper is to improve the performance of Fuzzy Rule-Based Classification Systems by means of the Theory of Interval-Valued Fuzzy Sets and a post-processing genetic tuning step. In order to build the Interval-Valued Fuzzy Sets we define a new function called weak ignorance for modeling the uncertainty associated with the definition of the membership functions. Next, we adapt the fuzzy partitions to the problem in an optimal way through a cooperative evolutionary tuning in which we handle both the degree of ignorance and the lateral position (based on the 2-tuples fuzzy linguistic representation) of the linguistic labels. The experimental study is carried out over a large collection of data-sets and it is supported by a statistical analysis. Our results show empirically that the use of our methodology outperforms the initial Fuzzy Rule-Based Classification System. The application of our cooperative tuning enhances the results provided by the use of the isolated tuning approaches and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.Spanish Government TIN2008-06681-C06-01 TIN2010-1505

A HEDGE ALGEBRAS BASED CLASSIFICATION REASONING METHOD WITH MULTI-GRANULARITY FUZZY PARTITIONING

During last years, lots of the fuzzy rule based classifier (FRBC) design methods have been proposed to improve the classification accuracy and the interpretability of the proposed classification models. Most of them are based on the fuzzy set theory approach in such a way that the fuzzy classification rules are generated from the grid partitions combined with the pre-designed fuzzy partitions using fuzzy sets. Some mechanisms are studied to automatically generate fuzzy partitions from data such as discretization, granular computing, etc. Even those, linguistic terms are intuitively assigned to fuzzy sets because there is no formalisms to link inherent semantics of linguistic terms to fuzzy sets. In view of that trend, genetic design methods of linguistic terms along with their (triangular and trapezoidal) fuzzy sets based semantics for FRBCs, using hedge algebras as the mathematical formalism, have been proposed. Those hedge algebras-based design methods utilize semantically quantifying mapping values of linguistic terms to generate their fuzzy sets based semantics so as to make use of fuzzy sets based-classification reasoning methods proposed in design methods based on fuzzy set theoretic approach for data classification. If there exists a classification reasoning method which bases merely on semantic parameters of hedge algebras, fuzzy sets-based semantics of the linguistic terms in fuzzy classification rule bases can be replaced by semantics - based hedge algebras. This paper presents a FRBC design method based on hedge algebras approach by introducing a hedge algebra- based classification reasoning method with multi-granularity fuzzy partitioning for data classification so that the semantic of linguistic terms in rule bases can be hedge algebras-based semantics. Experimental results over 17 real world datasets are compared to existing methods based on hedge algebras and the state-of-the-art fuzzy sets theoretic-based approaches, showing that the proposed FRBC in this paper is an effective classifier and produces good results

Learning positive-negative rule-based fuzzy associative classifiers with a good trade-off between complexity and accuracy

Nowadays, the call for transparency in Artificial Intelligence models is growing due to the need to understand how decisions derived from the methods are made when they ultimately affect human life and health. Fuzzy Rule-Based Classification Systems have been used successfully as they are models that are easily understood by models themselves. However, complex search spaces hinder the learning process, and in most cases, lead to problems of complexity (coverage and specificity). This problem directly affects the intention to use them to enable the user to analyze and understand the model. Because of this, we propose a fuzzy associative classification method to learn classifiers with an improved trade-off between accuracy and complexity. This method learns the most appropriate granularity of each variable to generate a set of simple fuzzy association rules with a reduced number of associations that consider positive and negative dependencies to be able to classify an instance depending on the presence or absence of certain items. The proposal also chooses the most interesting rules based on several interesting measures and finally performs a genetic rule selection and adjustment to reach the most suitable context of the selected rule set. The quality of our proposal has been analyzed using 23 real-world datasets, comparing them with other proposals by applying statistical analysis. Moreover, the study carried out on a real biomedical research problem of childhood obesity shows the improved trade-off between the accuracy and complexity of the models generated by our proposal.Funding for open access charge: Universidad de Granada / CBUA.ERDF and the Regional Government of Andalusia/Ministry of Economic Transformation, Industry, Knowledge and Universities (grant numbers P18-RT-2248 and B-CTS-536-UGR20)ERDF and Health Institute Carlos III/Spanish Ministry of Science, Innovation and Universities (grant number PI20/00711)Spanish Ministry of Science and Innovation (grant number PID2019-107793GB-I00

IIVFDT: Ignorance Functions based Interval-Valued Fuzzy Decision Tree with Genetic Tuning

The choice of membership functions plays an essential role in the success of fuzzy systems. This is a complex problem due to the possible lack of knowledge when assigning punctual values as membership degrees. To face this handicap, we propose a methodology called Ignorance functions based Interval-Valued Fuzzy Decision Tree with genetic tuning, IIVFDT for short, which allows to improve the performance of fuzzy decision trees by taking into account the ignorance degree. This ignorance degree is the result of a weak ignorance function applied to the punctual value set as membership degree. Our IIVFDT proposal is composed of four steps: (1) the base fuzzy decision tree is generated using the fuzzy ID3 algorithm; (2) the linguistic labels are modeled with Interval-Valued Fuzzy Sets. To do so, a new parametrized construction method of Interval-Valued Fuzzy Sets is defined, whose length represents such ignorance degree; (3) the fuzzy reasoning method is extended to work with this representation of the linguistic terms; (4) an evolutionary tuning step is applied for computing the optimal ignorance degree for each Interval-Valued Fuzzy Set. The experimental study shows that the IIVFDT method allows the results provided by the initial fuzzy ID3 with and without Interval-Valued Fuzzy Sets to be outperformed. The suitability of the proposed methodology is shown with respect to both several state-of-the-art fuzzy decision trees and C4.5. Furthermore, we analyze the quality of our approach versus two methods that learn the fuzzy decision tree using genetic algorithms. Finally, we show that a superior performance can be achieved by means of the positive synergy obtained when applying the well known genetic tuning of the lateral position after the application of the IIVFDT method.Spanish Government TIN2011-28488 TIN2010-1505

An evolutionary fuzzy system to support the replacement policy in water supply networks: The ranking of pipes according to their failure risk

Article number 107731In this study, an evolutionary fuzzy system is proposed to predict unexpected pipe failures in water supply networks. The system seeks to underpin the decisions of management companies regarding the maintenance and replacement plans of pipes. On the one hand, fuzzy logic provides high degrees of interpretability over other black box models, which is requested in engineering application where decisions have social consequences. On the other hand, the genetic algorithm helps to optimize the parameters that govern the model, specifically, for two purposes: (i) the selection of variables; and (ii) the optimization of membership functions. Data from a real water supply network are used to evaluate the accuracy of the developed system. Several graphs that depict the ranking of pipes according to their risk of failure against the network length to be replaced support the choice of the most successful model. In fact, results demonstrate that the annual replacement of 6.75% of the network length makes it possible to prevent 41.14% of unexpected pipe failuresEm

Learning lost temporal fuzzy association rules

Fuzzy association rule mining discovers patterns in transactions, such as shopping baskets in a supermarket, or Web page accesses by a visitor to a Web site. Temporal patterns can be present in fuzzy association rules because the underlying process generating the data can be dynamic. However, existing solutions may not discover all interesting patterns because of a previously unrecognised problem that is revealed in this thesis. The contextual meaning of fuzzy association rules changes because of the dynamic feature of data. The static fuzzy representation and traditional search method are inadequate. The Genetic Iterative Temporal Fuzzy Association Rule Mining (GITFARM) framework solves the problem by utilising flexible fuzzy representations from a fuzzy rule-based system (FRBS). The combination of temporal, fuzzy and itemset space was simultaneously searched with a genetic algorithm (GA) to overcome the problem. The framework transforms the dataset to a graph for efficiently searching the dataset. A choice of model in fuzzy representation provides a trade-off in usage between an approximate and descriptive model. A method for verifying the solution to the hypothesised problem was presented. The proposed GA-based solution was compared with a traditional approach that uses an exhaustive search method. It was shown how the GA-based solution discovered rules that the traditional approach did not. This shows that simultaneously searching for rules and membership functions with a GA is a suitable solution for mining temporal fuzzy association rules. So, in practice, more knowledge can be discovered for making well-informed decisions that would otherwise be lost with a traditional approach.EPSRC DT