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

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

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

Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users. The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem. We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.This work has been supported by the Spanish Ministry of Science and Technology under projects TIN2008-06681-C06-01 and TIN2007-65981

IVTURS: A linguistic fuzzy rule-based classification system based on a new interval-valued fuzzy reasoning method with tuning and rule selection

Interval-valued fuzzy sets have been shown to be a useful tool for dealing with the ignorance related to the definition of the linguistic labels. Specifically, they have been successfully applied to solve classification problems, performing simple modifications on the fuzzy reasoning method to work with this representation and making the classification based on a single number. In this paper we present IVTURS, a new linguistic fuzzy rule-based classification method based on a new completely interval-valued fuzzy reasoning method. This inference process uses interval-valued restricted equivalence functions to increase the relevance of the rules in which the equivalence of the interval membership degrees of the patterns and the ideal membership degrees is greater, which is a desirable behaviour. Furthermore, their parametrized construction allows the computation of the optimal function for each variable to be performed, which could involve a potential improvement in the system’s behaviour. Additionally, we combine this tuning of the equivalence with rule selection in order to decrease the complexity of the system. In this paper we name our method IVTURS-FARC, since we use the FARC-HD method to accomplish the fuzzy rule learning process. The experimental study is developed in three steps in order to ascertain the quality of our new proposal. First, we determine both the essential role that interval-valued fuzzy sets play in the method and the need for the rule selection process. Next, we show the improvements achieved by IVTURS-FARC with respect to the tuning of the degree of ignorance when it is applied in both an isolated way and when combined with the tuning of the equivalence. Finally, the significance of IVTURS-FARC is further depicted by means of a comparison by which it is proved to outperform the results of FARC-HD and FURIA, which are two high performing fuzzy classification algorithms.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2011-28488 and TIN2010-15055 and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765

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

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

Enhancing multi-class classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies

There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper we aim to improve the behaviour of FARC-HD fuzzy classifier in multi-class classification problems using decomposition strategies, and more specifically One-vs-One (OVO) and One-vs-All (OVA) strategies. However, when these strategies are applied on FARC-HD a problem emerges due to the low confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t-norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t-norm with overlap functions. To do so, we define n-dimensional overlap functions. The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using twenty datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.This work was supported in part by the Spanish Ministry of Science and Technology under projects TIN2011-28488, TIN-2012-33856 and TIN-2013- 40765-P and the Andalusian Research Plan P10-TIC-6858 and P11-TIC-7765

Transparent but Accurate Evolutionary Regression Combining New Linguistic Fuzzy Grammar and a Novel Interpretable Linear Extension

Scientists must understand what machines do (systems should not behave like a black box), because in many cases how they predict is more important than what they predict. In this work, we propose a new extension of the fuzzy linguistic grammar and a mainly novel interpretable linear extension for regression problems, together with an enhanced new linguistic tree-based evolutionary multiobjective learning approach. This allows the general behavior of the data covered, as well as their specific variability, to be expressed as a single rule. In order to ensure the highest transparency and accuracy values, this learning process maximizes two widely accepted semantic metrics and also minimizes both the number of rules and the model mean squared error. The results obtained in 23 regression datasets show the effectiveness of the proposed method by applying statistical tests to the said metrics, which cover the different aspects of the interpretability of linguistic fuzzy models. This learning process has obtained the preservation of high-level semantics and less than 5 rules on average, while it still clearly outperforms some of the previous state-of-the-art linguistic fuzzy regression methods for learning interpretable regression linguistic fuzzy systems, and even to a competitive, pure accuracyoriented linguistic learning approach. Finally, we analyze a case study in a real problem related to childhood obesity, and a real expert carries out the analysis shown.Andalusian Government P18-RT-2248Health Institute Carlos III/Spanish Ministry of Science, Innovation and Universities PI20/00711Spanish Government PID2019-107793GB-I00 PID2020-119478GB-I0

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