Generating Interpretable Fuzzy Systems for Classification Problems

En este artículo se presenta un nuevo método para generar sistemas difusos interpretables, a partir de datos experimentalesde entrada y salida, para resolver problemas de clasificación. En la partición antecedente se emplean conjuntos triangulares con interpolación de 0.5 lo cual evita la presencia de solapamientos complejos que suceden en otros métodos. Los consecuentes, tipo Singleton, son generados por la proyección de los valores modales de cada función de membresía triangular en el espacio de salida y se emplea el método de mínimos cuadrados para el ajuste de los consecuentes. El método propuesto consigue una mayor precisión que la alcanzada con los métodos actuales existentes, empleando un número reducido de reglas y parámetros y sin sacrificar la interpretabilidad del modelo difuso. El enfoque propuesto es aplicado a dos problemas clásicos de clasificación: el Wisconsin Breast Cancer (WBC) y el Iris Data Classification Problem, para mostrar las ventajas del método y comparar los resultados con los alcanzados por otros investigadores.This paper presents a new method to generate interpretable fuzzy systems from training data to deal with classification problems. The antecedent partition uses triangular sets with 0.5 interpolations avoiding the presence of complex overlapping that happens in another method. Singleton consequents are generated form the projection of the modal values of each triangular membership function into the output space. Least square method is used to adjust the consequents. The proposed method gets a higher average classification accuracy rate than the existing methods with a reduced number of rules andparameters and without sacrificing the fuzzy system interpretability. The proposed approach is applied to two classical classification problems: Iris data and the Wisconsin Breast Cancer classification problem

Classification of Explainable Artificial Intelligence Methods through Their Output Formats

Machine and deep learning have proven their utility to generate data-driven models with high accuracy and precision. However, their non-linear, complex structures are often difficult to interpret. Consequently, many scholars have developed a plethora of methods to explain their functioning and the logic of their inferences. This systematic review aimed to organise these methods into a hierarchical classification system that builds upon and extends existing taxonomies by adding a significant dimension—the output formats. The reviewed scientific papers were retrieved by conducting an initial search on Google Scholar with the keywords “explainable artificial intelligence”; “explainable machine learning”; and “interpretable machine learning”. A subsequent iterative search was carried out by checking the bibliography of these articles. The addition of the dimension of the explanation format makes the proposed classification system a practical tool for scholars, supporting them to select the most suitable type of explanation format for the problem at hand. Given the wide variety of challenges faced by researchers, the existing XAI methods provide several solutions to meet the requirements that differ considerably between the users, problems and application fields of artificial intelligence (AI). The task of identifying the most appropriate explanation can be daunting, thus the need for a classification system that helps with the selection of methods. This work concludes by critically identifying the limitations of the formats of explanations and by providing recommendations and possible future research directions on how to build a more generally applicable XAI method. Future work should be flexible enough to meet the many requirements posed by the widespread use of AI in several fields, and the new regulation

Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

We propose an automatic methodology framework for short- and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Nonparametric residual variance estimation plays a key role in driving the identification and learning procedures. Concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems. The learn from examples method introduced by Wang and Mendel (W&M) is used for identification. The Levenberg–Marquardt (L–M) optimization method is then applied for tuning. The W&M method produces compact and potentially accurate inference systems when applied after a proper variable selection stage. The L–M method yields the best compromise between accuracy and interpretability of results, among a set of alternatives. Delta test based residual variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs. Experiments on a diverse set of time series prediction benchmarks are compared against least-squares support vector machines (LS-SVM), optimally pruned extreme learning machine (OP-ELM), and k-NN based autoregressors. The advantages of the proposed methodology are shown in terms of linguistic interpretability, generalization capability and computational cost. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications.Ministerio de Ciencia e Innovación TEC2008-04920Junta de Andalucía P08-TIC-03674, IAC07-I-0205:33080, IAC08-II-3347:5626

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

On Cognitive Preferences and the Plausibility of Rule-based Models

It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex ones. In this position paper, we question this latter assumption by focusing on one particular aspect of interpretability, namely the plausibility of models. Roughly speaking, we equate the plausibility of a model with the likeliness that a user accepts it as an explanation for a prediction. In particular, we argue that, all other things being equal, longer explanations may be more convincing than shorter ones, and that the predominant bias for shorter models, which is typically necessary for learning powerful discriminative models, may not be suitable when it comes to user acceptance of the learned models. To that end, we first recapitulate evidence for and against this postulate, and then report the results of an evaluation in a crowd-sourcing study based on about 3.000 judgments. The results do not reveal a strong preference for simple rules, whereas we can observe a weak preference for longer rules in some domains. We then relate these results to well-known cognitive biases such as the conjunction fallacy, the representative heuristic, or the recogition heuristic, and investigate their relation to rule length and plausibility.Comment: V4: Another rewrite of section on interpretability to clarify focus on plausibility and relation to interpretability, comprehensibility, and justifiabilit

Neuro-fuzzy knowledge processing in intelligent learning environments for improved student diagnosis

In this paper, a neural network implementation for a fuzzy logic-based model of the diagnostic process is proposed as a means to achieve accurate student diagnosis and updates of the student model in Intelligent Learning Environments. The neuro-fuzzy synergy allows the diagnostic model to some extent "imitate" teachers in diagnosing students' characteristics, and equips the intelligent learning environment with reasoning capabilities that can be further used to drive pedagogical decisions depending on the student learning style. The neuro-fuzzy implementation helps to encode both structured and non-structured teachers' knowledge: when teachers' reasoning is available and well defined, it can be encoded in the form of fuzzy rules; when teachers' reasoning is not well defined but is available through practical examples illustrating their experience, then the networks can be trained to represent this experience. The proposed approach has been tested in diagnosing aspects of student's learning style in a discovery-learning environment that aims to help students to construct the concepts of vectors in physics and mathematics. The diagnosis outcomes of the model have been compared against the recommendations of a group of five experienced teachers, and the results produced by two alternative soft computing methods. The results of our pilot study show that the neuro-fuzzy model successfully manages the inherent uncertainty of the diagnostic process; especially for marginal cases, i.e. where it is very difficult, even for human tutors, to diagnose and accurately evaluate students by directly synthesizing subjective and, some times, conflicting judgments

Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms

AbstractThe identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this paper a multi-objective evolutionary approach is proposed to determine a Pareto-optimum set of fuzzy systems with different compromises between their accuracy and complexity. In particular, two fundamental and competing objectives concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained system. Another key aspect of the algorithm presented in this work is the use of some new expert evolutionary operators, specifically designed for the problem of fuzzy function approximation, that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm

MODELLING EXPECTATIONS WITH GENEFER- AN ARTIFICIAL INTELLIGENCE APPROACH

Economic modelling of financial markets means to model highly complex systems in which expectations can be the dominant driving forces. Therefore it is necessary to focus on how agents form their expectations. We believe that they look for patterns, hypothesize, try, make mistakes, learn and adapt. AgentsÆ bounded rationality leads us to a rule-based approach which we model using Fuzzy Rule-Bases. E. g. if a single agent believes the exchange rate is determined by a set of possible inputs and is asked to put their relationship in words his answer will probably reveal a fuzzy nature like: "IF the inflation rate in the EURO-Zone is low and the GDP growth rate is larger than in the US THEN the EURO will rise against the USD". æLowÆ and ælargerÆ are fuzzy terms which give a gradual linguistic meaning to crisp intervalls in the respective universes of discourse. In order to learn a Fuzzy Fuzzy Rule base from examples we introduce Genetic Algorithms and Artificial Neural Networks as learning operators. These examples can either be empirical data or originate from an economic simulation model. The software GENEFER (GEnetic NEural Fuzzy ExplorER) has been developed for designing such a Fuzzy Rule Base. The design process is modular and comprises Input Identification, Fuzzification, Rule-Base Generating and Rule-Base Tuning. The two latter steps make use of genetic and neural learning algorithms for optimizing the Fuzzy Rule-Base.