Fuzzy Inductive Reasoning Research Articles

Forest Fire Forecasting Using Fuzzy Logic Models

In this study, we explored hybrid fuzzy logic modelling techniques to predict the burned area of forest fires. Fast detection is crucial for successful firefighting, and a model with an accurate prediction ability is extremely useful for optimizing fire management. Fuzzy Inductive Reasoning (FIR) and the Adaptive Neuro-Fuzzy Inference System (ANFIS) are two powerful fuzzy techniques for modelling burned areas of forests in Portugal. The results obtained from them were compared with those of other artificial intelligence techniques applied to the same datasets found in the literature.

An e-Learning Toolbox Based on Rule-Based Fuzzy Approaches

In this paper, an e-Learning toolbox based on a set of fuzzy logic data mining techniques is presented. The toolbox is mainly based on the fuzzy inductive reasoning (FIR) methodology and two of its key extensions: (i) the linguistic rules extraction algorithm (LR-FIR), which extracts comprehensible and consistent sets of rules describing students’ learning behavior, and (ii) the causal relevance approach (CR-FIR), which allows to reduce uncertainty during a student’s performance prediction stage, and provides a relative weighting of the features involved in the evaluation process. In addition, the presented toolbox enables, in an incremental way, detecting and grouping students with respect to their learning behavior, with the main goal to timely detect failing students, and properly provide them with suitable and actionable feedback. The proposed toolbox has been applied to two different datasets gathered from two courses at the Latin American Institute for Educational Communication virtual campus. The introductory and didactic planning courses were analyzed using the proposed toolbox. The results obtained by the functionalities offered by the platform allow teachers to make decisions and carry out improvement actions in the current course, i.e., to monitor specific student clusters, to analyze possible changes in the different evaluable activities, or to reduce (to some extent) teacher workload.

Energy Performance Forecasting of Residential Buildings Using Fuzzy Approaches

The energy consumption used for domestic purposes in Europe is, to a considerable extent, due to heating and cooling. This energy is produced mostly by burning fossil fuels, which has a high negative environmental impact. The characteristics of a building are an important factor to determine the necessities of heating and cooling loads. Therefore, the study of the relevant characteristics of the buildings, regarding the heating and cooling needed to maintain comfortable indoor air conditions, could be very useful in order to design and construct energy-efficient buildings. In previous studies, different machine-learning approaches have been used to predict heating and cooling loads from the set of variables: relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area and glazing area distribution. However, none of these methods are based on fuzzy logic. In this research, we study two fuzzy logic approaches, i.e., fuzzy inductive reasoning (FIR) and adaptive neuro fuzzy inference system (ANFIS), to deal with the same problem. Fuzzy approaches obtain very good results, outperforming all the methods described in previous studies except one. In this work, we also study the feature selection process of FIR methodology as a pre-processing tool to select the more relevant variables before the use of any predictive modelling methodology. It is proven that FIR feature selection provides interesting insights into the main building variables causally related to heating and cooling loads. This allows better decision making and design strategies, since accurate cooling and heating load estimations and correct identification of parameters that affect building energy demands are of high importance to optimize building designs and equipment specifications.

Modeling the control of the central nervous system over the cardiovascular system using support vector machines

The control of the central nervous system (CNS) over the cardiovascular system (CS) has been modeled using different techniques, such as fuzzy inductive reasoning, genetic fuzzy systems, neural networks, and nonlinear autoregressive techniques; the results obtained so far have been significant, but not solid enough to describe the control response of the CNS over the CS. In this research, support vector machines (SVMs) are used to predict the response of a branch of the CNS, specifically, the one that controls an important part of the cardiovascular system. To do this, five models are developed to emulate the output response of five controllers for the same input signal, the carotid sinus blood pressure (CSBP). These controllers regulate parameters such as heart rate, myocardial contractility, peripheral and coronary resistance, and venous tone. The models are trained using a known set of input-output response in each controller; also, there is a set of six input-output signals for testing each proposed model. The input signals are processed using an all-pass filter, and the accuracy performance of the control models is evaluated using the percentage value of the normalized mean square error (MSE). Experimental results reveal that SVM models achieve a better estimation of the dynamical behavior of the CNS control compared to others modeling systems. The main results obtained show that the best case is for the peripheral resistance controller, with a MSE of 1.20e-4%, while the worst case is for the heart rate controller, with a MSE of 1.80e-3%. These novel models show a great reliability in fitting the output response of the CNS which can be used as an input to the hemodynamic system models in order to predict the behavior of the heart and blood vessels in response to blood pressure variations.

Fuzzy inductive reasoning forecasting strategies able to cope with missing data: A smart grid application

Dealing with missing data is of great practical and theoretical interest in forecasting applications. In this study, we deal with the problem of forecasting with missing data in smart grid and BEMS applications, where the information from home area sensors and/or smart meters is sometimes missing, which may hinder or even prevent the forecasting of the next hours and days. In concrete, we focus in a Soft Computing technique called Fuzzy Inductive Reasoning (FIR) and its improved version that can cope with missing information in the forecasting process: flexible FIR. In this article eight different strategies for flexible FIR forecasting are defined and studied taking into account: causal relevance of input variables, consistency of predictions, inertia criterion and K-Nearest Neighbours. Furthermore, we evaluate the implications of prediction accuracy and number of predictions, when the number of Missing Values (MVs) in the training dataset is increased progressively. To this end, a real smart grid forecasting application, i.e. electricity load forecasting, has been chosen in this study. The results show that all eight strategies proposed are able to cope with MVs and take advantage of the inherent information in the data, with better results in those strategies making use of causal relevance. In addition, the robustness of flexible FIR and its eight strategies are proved taking into account that the percentage of electricity load predictions from the test dataset is on average 96.15% when the %MVs in training dataset was around 73%.

Fuzzy inductive reasoning: a consolidated approach to data-driven construction of complex dynamical systems

Fuzzy inductive reasoning (FIR) is a modelling and simulation methodology derived from the General Systems Problem Solver. It compares favourably with other soft computing methodologies, such as neural networks, genetic or neuro-fuzzy systems, and with hard computing methodologies, such as AR, ARIMA, or NARMAX, when it is used to predict future behaviour of different kinds of systems. This paper contains an overview of the FIR methodology, its historical background, and its evolution.

Genetic Learning of Fuzzy Parameters in Predictive and Decision Support Modelling

Abstract In this research a genetic fuzzy system (GFS) is proposed that performs discretization parameter learning in the context of the Fuzzy Inductive Reasoning (FIR) methodology and the Linguistic Rule FIR (LR-FIR) algorithm. The main goal of the GFS is to take advantage of the potentialities of GAs to learn the fuzzification parameters of the FIR and LR-FIR approaches in order to obtain reliable and useful predictive (FIR) models and decision support (LR-FIR) models. The GFS is evaluated in an e-learning context.

End Effect Processing for Empirical Mode Decomposition Using Fuzzy Inductive Reasoning

This paper focuses on the end effect problem of the empirical mode decomposition (EMD) algorithm, which results in a serious distortion in the EMD sifting process. A new method based on fuzzy inductive reasoning (FIR) is proposed to overcome the end effect. Fuzzy inductive reasoning method has simple inferring rules and strong predictive capability. The fuzzy inductive reasoning based method uses the sequence near the end as the input signal of fuzzy inductive reasoning model. This predictive value can be obtained after fuzzification, qualitative modeling ,qualitative simulation and debluring. The simulation results have shown that the fuzzy inductive reasoning based method has equivalent performance to the neural network based method.

On the extraction of decision support rules from fuzzy predictive models

In several application areas like banking, insurance, medicine, education, business, to name just a few, there are huge, sometimes unstructured data collections, and there is a need to convert data into information. On the other hand, decision makers in industry are usually not statisticians, mathematicians, systems engineers, or AI experts. So it is important, to organize the results of the data analysis process and to present it in a form that can be easily interpreted by non-experts. One of the potential drawbacks affecting the application of computational intelligence (CI) methods in general to the analysis of data is the often limited interpretability of the results they yield. One way to overcome interpretability limitations is by explaining the operation of CI models using rule extraction methods. The interpretability of the model results should be greatly improved by their description in terms of reasonably simple and actionable rules that decision makers could rely on. In fact, rule extraction should provide whom the final responsibility for taking decisions rests, with an explanation about how a CI or related computer-based method has reached its decision. This paper describes a novel rule-extraction algorithm based on fuzzy logic, name LR-FIR (linguistic rules in FIR), that starts from the fuzzy inductive reasoning (FIR) methodology. FIR is able to obtain good qualitative relationships between the variables that compose the system and to predict the future behaviour of that system. The proposed algorithm (LR-FIR) is able to derive linguistic rules from a FIR model. The LR-FIR functioning is similar to those used in Boolean algebra. However the premises and consequences of rules are not necessarily binary in nature, hence the algorithm must be able to deal with multi-valued logic, and accept partial do-not-care conditions. Due to the fact that LR-FIR was developed within the FIR methodology, the obtained rules could be considered as predictive rules and deal naturally with the uncertainty captured in the FIR models. LR-FIR, in this paper, was evaluated using five data-sets from different domains: e-learning, global change temperature, brain tumour diagnosis, and two of the most used classical UCI data-sets: IRIS and Pima Indian Diabetes. The rules extracted by LR-FIR capture the main behaviour of each application, from the domain experts’ point of view, demonstrating in this sense, the efficiency of the proposed algorithm.

Confidence measures for predictions in fuzzy inductive reasoning

This paper deals with the assessment of the reliability of predictions made in the context of the fuzzy inductive reasoning methodology. The reliability of predictions is assessed by means of two separate confidence measures, a proximity measure and a similarity measure. A time series and a single-input/single-output system are used as two different applications to study the viability of these confidence measures.

Short-Term Load Forecasting Using Fuzzy Inductive Reasoning and Evolutionary Algorithms

In this paper, fuzzy inductive reasoning (FIR) is applied to the problem of short-term load forecasting (STLF) in power systems for a day in advance. The FIR model learns both past and future relations from the load and the temperature. The proposed optimization model uses an evolutionary algorithm based on a local random controlled search - simulated rebounding algorithm (SRA) - to choose the inputs to the FIR model. Using an optimization method to determine linear and nonlinear relationships between the variables, a parsimonious set of input variables can be identified improving the accuracy of the forecast. The input variables are updated when a new load pattern is happened or when relative errors are unacceptable. With this update is achieved, a better monitoring of the load trend due to the process is not strictly stationary. The FIR and SRA methodology is applied to the Ecuadorian power system as an application example. Results and comparisons with other STLF methodologies (autoregressive integrated moving average, artificial neural networks, and adaptive neuro-fuzzy inference system) are shown, and conclusions are derived.

Fuzzy inductive reasoning for variable selection analysis and modelling of biological systems

Fuzzy inductive reasoning (FIR) is a qualitative inductive modelling and simulation methodology for dealing with dynamical systems. It has proven to be a powerful tool for qualitative model identification and prediction of future behaviour of various kinds of dynamical systems, especially from the soft sciences, such as biology, biomedicine and ecology. This paper focuses on modelling aspects of the FIR methodology. It is shown that the FIR variable selection analysis is a useful tool not only for FIR but also for other classical quantitative methodologies such as nonlinear autoregressive moving average modelling with external inputs (NARMAX). The tool allows us to obtain models that interpret a system under study in optimal ways, in the sense that these models are well suited for predicting the future behaviour of the system they represent. The FIR variable selection analysis turns out to work well even in those applications where standard statistical variable selection analysis does not provide any useful information. In this paper, the FIR variable selection analysis is applied to a real system stemming from biology, namely, shrimp farming. The main goal is the identification of a growth model for occidental white shrimp (Penaeus vannamei), which allows farmers to plan the dates for seeding and harvesting the ponds in order to maximise their profits. FIR and NARMAX shrimp growth models are identified, and their prediction capabilities are compared to each other.

Causal relevance to improve the prediction accuracy of dynamical systems using inductive reasoning

In this paper, the concept of causal relevance (CR) is introduced in the context of the fuzzy inductive reasoning (FIR) modelling and simulation methodology. The idea behind CR is to quantify how much influence each system variable has, from the spatial and temporal points of view, on the prediction of the output. This paper introduces the FIR inference engine, and describes how it can be improved by means of the CR concept, helping to reduce uncertainty during the forecasting stage. The FIR inference engine is based on the k-nearest neighbour classification rule, commonly used in the field of pattern recognition, and uses a Euclidean distance measure to compute the distance between neighbours. In this paper, a weight-Euclidean distance measure is proposed that is able to find better quality neighbours by using the CR concept. Applications from different fields are studied in the light of the prediction process, and a comparison between the accuracy of the predictions obtained when using the classical inference engine and the CR option is performed. The results obtained from this research show that FIR predictions are more accurate and precise when the CR option is used, especially for systems where classical FIR forecasting performs rather poorly.

Learning fuzzy partitions in FIR methodology

The main goal of this research is the development of a hybrid genetic fuzzy system (GFS), composed by the fuzzy inductive reasoning (FIR) methodology and a genetic algorithm (GA) that is responsible of learning the fuzzy partitions needed in the recode process of FIR. A partition includes the number of fuzzy sets (classes) per variable and the membership function of each class. The resulting GFS is applied to two real problems, i.e. the estimation of the maintenance cost of medium voltage lines in Spanish towns and the prediction of ozone levels in Austria. The results obtained in each application are compared with some of the most popular classical statistical modeling methods, neural networks and other hybrid evolutionary data analysis techniques.

Optimization of fuzzy partitions for inductive reasoning using genetic algorithms

Fuzzy Inductive Reasoning (FIR) is a data-driven methodology that uses fuzzy and pattern recognition techniques to infer system models and to predict their future behavior. It is well known that variations on fuzzy partitions have a direct effect on the performance of the fuzzy-rule-based systems. The FIR methodology is not an exception. The performance of the model identification and prediction processes of FIR is highly influenced by the discretization parameters of the system variables, i.e. the number of classes of each variable and the membership functions that define its semantics. In this work, we design two new genetic fuzzy systems (GFSs) that improve this modeling and simulation technique. The main goal of the GFSs is to learn the fuzzification parameters of the FIR methodology. The new approaches are applied to two real modeling problems, the human central nervous system and an electrical distribution problem.

Visual-FIR: A tool for model identification and prediction of dynamical complex systems

A new platform for the fuzzy inductive reasoning (FIR) methodology has been designed and developed under the MATLAB environment. The new tool, named Visual-FIR, allows the identification of dynamic systems models in a user-friendly environment. FIR offers a pattern-based approach to modeling and predicting either univariate or multivariate time series, obtaining very good results when applied to various areas such as control, biology, and medicine. However, the available implementation of FIR was such that new code had to be developed for each new application studied. Visual-FIR resolves this limitation and offers a high-efficiency implementation. Furthermore, the Visual-FIR platform presents a new vision of the methodology based on process blocks and adds new features, increasing the overall capabilities of the FIR methodology. The DAMADICS benchmark problem is addressed in this research using the Visual-FIR approach.

Fault detection and identification using FIRFMS

This paper deals with two of the main tasks of fault monitoring systems (FMS): fault detection and fault identification. During fault detection, the FMS should recognize that the plant behavior is abnormal, and therefore, that the plant is not working properly. During fault identification, the FMS should conclude which type of failure has occurred. The main goal of this work is to present, in the context of the Fuzzy Inductive Reasoning Fault Monitoring System (FIRFMS), a new fault detection technique called enveloping and an enhancement of the fault identification method based on the model acceptability measure. Both contributions allow a more robust and reliable FIRFMS fault detection and identification processes. The enveloping technique and the model acceptability measure are applied to three applications of quite different areas. The first one corresponds to an electric circuit model previously used for such purpose in the literature. The second one is a biomedical system, the human central nervous system (CNS) control. It is the first attempt to apply the FIRFMS to support medical decisions. The third and last one corresponds to a water demand distribution system. The electric circuit is used to show that the enhanced FIRFMS outperforms the previous FIRFMS. The biomedical and water demand distribution systems are presented to show the good performance of the new FIRFMS.

Reasoning under uncertainty with FIR methodology

The aim of this research is to develop a new methodology called UNFIR (uncertainty in FIR) as an extension of the fuzzy inductive reasoning (FIR) technique. The main idea behind UNFIR is to expand the modeling capacity of the FIR methodology allowing it to work with classical fuzzy rules. On the one hand, UNFIR is able to automatically construct fuzzy rules starting from a set of pattern rules obtained by FIR. On the other hand, UNFIR affords the prediction of systems behavior by using a mixed pattern/fuzzy inference system that takes advantage of the uncertainty inherent to the data. The pattern rule base that the FIR methodology generates can be very large, obstructing the prediction process and reducing its efficiency. The new methodology preserves as much as possible the knowledge of the pattern rules in a compact fuzzy rule base. In this process some precision is lost but the robustness is considerably increased. The performance of UNFIR methodology as a systems’ prediction tool is also studied in this work. Three different applications are used for this purpose, i.e., a linear system, a non-linear system and an industrial process.

Estimating the horizon of predictability in time-series predictions using inductive modelling tools

This paper deals with the assessment of how far into the future a time series can be safely predicted using inductive modelling and extrapolation techniques. Three different time series are used to demonstrate the viability of the approaches presented in the paper: one time series representing the water demand of the city of Barcelona, another characterizing the water demand of a section of the city of Rotterdam, and a third describing weather data for the city of Tucson. Fuzzy inductive reasoning (FIR) is used to predict future values of these time series on the basis of their own past. FIR predictions come with two different built-in measures of confidence that can be used to obtain a quantitative estimate of how far into the future a time series can be predicted.

Reconstruction analysis-based algorithm to decompose a complex system into subsystems

Two previous papers [Mirats et al. (2002a) “On the selection of variables for Qualitative Modelling of Dynamical Systems”, International Journal of General Systems 31(5) pp. 435–467; Mirats et al. (2002b) “Variable selection procedures and efficient suboptimal mask search algorithms in Fuzzy Inductive Reasoning”, International Journal of General Systems 31(5), pp. 469–498] were devoted to the selection of a set of variables that can best be used to model (reconstruct) a given output variable, whereby only static relations were analysed. Yet even after reducing the set of variables in this fashion, the number of remaining variables may still be formidable for large-scale systems. The present paper aims at tackling this problem by discovering substructures within the whole set of the system variables. Hence whereas previous research dealt with the problem of model reduction by means of reducing the set of variables to be considered for modelling, the present paper focuses on model structuring as a means to subdivide the overall modelling task into subtasks that are hopefully easier to handle. The second and third sections analyse this problem from a system-theoretic perspective, presenting the reconstruction analysis (RA) methodology, an informational approach to the problem of decomposing a large-scale system into subsystems. The fourth section uses the fuzzy inductive reasoning (FIR) methodology to find a possible structure of a system. The study performed in this paper only considers static relations.