Prediction interval construction using interval type-2 fuzzy logic systems

This study proposes a novel non-parametric method for construction of prediction intervals (PIs) using interval type-2 Takagi-Sugeno-Kang fuzzy logic systems (IT2 TSK FLSs). The key idea in the proposed method is to treat the left and right end points of the type-reduced set as the lower and upper bounds of a PI. This allows us to construct PIs without making any special assumption about the data distribution. A new training algorithm is developed to satisfy conditions imposed by the associated confidence level on PIs. Proper adjustment of premise and consequent parameters of IT2 TSK FLSs is performed through the minimization of a PI-based objective function, rather than traditional error-based cost functions. This new cost function covers both validity and informativeness aspects of PIs. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Quantitative measures are applied for assessing the quality of PIs constructed using IT2 TSK FLSs. The demonstrated results for four benchmark case studies with homogenous and heterogeneous noise clearly show the proposed method is capable of generating high quality PIs useful for decision-making.

Approximation of centroid end-points and switch points for replacing type reduction algorithms

Despite several years of research, type reduction (TR) operation in interval type-2 fuzzy logic system (IT2FLS) cannot perform as fast as a type-1 defuzzifier. In particular, widely used Karnik-Mendel (KM) TR algorithm is computationally much more demanding than alternative TR approaches. In this work, a data driven framework is proposed to quickly, yet accurately, estimate the output of the KM TR algorithm using simple regression models. Comprehensive simulation performed in this study shows that the centroid end-points of KM algorithm can be approximated with a mean absolute percentage error as low as 0.4%. Also, switch point prediction accuracy can be as high as 100%. In conjunction with the fact that simple regression model can be trained with data generated using exhaustive defuzzification method, this work shows the potential of proposed method to provide highly accurate, yet extremely fast, TR approximation method. Speed of the proposed method should theoretically outperform all available TR methods while keeping the uncertainty information intact in the process.

Effect of different initializations on EKM algorithm

As an integral part of interval type-2 fuzzy logic system (IT2FLS), type reduction (TR) plays a vital role in determining the performance of IT2FLS. Out of many type reduction algorithms, only Karnik-Mendel type TR algorithms capture the essence of interval type-2 fuzzy sets in type reduction. Enhanced Karnik-Mendel (EKM) algorithm is the most commonly used TR algorithm. In this work, we propose three new initializations for EKM algorithm. It is shown they are performing better than EKM and one of the proposed initializations significantly outperforms others. The performance gain can be upto 40% as per comprehensive simulation results demonstrated in this paper. Our findings are justified by computational time savings and iteration requirement for switch point search.

Switch point finding using polynomial regression for fuzzy type reduction algorithms

Karnik-Mendel (KM) algorithm is the most widely used type reduction (TR) method in literature for the design of interval type-2 fuzzy logic systems (IT2FLS). Its iterative nature for finding left and right switch points is its Achilles heel. Despite a decade of research, none of the alternative TR methods offer uncertainty measures equivalent to KM algorithm. This paper takes a data-driven approach to tackle the computational burden of this algorithm while keeping its key features. We propose a regression method to approximate left and right switch points found by KM algorithm. Approximator only uses the firing intervals, rnles centroids, and FLS strnctural features as inputs. Once training is done, it can precisely approximate the left and right switch points through basic vector multiplications. Comprehensive simulation results demonstrate that the approximation accuracy for a wide variety of FLSs is 100%. Flexibility, ease of implementation, and speed are other features of the proposed method.

Evaluation and comparison of type reduction algorithms from a forecast accuracy perspective

A variety of type reduction (TR) algorithms have been proposed for interval type-2 fuzzy logic systems (IT2 FLSs). The focus of existing literature is mainly on computational requirements of TR algorithm. Often researchers give more rewards to computationally less expensive TR algorithms. This paper evaluates and compares five frequently used TR algorithms from a forecasting performance perspective. Algorithms are judged based on the generalization power of IT2 FLS models developed using them. Four synthetic and real world case studies with different levels of uncertainty are considered to examine effects of TR algorithms on forecasts accuracies. It is found that Coupland-Jonh TR algorithm leads to models with a better forecasting performance. However, there is no clear relationship between the width of the type reduced set and TR algorithm.

Hardware implementation of type-2 programmable fuzzifier

The design of full programmable type-2 membership function circuit is presented in this paper. This circuit is used to implement the fuzzifier block of Type-2 Fuzzy Logic Controller chip. In this paper the type-2 fuzzy set was obtained by blurring the width of the type-1 fuzzy set. This circuit allows programming the height and the shape of the membership function. It operates in current mode, with supply voltage of 3.3V. The simulation results of interval type-2 membership function circuit have been done in CMOS 0.35μm technology using Mentor Graphics software. © 2011 IEEE.

Effects of type reduction algorithms on forecasting accuracy of IT2FLS models

Type reduction (TR) is one of the key components of interval type-2 fuzzy logic systems (IT2FLSs). Minimizing the computational requirements has been one of the key design criteria for developing TR algorithms. Often researchers give more rewards to computationally less expensive TR algorithms. This paper evaluates and compares five frequently used TR algorithms based on their contribution to the forecasting performance of IT2FLS models. Algorithms are judged based on the generalization power of IT2FLS models developed using them. Synthetic and real world case studies with different levels of uncertainty are considered to examine effects of TR algorithms on forecasts' accuracies. As per obtained results, Coupland-Jonh TR algorithm leads to models with a higher and more stable forecasting performance. However, there is no obvious and consistent relationship between the widths of the type reduced set and the TR algorithm. © 2013 Elsevier B.V.

Estimação do risco de morte de recém-nascidos utilizando logica fuzzy tipo-2 intervalar

The main objective of the presented study is the development of a predictive interval type-2 fuzzy inference system in order to estimate the mortality risk for a newborn, to be used as an auxiliary tool for decision making in medical centers where there is a lack of professionals for this purpose and, afterwards, to compare its performance to a type-1 fuzzy system. The input variables were chosen due to their acquisition ‘simplicity, not involving any invasive tests, such as blood tests or other specific tests. The variables are easily obtained in the first few minutes of life: birth weight, gestational age at delivery, 5-minute Apgar score and previous report of stillbirth. Databases from the DATASUS were used to validate the model. 1351 records from the city of São José dos Campos, a mid-sized city in the São Paulo state’s countryside, were considered in this study. Finally, an analysis using the ROC curve was performed to estimate the model’s accuracy

About t-norms on type-2 fuzzy sets.

Walker et al. defined two families of binary operations on M (set of functions of [0,1] in [0,1]), and they determined that, under certain conditions, those operations are t-norms (triangular norm) or t-conorms on L (all the normal and convex functions of M). We define binary operations on M, more general than those given by Walker et al., and we study many properties of these general operations that allow us to deduce new t-norms and t-conorms on both L, and M.

Fuzzy logic optimized wireless sensor network routing protocol

Wireless sensor networks (WSNs) are used in health monitoring, tracking and security applications. Such networks transfer data from specific areas to a nominated destination. In the network, each sensor node acts as a routing element for other sensor nodes during the transmission of data. This can increase energy consumption of the sensor node. In this paper, we propose a routing protocol for improving network lifetime and performance. The proposed protocol uses type-2 fuzzy logic to minimize the effects of uncertainty produced by the environmental noise. Simulation results show that the proposed protocol performs better than a recently developed routing protocol in terms of extending network lifetime and saving energy and also reducing data packet lost.

Classification of healthcare data using genetic fuzzy logic system and wavelets

Healthcare plays an important role in promoting the general health and well-being of people around the world. The difficulty in healthcare data classification arises from the uncertainty and the high-dimensional nature of the medical data collected. This paper proposes an integration of fuzzy standard additive model (SAM) with genetic algorithm (GA), called GSAM, to deal with uncertainty and computational challenges. GSAM learning process comprises three continual steps: rule initialization by unsupervised learning using the adaptive vector quantization clustering, evolutionary rule optimization by GA and parameter tuning by the gradient descent supervised learning. Wavelet transformation is employed to extract discriminative features for high-dimensional datasets. GSAM becomes highly capable when deployed with small number of wavelet features as its computational burden is remarkably reduced. The proposed method is evaluated using two frequently-used medical datasets: the Wisconsin breast cancer and Cleveland heart disease from the UCI Repository for machine learning. Experiments are organized with a five-fold cross validation and performance of classification techniques are measured by a number of important metrics: accuracy, F-measure, mutual information and area under the receiver operating characteristic curve. Results demonstrate the superiority of the GSAM compared to other machine learning methods including probabilistic neural network, support vector machine, fuzzy ARTMAP, and adaptive neuro-fuzzy inference system. The proposed approach is thus helpful as a decision support system for medical practitioners in the healthcare practice.

A fuzzy logic system applied in lightning models

This paper describes a novel approach for mapping lightning processes using fuzzy logic. The estimation process is carried out using a fuzzy system based on Sugeno's architecture. Simulation results confirm that proposed approach can be efficiently used in these types of problem.

A new energy efficient cluster-head and backup selection scheme in WSN

Despite significant advancements in wireless sensor networks (WSNs), energy conservation remains one of the most important research challenges. Proper organization of nodes (clustering) is one of the major techniques to expand the lifespan of the whole network through aggregating data at the cluster head. The cluster head is the backbone of the entire cluster. That means if a cluster head fails to accomplish its function, the received and collected data by cluster head can be lost. Moreover, the energy consumption following direct communications from sources to base stations will be increased. In this paper, we propose a type-2 fuzzy based self-configurable cluster head selection (SCCH) approach to not only consider the selection criterion of the cluster head but also present the cluster backup approach. Thus, in case of cluster failure, the system still works in an efficient way. The novelty of this protocol is the ability of handling communication uncertainty, which is an inherent operational aspect of sensor networks. The experiment results indicate SCCH performs better than other recently developed methods.