Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

Toward Human-Understandable, Explainable AI

Recent increases in computing power, coupled with rapid growth in the availability and quantity of data have rekindled our interest in the theory and applications of artificial intelligence (AI). However, for AI to be confidently rolled out by industries and governments, users want greater transparency through explainable AI (XAI) systems. The author introduces XAI concepts, and gives an overview of areas in need of further exploration-such as type-2 fuzzy logic systems-to ensure such systems can be fully understood and analyzed by the lay user

A Type-2 Fuzzy Logic Based System for Malaria Epidemic Prediction in Ethiopia

Malaria is the most prevalent mosquito-borne disease throughout tropical and subtropical regions of the world with severe medical, economic, and social impact. Malaria is a serious public health problem in Ethiopia since 1959, even if, its morbidity and mortality have been reduced starting from 2001. Various studies were conducted to predict the malaria epidemic using mathematical and statistical approaches, nevertheless, they had no learning capabilities. In this paper, we present a Type-2 Fuzzy Logic Based System for Malaria epidemic prediction in Ethiopia which was trained using real data collected throughout Ethiopia from 2013 to 2017. Fuzzy Logic Based Systems provide a transparent model which employs IF-Then rules for the prediction that could be easily analyzed and interpreted by decision-makers. This is quite important to fight the sources of Malaria and take the needed preventive measures where the generated rules from our system were able to explain the situations and intensity of input factors which contributed to Malaria epidemic incidence up to three months ahead. The presented Type-2 Fuzzy Logic System (T2FLS) learns its rules and fuzzy set parameters from data and was able to outperform its counterparts T1FLS in 2% and ANFIS in 0.33% in the accuracy of prediction of Malaria epidemic in Ethiopia. In addition, the proposed system did shed light on the main causes behind such outbreaks in Ethiopia because of its high level of interpretabilit

A Type-2 Fuzzy Logic Based System for Decision Support to Minimize Financial Default in the Sudanese Banking Sector

The recent global financial-economic crisis has led to the collapse of several companies from all over the world. This has created the need for powerful frameworks which can predict and reduce the potential risks in financial applications. Such frameworks help organizations to enhance their services quality and productivity as well as reducing the financial risk. The widely used techniques to build predictive models in the financial sector are based on statistical regression, which is deployed in many financial applications such as risk forecasting, customers’ loan default and fraud detection. However, in the last few years, the use of Artificial Intelligence (AI) techniques has increased in many financial institutions because they can provide powerful predictive models. However, the vast majority of the existing AI techniques employ black box models like Support Vector Machine (SVMs) and Neural Network (NNs) which are not able to give clear and transparent reasoning to explain the extracted decision. However, nowadays transparent reasoning models are highly needed for financial applications. This paper presents a type-2 fuzzy logic system for predicting default in financial systems. the researchers used a real dataset collected from the banking sector in Sudan. The proposed system resulted in transparent outputs which could be easily understood, analyzed and augmented by the human stakeholders. Besides, the proposed system resulted in an average recall of 83.5%, which outperformed its type-1 counterpart by 20.66%

Employing zSlices based general type-2 fuzzy sets to model multi level agreement

In this paper, we introduce the concept of Multi Level Agreement (MLA) based on (zSlices based) general type-2 fuzzy sets. We define the notion of MLA and describe how it can be computed based on a series of interval type-2 fuzzy sets. We provide examples, visualizing the nature of MLA sets and discuss their properties and interpretation. Moreover, we specifically address the reason for introducing MLA in order to allow the modeling of agreement in real world applications using fuzzy sets while still maintaining an uncertainty model and show that the use of general type-2 fuzzy sets is essential for MLA as classical sets, type-1 and interval type-2 fuzzy sets do not provide a degree of freedom which could be employed to model agreement. © 2011 IEEE

A Self-Tuning zSlices-Based General Type-2 Fuzzy PI Controller

The interval type-2 fuzzy Proportional-Integral (PI) controller (IT2-FPI) might be able to handle high levels of uncertainties to produce a satisfactory control performance, which could be potentially due to the robust performance as a result of the smoother control surface around the steady state. However, the transient state and disturbance rejection performance of the IT2-FPI may degrade in comparison with the type-1 fuzzy PI (T1-FPI) counterpart. This drawback can be resolved via general type-2 fuzzy PI controllers which can provide a tradeoff between the robust control performance of the IT2-FPI and the acceptable transient and disturbance rejection performance of the type-1 PI controllers. In this paper, we will present a zSlices-based general type-2 fuzzy PI controller (zT2-FPI), where the secondary membership functions (SMFs) of the antecedent general type-2 fuzzy sets are adjusted in an online manner. We will examine the effect of the SMF on the closed-system control performance to investigate their induced performance improvements. This paper will focus on the case followed in conventional or self-tuning fuzzy controller design strategies, where the aim is to decrease the integral action sufficiently around the steady state to have robust system performance against noises and parameter variations. The zSlices approach will give the opportunity to construct the zT2-FPI controller as a collection of IT2-FPI and T1-FPI controllers. We will present a new way to design a zT2-FPI controller based on a single tuning parameter where the features of T1-FPI (speed) and IT2-FPI (robustness) are combined without increasing the computational complexity much when compared with the IT2-FPI structure. This will allow the proposed zT2-FPI controller to achieve the desired transient state response and provide an efficient disturbance rejection and robust control performance. We will present several simulation studies on benchmark systems, in addition to real-world experiments that were performed using the PIONEER 3-DX mobile robot that will act as a platform to evaluate the proposed systems. The results will show that the control performance of the self-tuning zT2-FPI control structure enhances both the transient state and disturbance rejection performances when compared with the type-1 and IT2-FPI counterparts. In addition, the self-tuning zT2-FPI is more robust to disturbances, noise, and uncertainties when compared with the type-1 and interval type-2 fuzzy counterparts

A big bang-big crunch optimization based approach for interval type-2 fuzzy PID controller design

In this paper, we will present a big bang-big crunch optimization (BB-BC) based approach for the design of an interval type-2 fuzzy PID controller. The implemented global optimization algorithm has a low computational cost and a high convergence speed. As a consequence, the BB-BC method is a very efficient search algorithm when the number of the optimization parameters is relatively big. The optimized type-2 fuzzy controller is compared with PID and type-1 fuzzy PID controllers which were optimized with either the BB-BC optimization method or conventional design strategies. The paper will also show the effect the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets on the closed loop system performance. We will present a comparative study performed on the highly nonlinear cascaded tank process to show the superiority of the optimized interval type-2 fuzzy PID controller compared to its optimized PID, type-1 counterparts. © 2013 IEEE

A Big-Bang Big-Crunch Type-2 Fuzzy Logic-based System for Malaria Epidemic Prediction in Ethiopia

ABSTRACT- Malaria is a life-threatening disease caused by Plasmodium parasite infection with huge medical, economic, and social impact. Malaria is one of a serious public health problem in Ethiopia since 1959, even if, its morbidity and mortality have been reduced starting from 2001. Various studies were conducted to predict the Malaria epidemic using mathematical and statistical regression approaches, nevertheless, they had no learning capabilities. In this paper, we presented a type-2 fuzzy logic-based system for Malaria epidemic prediction (MEP) in Ethiopia which has been optimized by the Big-Bang Big-Crunch (BBBC) approach to maximizing the model accuracy and interpretability to predict for the future occurrence of Malaria. We compared the proposed BBBC optimized type-2 fuzzy logic-based system against its counterpart T1FLS, non-optimized T2FLS, ANFIS and ANN. The results show that the optimized proposed T2FLS provides a more interpretable model that predicts the future occurrence of Malaria from one up to three months ahead with optimal accuracy. This helps to answer the question of when and where must make preparation to prevent and control the occurrence of Malaria epidemic since the generated rules from our system were able to explain the situations and intensity of input factors which contributed to the Malaria epidemic and outbreak

Parallel Type-2 Fuzzy Logic Co-Processors for Engine Management

Marine diesel engines operate in highly dynamic and uncertain environments, hence they require robust and accurate speed controllers that can handle the encountered uncertainties. Type-2 Fuzzy Logic Controllers (FLCs) have shown that they can handle such uncertainties and give a superior performance to the existing commercial controllers. However, there are a number of computational bottlenecks that pose as significant barriers to the widespread deployment of type-2 FLCs in commercial embedded control systems. This paper explores the use of parallel hardware implementations of interval type-2 FLC as a means to eradicate these barriers thus producing bespoke co-processors for a soft core implementation of a FPGA based 32 bit RISC micro-processor. These co-processors will perform functions such as fuzzification and type reduction and are currently utilised as part of a larger embedded interval Type-2 Fuzzy Engine Management System (T2FEMS). Numerous timing comparisons were undertaken between the co-processors and their sequential counterparts where the type-2 co-processors reduced significantly the computational cycles required by the type-2 FLC. This reduction in computational cycles allowed the T2FEMS to produce faster control responses whilst offering a superior control performance to the commercial engine management systems. Thus the proposed co-processors enable us to fully explore the potential of interval and possibly general type-2 FLCs in commercial embedded applications. © 2007 IEEE

Comparing the Performance Potentials of Singleton and Non-singleton Type-1 and Interval Type-2 Fuzzy Systems in Terms of Sculpting the State Space

This paper provides a novel and better understanding of the performance potential of a nonsingleton (NS) fuzzy system over a singleton (S) fuzzy system. It is done by extending sculpting the state space works from S to NS fuzzification and demonstrating uncertainties about measurements, modeled by NS fuzzification: first, fire more rules more often, manifested by a reduction (increase) in the sizes of first-order rule partitions for those partitions associated with the firing of a smaller (larger) number of rules—the coarse sculpting of the state space; second, this may lead to an increase or decrease in the number of type-1 (T1) and interval type-2 (IT2) first-order rule partitions, which now contain rule pairs that can never occur for S fuzzification—a new rule crossover phenomenon —discovered using partition theory; and third, it may lead to a decrease, the same number, or an increase in the number of second-order rule partitions, all of which are system dependent—the fine sculpting of the state space. The authors' conjecture is that it is the additional control of the coarse sculpting of the state space, accomplished by prefiltering and the max–min (or max-product) composition, which provides an NS T1 or IT2 fuzzy system with the potential to outperform an S T1 or IT2 system when measurements are uncertain