# Fuzzy Logic

### Overview of artificial intelligence in medicine

Alan Turing (1950) was one of the founders of modern computers and AI. The "Turing test" was based on the fact that the intelligent behavior of a computer is the ability to achieve human level performance in cognition related tasks.[1] The 1980s and 1990s saw a surge in interest in AI. Artificial intelligent techniques such as fuzzy expert systems, Bayesian networks, artificial neural networks, and hybrid intelligent systems were used in different clinical settings in health care. In 2016, the biggest chunk of investments in AI research were in healthcare applications compared with other sectors.[2] AI in medicine can be dichotomized into two subtypes: Virtual and physical.[3]

### On the Efficiency of the Neuro-Fuzzy Classifier for User Knowledge Modeling Systems

User knowledge modeling systems are used as the most effective technology for grabbing new user's attention. Moreover, the quality of service (QOS) is increased by these intelligent services. This paper proposes two user knowledge classifiers based on artificial neural networks used as one of the influential parts of knowledge modeling systems. We employed multi-layer perceptron (MLP) and adaptive neural fuzzy inference system (ANFIS) as the classifiers. Moreover, we used real data contains the user's degree of study time, repetition number, their performance in exam, as well as the learning percentage, as our classifier's inputs. Compared with well-known methods like KNN and Bayesian classifiers used in other research with the same data sets, our experiments present better performance. Although, the number of samples in the train set is not large enough, the performance of the neuro-fuzzy classifier in the test set is 98.6% which is the best result in comparison with others. However, the comparison of MLP toward the ANFIS results presents performance reduction, although the MLP performance is more efficient than other methods like Bayesian and KNN. As our goal is evaluating and reporting the efficiency of a neuro-fuzzy classifier for user knowledge modeling systems, we utilized many different evaluation metrics such as Receiver Operating Characteristic and the Area Under its Curve, Total Accuracy, and Kappa statistics.

### Zap Q-Learning With Nonlinear Function Approximation

The Zap stochastic approximation (SA) algorithm was introduced recently as a means to accelerate convergence in reinforcement learning algorithms. While numerical results were impressive, stability (in the sense of boundedness of parameter estimates) was established in only a few special cases. This class of algorithms is generalized in this paper, and stability is established under very general conditions. This general result can be applied to a wide range of algorithms found in reinforcement learning. Two classes are considered in this paper: (i)The natural generalization of Watkins' algorithm is not always stable in function approximation settings. Parameter estimates may diverge to infinity even in the \textit{linear} function approximation setting with a simple finite state-action MDP. Under mild conditions, the Zap SA algorithm provides a stable algorithm, even in the case of \textit{nonlinear} function approximation. (ii) The GQ algorithm of Maei et.~al.~2010 is designed to address the stability challenge. Analysis is provided to explain why the algorithm may be very slow to converge in practice. The new Zap GQ algorithm is stable even for nonlinear function approximation.

### A literature review on current approaches and applications of fuzzy expert systems

The main purposes of this study are to distinguish the trends of research in publication exits for the utilisations of the fuzzy expert and knowledge-based systems that is done based on the classification of studies in the last decade. The present investigation covers 60 articles from related scholastic journals, International conference proceedings and some major literature review papers. Our outcomes reveal an upward trend in the up-to-date publications number, that is evidence of growing notoriety on the various applications of fuzzy expert systems. This raise in the reports is mainly in the medical neuro-fuzzy and fuzzy expert systems. Moreover, another most critical observation is that many modern industrial applications are extended, employing knowledge-based systems by extracting the experts' knowledge.

### Lattice-Based Fuzzy Medical Expert System for Low Back Pain Management

Low Back Pain (LBP) is a common medical condition that deprives many individuals worldwide of their normal routine activities. In the absence of external biomarkers, diagnosis of LBP is quite challenging. It requires dealing with several clinical variables, which have no precisely quantified values. Aiming at the development of a fuzzy medical expert system for LBP management, this research proposes an attractive lattice-based knowledge representation scheme for handling imprecision in knowledge, offering a suitable design methodology for a fuzzy knowledge base and a fuzzy inference system. The fuzzy knowledge base is constructed in modular fashion, with each module capturing interrelated medical knowledge about the relevant clinical history, clinical examinations and laboratory investigation results. This approach in design ensures optimality, consistency and preciseness in the knowledge base and scalability. The fuzzy inference system, which uses the Mamdani method, adopts the triangular membership function for fuzzification and the Centroid of Area technique for defuzzification. A prototype of this system has been built using the knowledge extracted from the domain expert physicians. The inference of the system against a few available patient records at the ESI Hospital, Sealdah has been checked. It was found to be acceptable by the verifying medical experts.

### Artificial Neural Networks and Adaptive Neuro-fuzzy Models for Prediction of Remaining Useful Life

The U.S. water distribution system contains thousands of miles of pipes constructed from different materials, and of various sizes, and age. These pipes suffer from physical, environmental, structural and operational stresses, causing deterioration which eventually leads to their failure. Pipe deterioration results in increased break rates, reduced hydraulic capacity, and detrimental impacts on water quality. Therefore, it is crucial to use accurate models to forecast deterioration rates along with estimating the remaining useful life of the pipes to implement essential interference plans in order to prevent catastrophic failures. This paper discusses a computational model that forecasts the RUL of water pipes by applying Artificial Neural Networks (ANNs) as well as Adaptive Neural Fuzzy Inference System (ANFIS). These models are trained and tested acquired field data to identify the significant parameters that impact the prediction of RUL. It is concluded that, on average, with approximately 10\% of wall thickness loss in existing cast iron, ductile iron, asbestos-cement, and steel water pipes, the reduction of the remaining useful life is approximately 50%

### On Convergence Rate of Adaptive Multiscale Value Function Approximation For Reinforcement Learning

In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable functions, multiresolution analysis enables us to construct a wavelet system from which the basis functions are selected adaptively, resulting in a tree structure. Furthermore, we present the convergence rate of our multiscale approximation which does not depend on the regularity of basis functions.

### Optimize TSK Fuzzy Systems for Big Data Classification Problems: Bag of Tricks

Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily applicable to big data problems, especially when the size and the dimensionality of the data are both large. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy systems for big data classification problems. It integrates three novel techniques: 1) uniform regularization (UR), which is a regularization term added to the loss function to make sure the rules have similar average firing levels, and hence better generalization performance; 2) random percentile initialization (RPI), which initializes the membership function parameters efficiently and reliably; and, 3) batch normalization (BN), which extends BN from deep neural networks to TSK fuzzy systems to speedup the convergence and improve generalization. Experiments on nine datasets from various application domains, with varying size and feature dimensionality, demonstrated that each of UR, RPI and BN has its own unique advantages, and integrating all three together can achieve the best classification performance.

### Deep Gaussian networks for function approximation on data defined manifolds

In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or sphere. In practice, the data might not be dense on these domains, and therefore, the approximation theory results are observed to be too conservative. In manifold learning, one assumes instead that the data is sampled from an unknown manifold; i.e., the manifold is defined by the data itself. Function approximation on this unknown manifold is then a two stage procedure: first, one approximates the Laplace-Beltrami operator (and its eigen-decomposition) on this manifold using a graph Laplacian, and next, approximates the target function using the eigen-functions. In this paper, we propose a more direct approach to function approximation on unknown, data defined manifolds without computing the eigen-decomposition of some operator, and estimate the degree of approximation in terms of the manifold dimension. This leads to similar results in function approximation using deep networks where each channel evaluates a Gaussian network on a possibly unknown manifold.

### Kernels on fuzzy sets: an overview

This paper introduces the concept of kernels on fuzzy sets as a similarity measure for $[0,1]$-valued functions, a.k.a. \emph{membership functions of fuzzy sets}. We defined the following classes of kernels: the cross product, the intersection, the non-singleton and the distance-based kernels on fuzzy sets. Applicability of those kernels are on machine learning and data science tasks where uncertainty in data has an ontic or epistemistic interpretation.