Fuzzy Logic


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

arXiv.org Artificial Intelligence

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

arXiv.org Artificial Intelligence

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.


Gradient Q$(\sigma, \lambda)$: A Unified Algorithm with Function Approximation for Reinforcement Learning

arXiv.org Machine Learning

Full-sampling (e.g., Q-learning) and pure-expectation (e.g., Expected Sarsa) algorithms are efficient and frequently used techniques in reinforcement learning. Q$(\sigma,\lambda)$ is the first approach unifies them with eligibility trace through the sampling degree $\sigma$. However, it is limited to the tabular case, for large-scale learning, the Q$(\sigma,\lambda)$ is too expensive to require a huge volume of tables to accurately storage value functions. To address above problem, we propose a GQ$(\sigma,\lambda)$ that extends tabular Q$(\sigma,\lambda)$ with linear function approximation. We prove the convergence of GQ$(\sigma,\lambda)$. Empirical results on some standard domains show that GQ$(\sigma,\lambda)$ with a combination of full-sampling with pure-expectation reach a better performance than full-sampling and pure-expectation methods.


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

arXiv.org Machine Learning

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

arXiv.org Machine 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

arXiv.org Machine Learning

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

arXiv.org Machine Learning

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.


Sensitivity study of ANFIS model parameters to predict the pressure gradient with combined input and outputs hydrodynamics parameters in the bubble column reactor

arXiv.org Artificial Intelligence

Intelligent algorithms are recently used in the optimization process in chemical engineering and application of multiphase flows such as bubbling flow. This overview of modeling can be a great replacement with complex numerical methods or very time-consuming and disruptive measurement experimental process. In this study, we develop the adaptive network-based fuzzy inference system (ANFIS) method for mapping inputs and outputs together and understand the behavior of the fluid flow from other output parameters of the bubble column reactor. Neural cells can fully learn the process in their memory and after the training stage, the fuzzy structure predicts the multiphase flow data. Four inputs such as x coordinate, y coordinate, z coordinate, and air superficial velocity and one output such as pressure gradient are considered in the learning process of the ANFIS method. During the learning process, the different number of the membership function, type of membership functions and the number of inputs are examined to achieve the intelligent algorithm with high accuracy. The results show that as the number of inputs increases the accuracy of the ANFIS method rises up to R^2>0.99 almost for all cases, while the increment in the number of rules has a effect on the intelligence of artificial algorithm. This finding shows that the density of neural objects or higher input parameters enables the moded for better understanding. We also proposed a new evaluation of data in the bubble column reactor by mapping inputs and outputs and shuffle all parameters together to understand the behaviour of the multiphase flow as a function of either inputs or outputs. This new process of mapping inputs and outputs data provides a framework to fully understand the flow in the fluid domain in a short time of fuzzy structure calculation.


ParaFIS:A new online fuzzy inference system based on parallel drift anticipation

arXiv.org Artificial Intelligence

This paper proposes a new architecture of incremen-tal fuzzy inference system (also called Evolving Fuzzy System-EFS). In the context of classifying data stream in non stationary environment, concept drifts problems must be addressed. Several studies have shown that EFS can deal with such environment thanks to their high structural flexibility. These EFS perform well with smooth drift (or incremental drift). The new architecture we propose is focused on improving the processing of brutal changes in the data distribution (often called brutal concept drift). More precisely, a generalized EFS is paired with a module of anticipation to improve the adaptation of new rules after a brutal drift. The proposed architecture is evaluated on three datasets from UCI repository where artificial brutal drifts have been applied. A fit model is also proposed to get a "reactivity time" needed to converge to the steady-state and the score at end. Both characteristics are compared between the same system with and without anticipation and with a similar EFS from state-of-the-art. The experiments demonstrates improvements in both cases.


Provably Efficient Reinforcement Learning with Linear Function Approximation

arXiv.org Machine Learning

Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational and statistical efficiency, especially given the need to manage the exploration/exploitation tradeoff. As a result, a core RL question remains open: how can we design provably efficient RL algorithms that incorporate function approximation? This question persists even in a basic setting with linear dynamics and linear rewards, for which only linear function approximation is needed. This paper presents the first provable RL algorithm with both polynomial runtime and polynomial sample complexity in this linear setting, without requiring a "simulator" or additional assumptions. Concretely, we prove that an optimistic modification of Least-Squares Value Iteration (LSVI)---a classical algorithm frequently studied in the linear setting---achieves $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret, where $d$ is the ambient dimension of feature space, $H$ is the length of each episode, and $T$ is the total number of steps. Importantly, such regret is independent of the number of states and actions.