Type-2 fuzzy sets applied to multivariable self-organizing fuzzy logic controllers for regulating anesthesia

In this paper, novel interval and general type-2 self-organizing fuzzy logic controllers (SOFLCs) are proposed for the automatic control of anesthesia during surgical procedures. The type-2 SOFLC is a hierarchical adaptive fuzzy controller able to generate and modify its rule-base in response to the controller's performance. The type-2 SOFLC uses type-2 fuzzy sets derived from real surgical data capturing patient variability in monitored physiological parameters during anesthetic sedation, which are used to define the footprint of uncertainty (FOU) of the type-2 fuzzy sets. Experimental simulations were carried out to evaluate the performance of the type-2 SOFLCs in their ability to control anesthetic delivery rates for maintaining desired physiological set points for anesthesia (muscle relaxation and blood pressure) under signal and patient noise. Results show that the type-2 SOFLCs can perform well and outperform previous type-1 SOFLC and comparative approaches for anesthesia control producing lower performance errors while using better defined rules in regulating anesthesia set points while handling the control uncertainties. The results are further supported by statistical analysis which also show that zSlices general type-2 SOFLCs are able to outperform interval type-2 SOFLC in terms of their steady state performance

A Linear General Type-2 Fuzzy Logic Based Computing With Words Approach for Realising an Ambient Intelligent Platform for Cooking Recipes Recommendation

This paper addresses the need to enhance transparency in ambient intelligent environments by developing more natural ways of interaction, which allow the users to communicate easily with the hidden networked devices rather than embedding obtrusive tablets and computing equipment throughout their surroundings. Ambient intelligence vision aims to realize digital environments that adapt to users in a responsive, transparent, and context-aware manner in order to enhance users' comfort. It is, therefore, appropriate to employ the paradigm of “computing with words” (CWWs), which aims to mimic the ability of humans to communicate transparently and manipulate perceptions via words. One of the daily activities that would increase the comfort levels of the users (especially people with disabilities) is cooking and performing tasks in the kitchen. Existing approaches on food preparation, cooking, and recipe recommendation stress on healthy eating and balanced meal choices while providing limited personalization features through the use of intrusive user interfaces. Herein, we present an application, which transparently interacts with users based on a novel CWWs approach in order to predict the recipe's difficulty level and to recommend an appropriate recipe depending on the user's mood, appetite, and spare time. The proposed CWWs framework is based on linear general type-2 (LGT2) fuzzy sets, which linearly quantify the linguistic modifiers in the third dimension in order to better represent the user perceptions while avoiding the drawbacks of type-1 and interval type-2 fuzzy sets. The LGT2-based CWWs framework can learn from user experiences and adapt to them in order to establish more natural human-machine interaction. We have carried numerous real-world experiments with various users in the University of Essex intelligent flat. The comparison analysis between interval type-2 fuzzy sets and LGT2 fuzzy sets demonstrates up to 55.43% improvement when general type-2 fuzzy sets are used than when interval type-2 fuzzy sets are used instead. The quantitative and qualitative analysis both show the success of the system in providing a natural interaction with the users for recommending food recipes where the quantitative analysis shows the high statistical correlation between the system output and the users' feedback; the qualitative analysis presents social scienc

Performance Analysis of Extracted Rule-Base Multivariable Type-2 Self-Organizing Fuzzy Logic Controller Applied to Anesthesia

We compare type-1 and type-2 self-organizing fuzzy logic controller (SOFLC) using expert initialized and pretrained extracted rule-bases applied to automatic control of anaesthesia during surgery. We perform experimental simulations using a nonfixed patient model and signal noise to account for environmental and patient drug interaction uncertainties. The simulations evaluate the performance of the SOFLCs in their ability to control anesthetic delivery rates for maintaining desired physiological set points for muscle relaxation and blood pressure during a multistage surgical procedure. The performances of the SOFLCs are evaluated by measuring the steady state errors and control stabilities which indicate the accuracy and precision of control task. Two sets of comparisons based on using expert derived and extracted rule-bases are implemented as Wilcoxon signed-rank tests. Results indicate that type-2 SOFLCs outperform type-1 SOFLC while handling the various sources of uncertainties. SOFLCs using the extracted rules are also shown to outperform those using expert derived rules in terms of improved control stability

From interval-valued data to general type-2 fuzzy sets

In this paper, a new approach is presented to model interval-based data using fuzzy sets (FSs). Specifically, we show how both crisp and uncertain intervals (where there is uncertainty about the endpoints of intervals) collected from individual or multiple survey participants over single or repeated surveys can be modeled using type-1, interval type-2, or general type-2 FSs based on zSlices. The proposed approach is designed to minimize any loss of information when transferring the interval-based data into FS models, and to avoid, as much as possible, assumptions about the distribution of the data. Furthermore, our approach does not rely on data preprocessing or outlier removal, which can lead to the elimination of important information. Different types of uncertainty contained within the data, namely intra- and inter-source uncertainty, are identified and modeled using the different degrees of freedom of type-2 FSs, thus providing a clear representation and separation of these individual types of uncertainty present in the data. We provide full details of the proposed approach, as well as a series of detailed examples based on both real-world and synthetic data. We perform comparisons with analogue techniques to derive FSs from intervals, namely the interval approach and the enhanced interval approach, and highlight the practical applicability of the proposed approach

A Self-Adaptive Online Brain Machine Interface of a Humanoid Robot through a General Type-2 Fuzzy Inference System

This paper presents a self-adaptive general type-2 fuzzy inference system (GT2 FIS) for online motor imagery (MI) decoding to build a brain-machine interface (BMI) and navigate a bi-pedal humanoid robot in a real experiment, using EEG brain recordings only. GT2 FISs are applied to BMI for the first time in this study. We also account for several constraints commonly associated with BMI in real practice: 1) maximum number of electroencephalography (EEG) channels is limited and fixed, 2) no possibility of performing repeated user training sessions, and 3) desirable use of unsupervised and low complexity features extraction methods. The novel learning method presented in this paper consists of a self-adaptive GT2 FIS that can both incrementally update its parameters and evolve (a.k.a. self-adapt) its structure via creation, fusion and scaling of the fuzzy system rules in an online BMI experiment with a real robot. The structure identification is based on an online GT2 Gath-Geva algorithm where every MI decoding class can be represented by multiple fuzzy rules (models). The effectiveness of the proposed method is demonstrated in a detailed BMI experiment where 15 untrained users were able to accurately interface with a humanoid robot, in a single thirty-minute experiment, using signals from six EEG electrodes only

Type-2 Fuzzy Logic based Systems for Adaptive Learning and Teaching within Intelligent E-Learning Environments

The recent years have witnessed an increased interest in e-learning platforms that incorporate adaptive learning and teaching systems that enable the creation of adaptive learning environments to suit individual student needs. The efficiency of these adaptive educational systems relies on the methodology used to accurately gather and examine information pertaining to the characteristics and needs of students and relies on the way that information is processed to form an adaptive learning context. The vast majority of existing adaptive educational systems do not learn from the users’ behaviours to create white-box models to handle the high level of uncertainty and that could be easily read and analysed by the lay user. The data generated from interactions, such as teacher–learner or learner–system interactions within asynchronous environments, provide great opportunities to realise more adaptive and intelligent e-learning platforms rather than propose prescribed pedagogy that depends on the idea of a few designers and experts. Another limitation of current adaptive educational systems is that most of the existing systems ignore gauging the students' engagements levels and mapping them to suitable delivery needs which match the students' knowledge and preferred learning styles. It is necessary to estimate the degree of students’ engagement with the course contents. Such feedback is highly important and useful for assessing the teaching quality and adjusting the teaching delivery in small and large-scale online learning platforms. Furthermore, most of the current adaptive educational systems are used within asynchronous e-learning contexts as self-paced e-learning products in which learners can study in their own time and at their own speed, totally ignorant of synchronous e-learning settings of teacher-led delivery of the learning material over a communication tool in real time. This thesis presents novel theoretical and practical architectures based on computationally lightweight T2FLSs for lifelong learning and adaptation of learners’ and teachers’ behaviours in small- and large-scale asynchronous and synchronous e-learning platforms. In small-scale asynchronous and synchronous e-learning platforms, the presented architecture augments an engagement estimate system using a noncontact, low-cost, and multiuser support 3D sensor Kinect (v2). This is able to capture reliable features including head pose direction and hybrid features of facial expression to enable convenient and robust estimation of engagement in small-scale online and onsite learning in an unconstrained and natural environment in which users are allowed to act freely and move without restrictions. We will present unique real-world experiments in large and small-scale e-learning platforms carried out by 1,916 users from King Abdul-Aziz and Essex universities in Saudi Arabia and the UK over the course of teaching Excel and PowerPoint in which the type 2 system is learnt and adapted to student and teacher behaviour. The type-2 fuzzy system will be subjected to extended and varied knowledge, engagement, needs, and a high level of uncertainty variation in e-learning environments outperforming the type 1 fuzzy system and non-adaptive version of the system by producing better performance in terms of improved learning, completion rates, and better user engagements

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

On transitioning from type-1 to interval type-2 fuzzy logic systems

Capturing the uncertainty arising from system noise has been a core feature of fuzzy logic systems (FLSs) for many years. This paper builds on previous work and explores the methodological transition of type-l (Tl) to interval type-2 fuzzy sets (IT2 FSs) for given "levels" of uncertainty. Specifically, we propose to transition from Tl to IT2 FLSs through varying the size of the Footprint Of Uncertainty (FOU) of their respective FSs while maintaining the original FS shape (e.g., triangular) and keeping the size of the FOU over the FS as constant as possible. The latter is important as it enables the systematic relating of FOU size to levels of uncertainty and vice versa, while the former enables an intuitive comparison between the Tl and T2 FSs. The effectiveness of the proposed method is demonstrated through a series of experiments using the well-known Mackey-Glass (MG) time series prediction problem. The results are compared with the results of the IT2 FS creation method introduced in [1] which follows a similar methodology as the proposed approach but does not maintain the membership function (MF) shape

Novel methods of measuring the similarity and distance between complex fuzzy sets

This thesis develops measures that enable comparisons of subjective information that is represented through fuzzy sets. Many applications rely on information that is subjective and imprecise due to varying contexts and so fuzzy sets were developed as a method of modelling uncertain data. However, making relative comparisons between data-driven fuzzy sets can be challenging. For example, when data sets are ambiguous or contradictory, then the fuzzy set models often become non-normal or non-convex, making them difficult to compare. This thesis presents methods of comparing data that may be represented by such (complex) non-normal or non-convex fuzzy sets. The developed approaches for calculating relative comparisons also enable fusing methods of measuring similarity and distance between fuzzy sets. By using multiple methods, more meaningful comparisons of fuzzy sets are possible. Whereas if only a single type of measure is used, ambiguous results are more likely to occur. This thesis provides a series of advances around the measuring of similarity and distance. Based on them, novel applications are possible, such as personalised and crowd-driven product recommendations. To demonstrate the value of the proposed methods, a recommendation system is developed that enables a person to describe their desired product in relation to one or more other known products. Relative comparisons are then used to find and recommend something that matches a person's subjective preferences. Demonstrations illustrate that the proposed method is useful for comparing complex, non-normal and non-convex fuzzy sets. In addition, the recommendation system is effective at using this approach to find products that match a given query

Learning of Type-2 Fuzzy Logic Systems using Simulated Annealing.

This thesis reports the work of using simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of type-1 and type-2 fuzzy logic systems to maximise their modelling ability. Therefore, it presents the combination of simulated annealing with three models, type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and general type-2 fuzzy logic systems to model four bench-mark problems including real-world problems. These problems are: noise-free Mackey-Glass time series forecasting, noisy Mackey-Glass time series forecasting and two real world problems which are: the estimation of the low voltage electrical line length in rural towns and the estimation of the medium voltage electrical line maintenance cost. The type-1 and type-2 fuzzy logic systems models are compared in their abilities to model uncertainties associated with these problems. Also, issues related to this combination between simulated annealing and fuzzy logic systems including type-2 fuzzy logic systems are discussed. The thesis contributes to knowledge by presenting novel contributions. The first is a novel approach to design interval type-2 fuzzy logic systems using the simulated annealing algorithm. Another novelty is related to the first automatic design of general type-2 fuzzy logic system using the vertical slice representation and a novel method to overcome some parametrisation difficulties when learning general type-2 fuzzy logic systems. The work shows that interval type-2 fuzzy logic systems added more abilities to modelling information and handling uncertainties than type-1 fuzzy logic systems but with a cost of more computations and time. For general type-2 fuzzy logic systems, the clear conclusion that learning the third dimension can add more abilities to modelling is an important advance in type-2 fuzzy logic systems research and should open the doors for more promising research and practical works on using general type-2 fuzzy logic systems to modelling applications despite the more computations associated with it