This study combines two novel deterministic methods with a Convolutional Neural Network to develop a machine learning method that is aware of directionality of light in images. The first method detects shadows in terrestrial images by using a sliding-window algorithm that extracts specific hue and value features in an image. The second method interpolates light-sources by utilising a line-algorithm, which detects the direction of light sources in the image. Both of these methods are single-image solutions and employ deterministic methods to calculate the values from the image alone, without the need for illumination-models. They extract real-time geometry from the light source in an image, rather than mapping an illuminationmodel onto the image, which are the only models used today. Finally, those outputs are used to train a Convolutional Neural Network. This displays greater accuracy than previous methods for shadow detection and can predict light source-direction and thus orientation accurately, which is a considerable innovation for an unsupervised CNN. It is significantly faster than the deterministic methods. We also present a reference dataset for the problem of shadow and light direction detection.

Many decision making processes are based on choosing options with maximum utility. Often utility assessments are associated with uncertainty, which may be mathematically modeled by intervals of utilities. Intervals of utilities may be mapped to single utility values by so-called type reduction methods which have been originally developed in the context of interval type-2 defuzzification: the method by Nie and Tan (NT), consistent linear type reduction (CLTR), consistent quadratic type reduction (CQTR), and the uncertainty weight method (UW). This paper considers the problem of comparing pairs of utility intervals using type reduction methods. Three different possible relations between pairs of intervals (disjoint, overlapping, and inclusive) are distinguished in an extensive experimental study, which yields recommendations for the choice of type reduction methods with respect to the level of risk that the decision maker is willing to take. If the focus is on mean utility, then we recommend the Nie-Tan method. For more cautious decision making, when very low utilities should be avoided, we recommend consistent linear type reduction with a high value of the cautiousness parameter or consistent quadratic type reduction. For more risky decision making with a strong focus on very high utilities we recommend consistent linear type reduction with a low value of the cautiousness parameter.

We propose the application of interval type-2 fuzzy decision making (IT2FDM) to dynamic scheduling of deliveries in a just-in-time logistic process. Delivery decisions are based on order priorities computed from the expected decrease of customer satisfaction for each order. We compare IT2FDM with first in first out (FIFO), earliest due date first (EDDF), and (type-1) fuzzy decision making (FDM). In a simulation of a real world process for a duration of 600 days IT2FDM in comparison with the three other methods yields the highest just-in-time delivery rate, the highest average customer satisfaction, and the highest percentage of very satisfied customers. The increasing percentage of very satisfied customers at the same time leads to a slightly increasing percentage of not satisfied customers, but the trade- off between these percentages can be balanced by an appropriate choice of the risk parameter.

Fuzzy systems mimic human reasoning and provide solutions to problems under uncertainty via `computing with words'. This particular strength of fuzzy systems is often discarded in some real world applications where the fuzzy sets are designed for control problems or created through training using historical data. This study explores the interpretability of fuzzy systems by generating `meaningful' fuzzy sets using a dictionary constructed by humans and fuzzy transfer learning. The inverted pendulum control problem is used as a case study. The empirical results show that intepretability of a fuzzy system is achievable even for this problem at the expense of a `slightly' reduced performance.

Type-reduction of type-2 fuzzy sets is considered to be a defuzzification bottleneck because of the computational complexity involved in the process of type-reduction. In this paper, we prove that the closed-form Nie-Tan operator, which outputs the average of the upper and lower bounds of the footprint of uncertainty, is actually an accurate method for defuzzifying interval type-2 fuzzy sets.

In this paper, our aim is to compare and contrast various ways of modeling uncertainty by using different type-2 fuzzy membership functions available in literature. In particular we focus on a novel type-2 fuzzy membership function, - “Elliptic membership function”. After briefly explaining the motivation behind the suggestion of the elliptic membership function, we analyse the uncertainty distribution along its support, and we compare its uncertainty modeling capability with the existing membership functions. We also show how the elliptic membership functions perform in fuzzy arithmetic. In addition to its extra advantages over the existing type-2 fuzzy membership functions such as having decoupled parameters for its support and width, this novel membership function has some similar features to the Gaussian and triangular membership functions in addition and multiplication operations. Finally, we have tested the prediction capability of elliptic membership functions using interval type-2 fuzzy logic systems on US Dollar/Euro exchange rate prediction problem. Throughout the simulation studies, an extreme learning machine is used to train the interval type-2 fuzzy logic system. The prediction results show that, in addition to their various advantages mentioned above, elliptic membership functions have comparable prediction results when compared to Gaussian and triangular membership functions.

Type-2 fuzzy logic systems make use of type-2 fuzzy sets (T2FS). To be able to deliver useful type-2 fuzzy logic applications we need to be able to perform meaningful operations on these sets. These operations should also be practically tractable. However, T2FS suffer the shortcoming of being complex by definition. Indeed, the third dimension, which is the source of extra parameters, is in itself the origin of extra computational cost. The quest for a representation that allow practical systems to be implemented is the motivation for our work. In this paper, we define the alpha-cut decomposition theorem for T2FS which is a new representation analogous to the alpha-cut representation of type-1 fuzzy sets and the extension principle. We show that this new decomposition theorem forms a methodology for extending mathematical concepts from crisp sets to T2FS directly. In the process of developing this theory, we also define a generalization that allows us to extend operations from interval T2FS or interval valued fuzzy sets to T2FS. These results will allow for the more applications of T2FS by expiating the parallelism that the research here affords.

Interval type-2 defuzzification maps an interval type-2 fuzzy set to a crisp number. We show that the semantic meaning of the interval type-2 fuzzy set (the associated opportunity or risk) has to be considered in the choice of an appropriate interval type-2 defuzzification method. Motivated by a list of “axioms” for type-1 defuzzification we introduce twelve mathematical properties for interval type-2 defuzzification that serve as a theoretical framework to assess different interval type-2 defuzzification methods. We show that the well-known Karnik-Mendel algorithm violates at least four of these twelve properties.

Traditionally, devices which are able to determine a users gaze are large, expensive and often restrictive. We investigate the prospect of using common webcams and mobile devices such as laptops, tablets and phones without modification as an alternative means for obtaining a users gaze. A person's gaze can be fundamentally determined by the pose of the head as well as the orientation of the eyes. This initial work investigates the first of these factors - an estimate of the 3D head pose (and subsequently the positions of the eye centres) relative to a camera device. Specifically, we seek a low cost algorithm that requires only a one-time calibration for an individual user, that can run in real-time on the aforementioned mobile devices with noisy camera data. We use our head tracker to estimate the 4 eye corners of a user over a 10 second video. We present the results at several different frames per second (fps) to analyse the impact on the tracker with lower quality cameras. We show that our algorithm is efficient enough to run at 75fps on a common laptop, but struggles with tracking loss when the fps is lower than 10fps.

In this paper we explore the centroid defuzzification operation in the context of specific data retrieval application. We present a novel implication and centroid defuzzification approach based on geometric fuzzy sets and systems. It is demonstrated that this new approach requires fewer operations and results in a significant reduction in processing time in our application.

This paper presents a new defuzzification algorithm for interval type-2 fuzzy sets. The algorithm exploits the fact that we can treat an interval type-2 fuzzy set as two type-2 fuzzy sets. We suggest in this paper that monotonicity is an important property for defuzzifiers and so we provide a definition of monotonicity for type-2 defuzzifiers based on previous work by Runkler. The research reported here shows that our new operator is monotonic and provides a defuzzified value that lies within the interval computed by the popular Karnik-Mendel algorithm.

Software design patterns describe recurring design problems and provide the essence of best practice solutions. It is useful and important, for various software engineering tasks, to know which design pattern is implemented where in a software design. However, this information is often lost due to poor or absent documentation, and so accurate recognition tools are required. The problem is that design patterns, given their abstract and vague nature, have a level of resistance to be automatically and accurately recognized. Although this vagueness or fuzziness can be captured and modelled by the fuzzy inference system, it has not yet been applied to solve this problem. This paper fills this gap by proposing an approach for design pattern recognition based on Adaptive Neuro Fuzzy Inference System. Our approach consists of two phases: space reduction phase and design pattern recognition phase. Both phases are implemented by ANFIS. We evaluate the approach by an experiment conducted to recognize six design patterns in an open source application. The results show that the approach is viable and promising.

In this paper, simulated annealing algorithm is used to design general type-2 fuzzy logic systems (GT2FLS) with the aid of interval type-2 fuzzy logic systems (IT2FLS). The proposed practical design methodology aims to reduce computations needed to get the best footprint of uncertainty (FOU) using IT2FLS. Simulated annealing is used to learn IT2FLS followed by learning the secondary membership functions in GT2FLS using a novel parameterization method. This methodology has been applied to four bench-mark problems. some practical issues have been discussed and some analysis of the results obtained by IT2FLS and GT2FLS has been drawn.

In previous work the Authors defined the alpha-cut representation for type-2 fuzzy sets. The strength of this representation is that it allows type-2 fuzzy sets to be fully defined by a collection of crisp sets. Each of these crisp sets may be independently processed within a fuzzy logic system prior to defuzzification. This independence means this representation is ideal for parallel implementation by minimizing the requirement for iteration and synchronisation. In this work we investigate the parallel implementation of type-2 fuzzy logic operations on a massively parallel graphics processor unit. We explore the performance characteristics of this parallel implementation and contrast with a serial implementation in a series of experiments.

Construction of interval type-2 fuzzy set models is the first step in the perceptual computer, which is an implementation of computing with words. The interval approach (IA) has, so far, been the only systematic method to construct such models from data intervals that are collected from a survey. However, as pointed out in this paper, it has some limitations, and its performance can be further improved. This paper proposes an enhanced interval approach (EIA) and demonstrates its performance on data that are collected from a web survey. The data part of the EIA has more strict and reasonable tests than the IA, and the fuzzy set part of the EIA has an improved procedure to compute the lower membership function. We also perform a convergence analysis to answer two important questions: 1) Does the output interval type-2 fuzzy set from the EIA converge to a stable model as increasingly more data intervals are collected, and 2) if it converges, then how many data intervals are needed before the resulting interval type-2 fuzzy set is sufficiently similar to the model obtained from infinitely many data intervals? We show that the EIA converges in a mean-square sense, and generally, 30 data intervals seem to be a good compromise between cost and accuracy.

The overall age of the population within the United Kingdom is increasing. By 2034 it is estimated that 23% of the population will be aged 65 and over compared to 18% aged under 16. With an ageing population there is an increased requirement for formal or informal care often within established institutions. The advent of intelligent assisted living environments such as smart homes may offer a reduction in the requirement for such care whilst maintaining levels of independence and safety within individuals own homes. The use of ambient intelligent technology such as Wireless Sensor Networks can produce a number of issues, two of which we have endeavoured to address within this paper. Firstly, the nature of the hardware often used produces discrete temporal data readings which are an unreliable source of event recognition. Through the use of a derivative of Allen's temporal algebra, we have produced a method to identify events from discrete temporal information. Additionally, the construction of the sensors and topology, and the large inherent uncertainties in the areas which they are deployed can both produce inconsistent and unreliable data. This paper has formulated a method to produce a confidence level in the events that have been recorded through a comparative analysis of the variance of multiple sensor events. The method developed was further enhanced through the fuzzification of the temporal relationships to more adequately express the detail contained.

In this paper, a combination of a Takagi-Sugeno fuzzy system (TSK) and simulated annealing is used to predict well known time series by searching for the best configuration of the fuzzy system. Simulated annealing is used to optimise the parameters of the antecedent and the consequent parts of the fuzzy system rules. The results of the proposed method are encouraging indicating that simulated annealing and fuzzy logic are able to combine well in time series prediction.

The Interval Approach (IA) [4] is a method for synthesizing an interval type-2 fuzzy set (IT2 FS) model for a word from data that are collected from a group of subjects. A key assumption made by the IA is: each person's data interval is random and uniformly distributed. This means, of course, that the IT2 FS model for the word is random. Consequently, one can question whether or not the IT2 FS model for the word converges in a stochastic sense. This paper focuses on this question. As a part of our study, we have had to modify some steps of the IA, the resulting being an Enhanced IA (EIA). The paper shows by means of some simulations, that the IT2 FS word models that are obtained from the EIA are converging in a mean-square sense. This provides substantial credence for using the EIA to obtain T2 FS word models.

In this paper two contrasting approaches to the defuzzification of generalised type-2 fuzzy sets are investigated. The sampling method is a direct approach, whereas the α-planes method extends interval defuzzification to generalised type-2 sets, and therefore has to be used in conjunction with an interval technique such as the Karnik-Mendel Iterative Procedure. Experimental evaluations are made of the sampling and α-planes methods, with respect to both efficiency and accuracy, showing both strategies to be efficient and good approximations.

Alpha-cuts and the extension principle form a methodology for extending mathematical concepts from crisp sets to fuzzy sets. They have been applied to many operations, and have also been extended to interval valued fuzzy sets. Recently, some researchers defined new representations of type-2 fuzzy sets, namely, the alpha-plane representation and the zSlice representation. In this paper we investigate an alternative representation utilising alpha-cuts and the extension principle for interval valued fuzzy sets and type-2 fuzzy sets.

Our research focuses on the use of sound to enhance the control of an autonomous indoor helicopter - Flyper. One of the many challenging problems in this project is managing the uncertainty which is present in input data and the control actions; this paper focuses on managing the uncertainty in the input data. We present a fuzzy logic system which infers how much confidence should be placed on a control decision based on the data which was used to make that decision. The input data is a supervised and sound based position estimate of the flying robot. The output of the fuzzy inference system provides us with a confidence parameter used to attenuate the position control of the autonomous helicopter. We performed test flights with and without the fuzzy confidence parameter and with and without artificial disturbance in form of concurrent speech. We employed a motion tracker to capture the helicopter's movement during all test flights. The analysis of the data collected shows encouraging results.

This paper defines non-specificity measures for interval and type-2 fuzzy sets. It relies heavily on alpha-cuts and alpha-planes. Some observations about this measure are discussed and analysed. An example of calculating these measures is presented.

In this paper we evolve the parameters of a proportional, integral, and derivative (PID) controller for an unstable, complex and nonlinear system. The individuals of the applied genetic algorithm (GA) are evaluated on the actual system rather than on a simulation of it, thus avoiding the ldquoreality gaprdquo. This makes implicit a formal model identification for the implementation of a simulator. This also calls for the GA to be approached in an unusual way, where we need to consider new aspects not normally present in the usual situations using an unnaturally consistent simulator for fitness evaluation. Although elitism is used in the GAs, no monotonic increase in fitness is exhibited by the algorithm. Instead, we show that the GApsilas individuals converge towards more robust solutions.

This paper describes the design and construction of the first hardware running a generalised type-2 fuzzy logic system. A rationale for the design is given and hardware representations are discussed. An integrated development environment, also developed as part of this project, for type-2 fuzzy system is described along with the software which links this IDE to the novel hardware. The performance of the novel type-2 development board is tested under two scenarios.

Generalized type-2 fuzzy logic systems cannot currently be used for practical problems because the amount of computation required to defuzzify a generalized type-2 fuzzy set is too large. This paper presents a new method for defuzzifing a type-2 fuzzy set. The new much faster technique is based on geometric representations and operations. The results of a real world example contained in this paper show this new approach to be over 200,000 times faster than type-reduction. We present a new method for assessing the accuracy of the membership function of a type-2 fuzzy set. This method is used to show that the new representation used by the defuzzifier is not detrimental to the accuracy of the set. We also discuss the differences between the new approach and type-reduction, identifying the origin of this massive improvement in execution speed.

In 2003, Coupland and John proposed an approach to type-2 fuzzy arithmetic using the representation theorem. While this approach was sound, it was conceded to be computationally expensive and required considerable preliminary calculations. We present a more computationally viable approach which we believe will make type-2 fuzzy logic more useful in applied scenarios.

Geometric Type-2 fuzzy sets allow us to model type-2 fuzzy sets using geometry providing significant improvement in speed of computation. This paper explores in detail how well the geometric approach models continuous type-2 fuzzy sets from an accuracy perspective. A new methodology is introduced for conducting the comparison. This methodology is used on some example sets and the performance of the geometric model is given. It shows that, in broad terms, geometric type-2 fuzzy sets are more accurate than the discrete equivalent.

This paper presents a novel approach to the representation of type-1 and type-2 fuzzy sets utilising computational geometry. To achieve this our approach borrows ideas from the field of computational geometry and applies these techniques in the novel setting of fuzzy logic. We provide new algorithms for various operations on type-1 and type-2 fuzzy sets and for defuzzification. Results of experiments indicate that this approach reduces the execution speed of these operations

The number of applications of interval type-2 fuzzy logic to real world problems is growing. To date such systems have used type-reduction or an approximation of type-reduction to arrive at a final crisp output from the system. This paper describes the novel direct defuzzifier for interval type-2 fuzzy sets. A number of fuzzy systems are compared with the direct defuzzifier. We compare each defuzzifiers output surface in a simple rule-based system. The direct defuzzifier compares favourably with the type-reduction method under the minimum t-norm. We found that the non-stationary approach provided interesting results.

This work introduces representations and methods that improve the inferencing speeds of type-2 fuzzy logic systems by exploiting methods from computational geometry. A new representation of a secondary membership function is given along with its operations. We give the results from some initial experiments looking at the inferencing speed of a small, limited system. The results show a four and a half fold increase in the inferencing speed of our methods over a comparable standard system. Our motivation is that by improving the performance of type-2 systems such technologies may become more widely applied

Type-2 fuzzy logic systems require considerable processing resources to arrive at a conclusion. This paper shows how this can be significantly reduced, focusing specifically on the meet operation. We show how to eliminate large amounts of redundancy from the operation and then present a geometric method that is even more efficient. Results from initial experiments into performance increases are given. These results show that our method can give a significant increase in performance for certain types of secondary memberships.