On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets

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 research, 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 defuzzifing interval type-2 fuzzy sets

A Comprehensive Study of the Efficiency of Type-Reduction Algorithms

Improving the efficiency of type-reduction algorithms continues to attract research interest. Recently, there have been some new type-reduction approaches claiming that they are more efficient than the well-known algorithms such as the enhanced Karnik-Mendel (EKM) and the enhanced iterative algorithm with stopping condition (EIASC). In a previous paper, we found that the computational efficiency of an algorithm is closely related to the platform, and how it is implemented. In computer science, the dependence on languages is usually avoided by focusing on the complexity of algorithms (using big O notation). In this paper, the main contribution is the proposal of two novel type-reduction algorithms. Also, for the first time, a comprehensive study on both existing and new type-reduction approaches is made based on both algorithm complexity and practical computational time under a variety of programming languages. Based on the results, suggestions are given for the preferred algorithms in different scenarios depending on implementation platform and application context

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

Circumventing the fuzzy type reduction for autonomous vehicle controller

Fuzzy type-2 controllers can easily deal with systems nonlinearity and utilise humans’ expertise to solve many complex control problems; they are also very good at processing uncertainty, which exists in many robotic systems, such as autonomous vehicles. However, their computational cost is high, especially at the type reduction stage. In this research, it is aimed to reduce the computation cost of the type reduction stage, thus to facilitate faster performance speed and increase the number of actions able to be operated in one microprocessor. Proposed here are adaptive integration principles with a binary successive search technique to locate the straight or semi-straight segments of a fuzzy set, thus to use them in achieving faster weighted average computation. This computation is very important because it runs frequently in many type reductions. A variable adaptation rate is suggested during the type reduction iterations to reduce the computation cost further. The influence of the proposed approaches on the fuzzy type-2 controller’s error has been mathematically analysed and then experimentally measured using a wall-following behaviour, which is the most important action for many autonomous vehicles. The resultant execution time-gain of the proposed technique has reached to 200%. This evaluated with respect to the execution time of the original, unmodified, type reduction procedure. This study develops a new accelerated version of the enhanced Karnik-Mendel type reducer by using better initialisations and better indexing scheme. The resulting performance time-gain reached 170%, with respect to the original version. A further cut in the type reduction time is achieved by proposing a One-Go type reduction procedure. This technique can reduce multiple sets altogether in one pass, thus eliminating much of the redundant calculations needed to carry out the reduction individually. All the proposed type reduction enhancements were evaluated in terms of their execution time-gain and performance error using every possible fuzzy firing level combination. Tests were then performed using a real autonomous vehicle, navigates in a relatively complex arena field with acute, right, obtuse, and reflex angled corners, to assure evaluating wide variety of operation conditions. A simplified state hold technique using Schmitt-trigger principles and dynamic sense pattern control was suggested and implemented to assure small rule base size and to obtain more accurate evaluation of the type reduction stages

EEG-Analysis for Cognitive Failure Detection in Driving Using Type-2 Fuzzy Classifiers

The paper aims at detecting on-line cognitive failures in driving by decoding the EEG signals acquired during visual alertness, motor-planning and motor-execution phases of the driver. Visual alertness of the driver is detected by classifying the pre-processed EEG signals obtained from his pre-frontal and frontal lobes into two classes: alert and non-alert. Motor-planning performed by the driver using the pre-processed parietal signals is classified into four classes: braking, acceleration, steering control and no operation. Cognitive failures in motor-planning are determined by comparing the classified motor-planning class of the driver with the ground truth class obtained from the co-pilot through a hand-held rotary switch. Lastly, failure in motor execution is detected, when the time-delay between the onset of motor imagination and the EMG response exceeds a predefined duration. The most important aspect of the present research lies in cognitive failure classification during the planning phase. The complexity in subjective plan classification arises due to possible overlap of signal features involved in braking, acceleration and steering control. A specialized interval/general type-2 fuzzy set induced neural classifier is employed to eliminate the uncertainty in classification of motor-planning. Experiments undertaken reveal that the proposed neuro-fuzzy classifier outperforms traditional techniques in presence of external disturbances to the driver. Decoding of visual alertness and motor-execution are performed with kernelized support vector machine classifiers. An analysis reveals that at a driving speed of 64 km/hr, the lead-time is over 600 milliseconds, which offer a safe distance of 10.66 meters

Type-2 Fuzzy Logic: Circumventing the Defuzzification Bottleneck

Type-2 fuzzy inferencing for generalised, discretised type-2 fuzzy sets has been impeded by the computational complexity of the defuzzification stage of the fuzzy inferencing system. Indeed this stage is so complex computationally that it has come to be known as the defuzzification bottleneck. The computational complexity derives from the enormous number of embedded sets that have to be individually processed in order to effect defuzzification. Two new approaches to type-2 defuzzification are presented, the sampling method and the Greenfield-Chiclana Collapsing Defuzzifier. The sampling method and its variant, elite sampling, are techniques for the defuzzification of generalised type-2 fuzzy sets. In these methods a relatively small sample of the totality of embedded sets is randomly selected and processed. The small sample size drastically reduces the computational complexity of the defuzzification process, so that it may be speedily accomplished. The Greenfield-Chiclana Collapsing Defuzzifier relies upon the concept of the representative embedded set, which is an embedded set having the same defuzzified value as the type-2 fuzzy set that is to be defuzzified. By a process termed collapsing the type-2 fuzzy set is converted into a type-1 fuzzy set which, as an approximation to the representative embedded set, is known as the representative embedded set approximation. This type-1 fuzzy set is easily defuzzified to give the defuzzified value of the original type-2 fuzzy set. By this method the computational complexity of type-2 defuzzification is reduced enormously, since the representative embedded set approximation replaces the entire collection of embedded sets. The strategy was conceived as a generalised method, but so far only the interval version has been derived mathematically. The grid method of discretisation for type-2 fuzzy sets is also introduced in this thesis. Work on the defuzzification of type-2 fuzzy sets began around the turn of the millennium. Since that time a number of investigators have contributed methods in this area. These different approaches are surveyed, and the major methods implemented in code prior to their experimental evaluation. In these comparative experiments the grid method of defuzzification is employed. The experimental results show beyond doubt that the collapsing method performs the best of the interval alternatives. However, though the sampling method performs well experimentally, the results do not demonstrate it to be the best performing generalised technique

Accuracy and complexity evaluation of defuzzification strategies for the discretised interval type-2 fuzzy set.

Other research group involved: Centre for Computational Intelligence (CCI).The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised interval type-2 fuzzy sets. The exhaustive method of defuzzification for type-2 fuzzy sets is extremely slow, owing to its enormous computational complexity. Several approximate methods have been devised in response to this bottleneck. In this paper we survey four alternative strategies for defuzzifying an interval type-2 fuzzy set: 1. The Karnik-Mendel Iterative Procedure, 2. the Wu-Mendel Approximation, 3. the Greenfield-Chiclana Collapsing Defuzzifier, and 4. the Nie-Tan Method. We evaluated the different methods experimentally for accuracy, by means of a comparative study using six representative test sets with varied characteristics, using the exhaustive method as the standard. A preliminary ranking of the methods was achieved using a multi-criteria decision making methodology based on the assignment of weights according to performance. The ranking produced, in order of decreasing accuracy, is 1. the Collapsing Defuzzifier, 2. the Nie-Tan Method, 3. the Karnik-Mendel Iterative Procedure, and 4. the Wu-Mendel Approximation. Following that, a more rigorous analysis was undertaken by means of the Wilcoxon Nonparametric Test, in order to validate the preliminary test conclusions. It was found that there was no evidence of a significant difference between the accuracy of the Collapsing and Nie-Tan Methods, and between that of the Karnik-Mendel Iterative Procedure and the Wu-Mendel Approximation. However, there was evidence to suggest that the collapsing and Nie-Tan Methods are more accurate than the Karnik-Mendel Iterative Procedure and the Wu-Mendel Approximation. In relation to efficiency, each method’s computational complexity was analysed, resulting in a ranking (from least computationally complex to most computationally complex) as follows: 1. the Nie-Tan Method, 2. the Karnik-Mendel Iterative Procedure (lowest complexity possible), 3. the Greenfield-Chiclana Collapsing Defuzzifier, 4. the Karnik-Mendel Iterative Procedure (highest complexity possible), and 5. the Wu-Mendel Approximation