Slicing Strategies for the Generalised Type-2 Mamdani Fuzzy Inferencing System

The final publication is available at Springer via http://dx.doi.org/[insert DOI]".As a three-dimensional object, there are a number of ways of slicing a generalised type-2 fuzzy set. In the context of the Mamdani Fuzzy Inferencing System, this paper concerns three accepted slicing strategies, the vertical slice, the wavy slice, and the horizontal slice or alpha -plane. Two ways of de ning the generalised type-2 fuzzy set, vertical slices and wavy slices, are presented. Fuzzi cation and inferencing is presented in terms of vertical slices. After that, the application of all three slicing strategies to defuzzi cation is described, and their strengths and weaknesses assessed

Geometric Defuzzification Revisited

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In this paper the Geometric Defuzzification strategy for type-2 fuzzy sets is reappraised. For both discretised and geometric fuzzy sets the techniques for type-1, interval type-2, and generalised type-2 defuzzification are presented in turn. In the type-2 case the accuracy of Geometric Defuzzification is assessed through a series of test runs on interval type-2 fuzzy sets, using Exhaustive Defuzzification as the benchmark method. These experiments demonstrate the Geometric Defuzzifier to be wildly inaccurate. The test sets take many shapes; they are not confined to those type-2 sets with rotational symmetry that have previously been acknowledged by the technique’s developers to be problematic as regards accuracy. Type-2 Geometric Defuzzification is then examined theoretically. The defuzzification strategy is demonstrated to be built upon a fallacious application of the concept of centroid. This explains the markedly inaccurate experimental results. Thus the accuracy issues of type-2 Geometric Defuzzification are revealed to be inevitable, fundamental and significant

The Collapsing Defuzzifier for discretised generalised type-2 fuzzy sets

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The Greenfield–Chiclana Collapsing Defuzzifier is an established efficient accurate technique for the defuzzification of the interval type-2 fuzzy set. This paper reports on the extension of the Collapsing Defuzzifier to the generalised type-2 fuzzy set. Existing techniques for the defuzzification of generalised type-2 fuzzy sets are presented after which the interval Collapsing Defuzzifier is summarised. The collapsing technique is then extended to generalised type-2 fuzzy sets, giving the Generalised Greenfield–Chiclana Collapsing Defuzzifier. This is contrasted experimentally with both the benchmark Exhaustive Defuzzifier and the α-Planes/Karnik–Mendel Iterative Procedure approach in relation to efficiency and accuracy. The GGCCD is demonstrated to be many times faster than the Exhaustive Defuzzifier and its accuracy is shown to be excellent. In relation to the α-Planes/Karnik–Mendel Iterative Procedure approach it is shown to be comparable in accuracy, but faster

The Stratic Defuzzifier for Discretised General Type-2 Fuzzy Sets

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Stratification is a feature of the type-reduced set of the general type-2 fuzzy set, from which a new technique for general type-2 defuzzification, Stratic Defuzzification, may be derived. Existing defuzzification strategies are summarised. The stratified structure is described, after which the Stratic Defuzzifier is presented and contrasted experimentally for accuracy and efficiency with both the Exhaustive Method of Defuzzification (to benchmark accuracy) and the alpha-Planes/Karnik–Mendel Iterative Procedure strategy, employing 5, 11, 21, 51 and 101 alpha-planes. The Stratic Defuzzifier is shown to be much faster than the Exhaustive Defuzzifier. In fact the Stratic Defuzzifier and the alpha-Planes/Karnik–Mendel Iterative Procedure Method are comparably speedy; the speed of execution correlates with the number of planes participating in the defuzzification process. The accuracy of the Stratic Defuzzifier is shown to be excellent. It is demonstrated to be more accurate than the alpha-Planes/Karnik–Mendel Iterative Procedure Method in four of six test cases, regardless of the number of -planes employed. In one test case, it is less accurate than the alpha-Planes/Karnik–Mendel Iterative Procedure Method, regardless of the number of alpha-planes employed. In the remaining test case, the alpha-Planes/Karnik–Mendel Iterative Procedure Method with 11 alpha-Planes gives the most accurate result, with the Stratic Defuzzifier coming second

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

Defuzzification of the Discretised Generalised Type-2 Fuzzy Set: Experimental Evaluation

CCI - Centre for Computational Intelligence NOTICE: this is the author’s version of a work that was accepted for publication in Information Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version can be found by following the DOIThe work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised generalised type-2 fuzzy sets as created by the inference stage of a Mamdani Fuzzy Inferencing System. 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 defuzzification bottleneck. In this paper we begin by surveying the main alternative strategies for defuzzifying a generalised type-2 fuzzy set: (1) Vertical Slice Centroid Type-Reduction; (2) the sampling method; (3) the elite sampling method; and (4) the $\alpha$-planes method. We then evaluate the different methods experimentally for accuracy and efficiency. For accuracy the exhaustive method is used as the standard. The test results are analysed statistically by means of the Wilcoxon Nonparametric Test and the elite sampling method shown to be the most accurate. In regards to efficiency, Vertical Slice Centroid Type-Reduction is demonstrated to be the fastest technique

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

EG-ICE 2021 Workshop on Intelligent Computing in Engineering

The 28th EG-ICE International Workshop 2021 brings together international experts working at the interface between advanced computing and modern engineering challenges. Many engineering tasks require open-world resolutions to support multi-actor collaboration, coping with approximate models, providing effective engineer-computer interaction, search in multi-dimensional solution spaces, accommodating uncertainty, including specialist domain knowledge, performing sensor-data interpretation and dealing with incomplete knowledge. While results from computer science provide much initial support for resolution, adaptation is unavoidable and most importantly, feedback from addressing engineering challenges drives fundamental computer-science research. Competence and knowledge transfer goes both ways