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

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

Elliptic membership functions and the modeling uncertainty in type-2 fuzzy logic systems as applied to time series prediction

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

Learning of interval and general type-2 fuzzy logic systems using simulated annealing: theory and practice

This paper reports the use of 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 interval and gen- eral type-2 fuzzy logic systems to maximize their modeling ability. The combination of simulated annealing with these models is presented in the modeling of four bench- mark problems including real-world problems. The type-2 fuzzy logic system models are compared in their ability to model uncertainties associated with these problems. Issues related to this combination between simulated annealing and fuzzy logic sys- tems, including type-2 fuzzy logic systems, are discussed. The results demonstrate that learning the third dimension in type-2 fuzzy sets with a deterministic defuzzifier can add more capability to modeling than interval type-2 fuzzy logic systems. This finding can be seen as an important advance in type-2 fuzzy logic systems research and should increase the level of interest in the modeling applications of general type-2 fuzzy logic systems, despite their greater computational load

Relative-fuzzy: a novel approach for handling complex ambiguity for software engineering of data mining models

There are two main defined classes of uncertainty namely: fuzziness and ambiguity, where ambiguity is ‘one-to-many’ relationship between syntax and semantic of a proposition. This definition seems that it ignores ‘many-to-many’ relationship ambiguity type of uncertainty. In this thesis, we shall use complex-uncertainty to term many-to-many relationship ambiguity type of uncertainty. This research proposes a new approach for handling the complex ambiguity type of uncertainty that may exist in data, for software engineering of predictive Data Mining (DM) classification models. The proposed approach is based on Relative-Fuzzy Logic (RFL), a novel type of fuzzy logic. RFL defines a new formulation of the problem of ambiguity type of uncertainty in terms of States Of Proposition (SOP). RFL describes its membership (semantic) value by using the new definition of Domain of Proposition (DOP), which is based on the relativity principle as defined by possible-worlds logic. To achieve the goal of proposing RFL, a question is needed to be answered, which is: how these two approaches; i.e. fuzzy logic and possible-world, can be mixed to produce a new membership value set (and later logic) that able to handle fuzziness and multiple viewpoints at the same time? Achieving such goal comes via providing possible world logic the ability to quantifying multiple viewpoints and also model fuzziness in each of these multiple viewpoints and expressing that in a new set of membership value. Furthermore, a new architecture of Hierarchical Neural Network (HNN) called ML/RFL-Based Net has been developed in this research, along with a new learning algorithm and new recalling algorithm. The architecture, learning algorithm and recalling algorithm of ML/RFL-Based Net follow the principles of RFL. This new type of HNN is considered to be a RFL computation machine. The ability of the Relative Fuzzy-based DM prediction model to tackle the problem of complex ambiguity type of uncertainty has been tested. Special-purpose Integrated Development Environment (IDE) software, which generates a DM prediction model for speech recognition, has been developed in this research too, which is called RFL4ASR. This special purpose IDE is an extension of the definition of the traditional IDE. Using multiple sets of TIMIT speech data, the prediction model of type ML/RFL-Based Net has classification accuracy of 69.2308%. This accuracy is higher than the best achievements of WEKA data mining machines given the same speech data