Switch point finding using polynomial regression for fuzzy type reduction algorithms

Karnik-Mendel (KM) algorithm is the most widely used type reduction (TR) method in literature for the design of interval type-2 fuzzy logic systems (IT2FLS). Its iterative nature for finding left and right switch points is its Achilles heel. Despite a decade of research, none of the alternative TR methods offer uncertainty measures equivalent to KM algorithm. This paper takes a data-driven approach to tackle the computational burden of this algorithm while keeping its key features. We propose a regression method to approximate left and right switch points found by KM algorithm. Approximator only uses the firing intervals, rnles centroids, and FLS strnctural features as inputs. Once training is done, it can precisely approximate the left and right switch points through basic vector multiplications. Comprehensive simulation results demonstrate that the approximation accuracy for a wide variety of FLSs is 100%. Flexibility, ease of implementation, and speed are other features of the proposed method.

A systematic design of interval type-2 fuzzy logic system using extreme learning machine for electricity load demand forecasting

This paper presents a novel design of interval type-2 fuzzy logic systems (IT2FLS) by utilizing the theory of extreme learning machine (ELM) for electricity load demand forecasting. ELM has become a popular learning algorithm for single hidden layer feed-forward neural networks (SLFN). From the functional equivalence between the SLFN and fuzzy inference system, a hybrid of fuzzy-ELM has gained attention of the researchers. This paper extends the concept of fuzzy-ELM to an IT2FLS based on ELM (IT2FELM). In the proposed design the antecedent membership function parameters of the IT2FLS are generated randomly, whereas the consequent part parameters are determined analytically by the Moore-Penrose pseudo inverse. The ELM strategy ensures fast learning of the IT2FLS as well as optimality of the parameters. Effectiveness of the proposed design of IT2FLS is demonstrated with the application of forecasting nonlinear and chaotic data sets. Nonlinear data of electricity load from the Australian National Electricity Market for the Victoria region and from the Ontario Electricity Market are considered here. The proposed model is also applied to forecast Mackey-glass chaotic time series data. Comparative analysis of the proposed model is conducted with some traditional models such as neural networks (NN) and adaptive neuro fuzzy inference system (ANFIS). In order to verify the structure of the proposed design of IT2FLS an alternate design of IT2FLS based on Kalman filter (KF) is also utilized for the comparison purposes.

Optimized fuzzy association rule mining for quantitative data

With the advance of computing and electronic technology, quantitative data, for example, continuous data (i.e., sequences of floating point numbers), become vital and have wide applications, such as for analysis of sensor data streams and financial data streams. However, existing association rule mining generally discover association rules from discrete variables, such as boolean data (`O' and `l') and categorical data (`sunny', `cloudy', `rainy', etc.) but very few deal with quantitative data. In this paper, a novel optimized fuzzy association rule mining (OFARM) method is proposed to mine association rules from quantitative data. The advantages of the proposed algorithm are in three folds: 1) propose a novel method to add the smoothness and flexibility of membership function for fuzzy sets; 2) optimize the fuzzy sets and their partition points with multiple objective functions after categorizing the quantitative data; and 3) design a two-level iteration to filter frequent-item-sets and fuzzy association-rules. The new method is verified by three different data sets, and the results have demonstrated the effectiveness and potentials of the developed scheme.