Being able to forecast time series accurately has been quite a popular subject for researchers both in the past and at present. However, the lack of ability of conventional analysis methods to forecast time series that are not smooth leads the scientists and researchers to resort to various forecasting models that have different mathematical backgrounds, such as artificial neural networks, fuzzy predictors, evolutionary and genetic algorithms. In this paper, the accuracies of different grey models such as GM(1,1), Grey Verhulst model, modified grey models using Fourier Series is investigated. Highly noisy data, the United States dollar to Euro parity between the dates 01.01.2005 and 30.12.2007, are used to compare the performances of the different models. The simulation results show that modified grey models have higher performances not only on model fitting but also on forecasting. Among these grey models, the modified GM(1,1) using Fourier series in time is the best in model fitting and forecasting.

Grey system theory-based models in time series prediction

Data uncertainty is an inherent property in various applications due to reasons such as outdated sources or imprecise measurement. When data mining techniques are applied to these data, their uncertainty has to be considered to obtain high quality results. We present UK-means clustering, an algorithm that enhances the K-means algorithm to handle data uncertainty. We apply UK-means to the particular pattern of moving-object uncertainty. Experimental results show that by considering uncertainty, a clustering algorithm can produce more accurate results.

Uncertain data mining : An example in clustering location data

The accuracy of performance measures in common multicriteria methods is usually assumed to be accurate. Grey theory is a new technique for performing prediction, relational analysis and decision‐making in many areas. This paper presents applicability of grey theory techniques for defining the utility of an alternative. Proposed assessment model covers well known method of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), method with attributes values determined at intervals (TOPSIS‐grey) and a new method of Simple Additive Weighting with Grey relations (SAW‐G). A case study of the assessment of contractors’ competitive ability was used to demonstrate the applicability and the effectiveness of the proposed approach. The results show that the methods of grey relations methodology can be implemented as an effective decision aid for tasks with uncertain data.

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Contractor selection for construction works by applying saw‐g and topsis grey techniques

Churn prediction using comprehensible support vector machine: An analytical CRM application

Optimization algorithms are proposed to tackle different complex problems in different areas. In this paper, we firstly put forward a new memetic evolutionary algorithm, named Monkey King Evolutionary (MKE) Algorithm, for global optimization. Then we make a deep analysis of three update schemes for the proposed algorithm. Finally we give an application of this algorithm to solve least gasoline consumption optimization (find the least gasoline consumption path) for vehicle navigation. Although there are many simple and applicable optimization algorithms, such as particle swarm optimization variants (including the canonical PSO, Inertia Weighted PSO, Constriction Coefficients PSO, Fully Informed Particle Swarm, Comprehensive Learning Particle Swarm Optimization, Dynamic Neighborhood Learning Particle Swarm). These algorithms are less powerful than the proposed algorithm in this paper. 28 benchmark functions from BBOB2009 and CEC2013 are used for the validation of robustness and accuracy. Comparison results show that our algorithm outperforms particle swarm optimizer variants not only on robustness and optimization accuracy, but also on convergence speed. Benchmark functions of CEC2008 for large scale optimization are also used to test the large scale optimization characteristic of the proposed algorithm, and it also outperforms others. Finally, we use this algorithm to find the least gasoline consumption path in vehicle navigation, and conducted experiments show that the proposed algorithm outperforms A* algorithm and Dijkstra algorithm as well.

Monkey King Evolution

In this study, the moving average autoregressive exogenous (ARX) prediction model is combined with grey systems theory and rough set (RS) theory to create an automatic stock market forecasting and portfolio selection mechanism. In the proposed approach, financial data are collected automatically every quarter and are input to an ARX prediction model to forecast the future trends of the collected data over the next quarter or half-year period. The forecast data is then reduced using a GM(1,N) model, clustered using a K-means clustering algorithm and then supplied to a RS classification module which selects appropriate investment stocks by applying a set of decision-making rules. Finally, a grey relational analysis technique is employed to specify an appropriate weighting of the selected stocks such that the portfolio's rate of return is maximized. The validity of the proposed approach is demonstrated using electronic stock data extracted from the financial database maintained by the Taiwan Economic Journal (TEJ). The predictive ability and portfolio results obtained using the proposed hybrid model are compared with those of a GM(1,1) prediction method. It is found that the hybrid method not only has a greater forecasting accuracy than the GM(1,1) method, but also yields a greater rate of return on the selected stocks.

A hybrid model for stock market forecasting and portfolio selection based on ARX, grey system and RS theories

This study proposes a technique based upon Fuzzy C-Means (FCM) classification theory and related fuzzy theories for choosing an appropriate value of the Variable Precision Rough Set (VPRS) threshold parameter (@b) when applied to the classification of continuous information systems. The VPRS model is then combined with a moving Average Autoregressive Exogenous (ARX) prediction model and Grey Systems theory to create an automatic stock market forecasting and portfolio selection mechanism. In the proposed mechanism, financial data are collected automatically every quarter and are input to an ARX prediction model to forecast the future trends of the collected data over the next quarter or half-year period. The forecast data are then reduced using a GM(1,N) model, classified using a FCM clustering algorithm, and then supplied to a VPRS classification module which selects appropriate investment stocks in accordance with a pre-determined set of decision-making rules. Finally, a grey relational analysis technique is employed to weight the selected stocks in such a way as to maximize the rate of return of the stock portfolio. The validity of the proposed approach is demonstrated using electronic stock data extracted from the financial database maintained by the Taiwan Economic Journal (TEJ). The portfolio results obtained using the proposed hybrid model are compared with those obtained using a Rough Set (RS) selection model. The effects of the number of attributes of the RS lower approximation set and VPRS @b-lower approximation set on the classification are systematically examined and compared. Overall, the results show that the proposed stock forecasting and stock selection mechanism not only yields a greater number of selected stocks in the @b-lower approximation set than in the RS approximation set, but also yields a greater rate of return.

Application of VPRS model with enhanced threshold parameter selection mechanism to automatic stock market forecasting and portfolio selection

This study proposes a method of cluster validity index that simultaneously provide the measurements of goodness of clustering on clustered data and of classification accuracy for complicated information systems based upon the PBMF-index method and rough set (RS) theory. The maximum value of this index, called the Huang-index, not only provides the best partitioning, but also obtains the optimal accuracy of classification for the approximation sets. The traditional PBMF-index method is only used to ensure the formation of a small number of compact clusters with large separation between at least two clusters. In contrast to the traditional PBMF-index method, the Huang-index method extends the applications of unsupervised optimal cluster to the fields of classification. In the proposed algorithm, all the attributes of the data are first clustered into groups using the Fuzzy C-means (FCM) method. The clustered data are then used to identify approximate regions and classification accuracy and to calculate centroids of clusters for decision attribute based on the RS theory. Finally, all those calculated data are put into the proposed index method to find the cluster validity index. The validity of the proposed approach is demonstrated using the data derived from a hypothetical function of two independent variables and electronic stock data extracted from the financial database maintained by the Taiwan Economic Journal (TEJ). The clustering results obtained using the proposed method are compared with the results obtained using the traditional PBMF-index partition method. The effects of the number of clusters on the partitions of clusters and the RS regions are systematically examined and compared. The results show that the proposed Huang-index method not only yields a superior clustering capability than the traditional clustering algorithm, but also yields a reliable classification and obtains a set of suitable decision rules extracted from the RS theory.

Applications of an enhanced cluster validity index method based on the Fuzzy C-means and rough set theories to partition and classification

This study proposes a method, designated as the GRP-index method, for the classification of continuous value datasets in which the instances do not provide any class information and may be imprecise and uncertain. The proposed method discretizes the values of the individual attributes within the dataset and achieves both the optimal number of clusters and the optimal classification accuracy. The proposed method consists of a genetic algorithm (GA) and an FRP-index method. In the FRP-index method, the conditional and decision attribute values of the instances in the dataset are fuzzified and discretized using the Fuzzy C-means (FCM) method in accordance with the cluster vectors given by the GA specifying the number of clusters per attribute. Rough set (RS) theory is then applied to determine the lower and upper approximate sets associated with each cluster of the decision attribute. The accuracy of approximation of each cluster of the decision attribute is then computed as the cardinality ratio of the lower approximate sets to the upper approximate sets. Finally, the centroids of the lower approximate sets associated with each cluster of the decision attribute are determined by computing the mean conditional and decision attribute values of all the instances within the corresponding sets. The cluster centroids and accuracy of approximation are then processed by a modified form of the PBMF-index function, designated as the RP-index function, in order to determine the optimality of the discretization/classification results. In the event that the termination criteria are not satisfied, the GA modifies the initial population of cluster vectors and the FCM, RS and RP-index function procedures are repeated. The entire process is repeated iteratively until the termination criteria are satisfied. The maximum value of the RP cluster validity index is then identified, and the corresponding cluster vector is taken as the optimal classification result. The validity of the proposed approach is confirmed by cross validation, and by comparing the classification results obtained for a typical stock market dataset with those obtained by non-supervised and pseudo-supervised classification methods. The results show that the proposed GRP-index method not only has a better discretization performance than the considered methods, but also achieves a better accuracy of approximation, and therefore provides a more reliable basis for the extraction of decision-making rules.

An enhanced classification method comprising a genetic algorithm, rough set theory and a modified PBMF-index function

The proposed multiple inputs and outputs (MIO) classification method designated as the FVM-index method integrates fuzzy set theory (FST), variable precision rough set (VPRS) theory, and a modified cluster validity index (MCVI) function, and is designed specifically to filter out the uncertainty and inaccuracy inherent in the surveyed MIO real-valued dataset; thereby improving the classification performance.The results confirm that the proposed FVM-index method provides a good MIO classification performance even in the presence of inaccuracy and uncertainty. As a result, it provides a robust approach for the extraction of reliable decision-making rules.The proposed FVM-index method could effectively applied to the real applications of augmented reality product design and data envelopment analysis. Many multiple-criteria decision-making (MCDM) methods have been proposed for decision-making environments. However, the performance of these methods is degraded by the uncertainty and inaccuracy which characterizes most practical decision-making environments as a result of the inherent prejudices and preferences of the decision-makers or experts and an insufficient volume of multiple inputs and outputs (MIO) information. Accordingly, the present study proposes an enhanced MIO classification method to address these limitations of existing MCDM methods. The proposed MIO classification method designated as the FVM-index method integrates fuzzy set theory (FST), variable precision rough set (VPRS) theory, and a modified cluster validity index (MCVI) function, and is designed specifically to filter out the uncertainty and inaccuracy inherent in the surveyed MIO real-valued dataset; thereby improving the classification performance. The effectiveness of the proposed approach is first demonstrated by comparing the MIO classification results obtained for three relating UCI datasets: (1) the original dataset; (2) a dataset with a large amount of inaccurate instances; and (3) an FVM-index filtered dataset extracted from the original dataset using a statistical approach. Then, the validity of the proposed approach is illustrated by using an Augmented Reality product design and a hospital related datasets. The results confirm that the proposed FVM-index method provides a good classification performance even in the presence of inaccuracy and uncertainty. As a result, it provides a robust approach for the extraction of reliable decision-making rules.

Kuang Yu Huang

Papers

A hybrid model for stock market forecasting and portfolio selection based on ARX, grey system and RS theories

Application of VPRS model with enhanced threshold parameter selection mechanism to automatic stock market forecasting and portfolio selection

Applications of an enhanced cluster validity index method based on the Fuzzy C-means and rough set theories to partition and classification

An enhanced classification method comprising a genetic algorithm, rough set theory and a modified PBMF-index function

A multi-attribute decision-making model for the robust classification of multiple inputs and outputs datasets with uncertainty