Prediction of uncertain structural responses using fuzzy time series

Numerical methods for the prediction of uncertain structural responses with the aid of fuzzy time series are presented. Uncertain data, uncertain measured actions, and uncertain structural responses over time are considered as time series comprised of fuzzy data. Uncertain data are described by means of a new incremental fuzzy representation, which permits a complete and accurate estimation of uncertainty. The fuzzy time series are regarded as realizations of a fuzzy random process. Methods for identification and quantification of the underlying fuzzy random process are developed. The concepts of model-free and of model-based forecasting are addressed. These concepts enable the prediction of data in the form of optimal forecasts, fuzzy forecast intervals, and fuzzy random forecasts. The algorithms are demonstrated by way of practical examples.     

Fuzzy forecasting based on fuzzy time series

This article presents an improved method of fuzzy time series to forecast university enrollments. The historical enrollment data of the University of Alabama were first adopted by Song and Chissom (Song, Q. and Chissom, B. S. (1993). Forecasting enrollment with fuzzy time series-part I, Fuzzy Sets and Systems, 54, 1–9; Song, Q. and Chissom, B. S. (1994). Forecasting enrollment with fuzzy time series-part II, Fuzzy Sets and Systems, 54, 267–277) to illustrate the forecasting process of the fuzzy time series. Later, Chen proposed a simpler method. In this article, we show that our method is as simple as Chen's method but more accurate. In forecasting the enrollment of the University of Alabama, the root mean square percentage error (RMSPE) of our method is 3.1113% while the RMSPE of Chen's method is 4.0516%, which shows that our method is doing much better.     

Deterministic fuzzy time series model for forecasting enrollments

The fuzzy time series has recently received increasing attention because of its capability of dealing with vague and incomplete data. There have been a variety of models developed to either improve forecasting accuracy or reduce computation overhead. However, the issues of controlling uncertainty in forecasting, effectively partitioning intervals, and consistently achieving forecasting accuracy with different interval lengths have been rarely investigated. This paper proposes a novel deterministic forecasting model to manage these crucial issues. In addition, an important parameter, the maximum length of subsequence in a fuzzy time series resulting in a certain state, is deterministically quantified. Experimental results using the University of Alabama’s enrollment data demonstrate that the proposed forecasting model outperforms the existing models in terms of accuracy, robustness, and reliability. Moreover, the forecasting model adheres to the consistency principle that a shorter interval length leads to more accurate results.     

A novel high-order weighted fuzzy time series model and its application in nonlinear time series prediction

Conventional time series forecast models can hardly develop the inherent rules of complex non-linear dynamic systems because the strict assumptions they need cannot always be met in reality, whereas fuzzy time series (FTS) techniques can be used even the records of times series have uncertainty and instability since they do not need strict assumptions. In previous study of FTS, the process of aggregating the past observations and assigning proper weights of fuzzy logical relationship groups are ignored, which may lead to poor forecasting accuracy since they are important aspects in time series prediction and analysis where determination of future trends depends only on past observations. In this paper, a novel high-order FTS model is constructed to make time series forecasting. Specifically, by applying the harmony search intelligence algorithm, the optimal lengths of intervals are tuned. Moreover, regularly increasing monotonic quantifiers are employed on fuzzy sets to obtain the weights of ordered weighted aggregation. Simultaneously, the weights of right-hand side of fuzzy logical relationship groups are explored to compensate the presence of bias in the prediction. In the part of empirical analysis, the developed model was applied to predict three well-known time series: numbers of enrollment of Alabama University, TAIEX and electricity load demand of New South Wales and the results obtained were compared with several counterparts, including some old and recently developed models. Experimental results demonstrate that the developed model cannot only achieve higher accuracy of prediction, but also capture the fuzzy features and characters.     

Linguistic time series forecasting using fuzzy recurrent neural network

It is known that one of the most spread forecasting methods is the time series analysis. A weakness of traditional crisp time series forecasting methods is that they process only measurement based numerical information and cannot deal with the perception-based historical data represented by linguistic values. Application of a new class of time series, a fuzzy time series whose values are linguistic values, can overcome the mentioned weakness of traditional forecasting methods. In this paper we propose a fuzzy recurrent neural network (FRNN) based time series forecasting method for solving forecasting problems in which the data can be presented as perceptions and described by fuzzy numbers. The FRNN allows effectively handle fuzzy time series to apply human expertise throughout the forecasting procedure and demonstrates more adequate forecasting results. Recurrent links in FRNN also allow for simplification of the overall network structure (size) and forecasting procedure. Genetic algorithm-based procedure is used for training the FRNN. The effectiveness of the proposed fuzzy time series forecasting method is tested on the benchmark examples.     

Constructing and applying an improved fuzzy time series model: Taking the tourism industry for example

This study develops an improved fuzzy time series models for forecasting short-term series data. The forecasts were obtained by comparing the proposed improved fuzzy time series, Hwang’s fuzzy time series, and heuristic fuzzy time series. The tourism from Taiwan to the United States was used to build the sample sets which were officially published annual data for the period of 1991–2001. The root mean square error and mean absolute percentage error are two criteria to evaluate the forecasting performance. Empirical results show that the proposed fuzzy time series and Hwang’s fuzzy time series are suitable for short-term predictions.     

Effective intervals determined by information granules to improve forecasting in fuzzy time series

Partitioning the universe of discourse and determining effective intervals are critical for forecasting in fuzzy time series. Equal length intervals used in most existing literatures are convenient but subjective to partition the universe of discourse. In this paper, we study how to partition the universe of discourse into intervals with unequal length to improve forecasting quality. First, we calculate the prototypes of data using fuzzy clustering, then form some subsets according to the prototypes. An unequal length partitioning method is proposed. We show that these intervals carry well-defined semantics. To verify the suitability and effectiveness of the approach, we apply the proposed method to forecast enrollment of students of Alabama University and Germany’s DAX stock index monthly values. Empirical results show that the unequal length partitioning can greatly improve forecast accuracy. Further more, the proposed method is very robust and stable for forecasting in fuzzy time series.     

A FCM-based deterministic forecasting model for fuzzy time series

The study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling uncertainty and vagueness inherent in the data collected. A variety of forecasting models including high-order models have been devoted to improving forecasting accuracy. However, the high-order forecasting approach is accompanied by the crucial problem of determining an appropriate order number. Consequently, such a deficiency was recently solved by Li and Cheng [S.-T. Li, Y.-C. Cheng, Deterministic Fuzzy time series model for forecasting enrollments, Computers and Mathematics with Applications 53 (2007) 1904–1920] using a deterministic forecasting method. In this paper, we propose a novel forecasting model to enhance forecasting functionality and allow processing of two-factor forecasting problems. In addition, this model applies fuzzy c-means (FCM) clustering to deal with interval partitioning, which takes the nature of data points into account and produces unequal-sized intervals. Furthermore, in order to cope with the randomness of initially assigned membership degrees of FCM clustering, Monte Carlo simulations are used to justify the reliability of the proposed model. The superior accuracy of the proposed model is demonstrated by experiments comparing it to other existing models using real-world empirical data.     

Adaptive crossover,mutation and selection using fuzzy system for genetic algorithms

Genetic algorithms use a tournament selection or a roulette selection to choice better population. But these selections couldn’t use heuristic information for specific problem. Fuzzy selection system by heuristic rule base help to find optimal solution efficiently. And adaptive crossover and mutation probabilistic rate is faster than using fixed value. In this paper, we want fuzzy selection system for genetic algorithms and adaptive crossover and mutation rate fuzzy system. This work was presented in part and awarded as Young Author Award at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

ARMA(p,q) type high order fuzzy time series forecast method based on fuzzy logic relations

Within classic time series approaches, a time series model can be studied under 3 groups, namely AR (autoregressive model), MA (moving averages model) and ARMA (autoregressive moving averages model). On the other hand, solutions are based mostly on fuzzy AR time series models in the fuzzy time series literature. However, just a few fuzzy ARMA time series models have proposed until now. Fuzzy AR time series models have been divided into two groups named first order and high order models in the literature, highlighting the impact of model degree on forecast performance. However, model structure has been disregarded in these fuzzy AR models. Therefore, it is necessary to eliminate the model specification error arising from not utilizing of MA variables in the fuzzy time series approaches. For this reason, a new high order fuzzy ARMA(p,q) time series solution algorithm based on fuzzy logic group relations including fuzzy MA variables along with fuzzy AR variables has been proposed in this study. The main purpose of this article is to show that the forecast performance can be significantly improved when the deficiency of not utilizing MA variables. The other aim is also to show that the proposed method is better than the other fuzzy ARMA time series models in the literature from the point of forecast performance. Therefore, the new proposed method has been compared regarding forecast performance against some methods commonly used in literature by applying them on gold prices in Turkey, Istanbul Stock Exchange (IMKB) and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX).     

A high order fuzzy time series forecasting model based on adaptive expectation and artificial neural networks

Many fuzzy time series approaches have been proposed in recent years. These methods include three main phases such as fuzzification, defining fuzzy relationships and, defuzzification. Aladag et al. [2] improved the forecasting accuracy by utilizing feed forward neural networks to determine fuzzy relationships in high order fuzzy time series. Another study for increasing forecasting accuracy was made by Cheng et al. [6]. In their study, they employ adaptive expectation model to adopt forecasts obtained from first order fuzzy time series forecasting model. In this study, we propose a novel high order fuzzy time series method in order to obtain more accurate forecasts. In the proposed method, fuzzy relationships are defined by feed forward neural networks and adaptive expectation model is used for adjusting forecasted values. Unlike the papers of Cheng et al. [6] and Liu et al. [14], forecast adjusting is done by using constraint optimization for weighted parameter. The proposed method is applied to the enrollments of the University of Alabama and the obtained forecasting results compared to those obtained from other approaches are available in the literature. As a result of comparison, it is clearly seen that the proposed method significantly increases the forecasting accuracy.     

Evolving modular networks with genetic algorithms: application to nonlinear time series

Abstract: A key problem of modular neural networks is finding the optimal aggregation of the different subtasks (or modules) of the problem at hand. Functional networks provide a partial solution to this problem, since the inter‐module topology is obtained from domain knowledge (functional relationships and symmetries). However, the learning process may be too restrictive in some situations, since the resulting modules (functional units) are assumed to be linear combinations of selected families of functions. In this paper, we present a non‐parametric learning approach for functional networks using feedforward neural networks for approximating the functional modules of the resulting architecture; we also introduce a genetic algorithm for finding the optimal intra‐module topology (the appropriate balance of neurons for the different modules according to the complexity of their respective tasks). Some benchmark examples from nonlinear time‐series prediction are used to illustrate the performance of the algorithm for finding optimal modular network architectures for specific problems.     

Fuzzy classifier design using genetic algorithms

A new method for design of a fuzzy-rule-based classifier using genetic algorithms (GAs) is discussed. The optimal parameters of the fuzzy classifier including fuzzy membership functions and the size and structure of fuzzy rules are extracted from the training data using GAs. This is done by introducing new representation schemes for fuzzy membership functions and fuzzy rules. An effectiveness measure for fuzzy rules is developed that allows for systematic addition or deletion of rules during the GA optimization process. A clustering method is utilized for generating new rules to be added when additions are required. The performance of the classifier is tested on two real-world databases (Iris and Wine) and a simulated Gaussian database. The results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules. The performance is also compared to other fuzzy classifiers tested on the same databases.     

Fuzzy portfolio selection using genetic algorithm

This paper presents the development of fuzzy portfolio selection model in investment. Fuzzy logic is utilized in the estimation of expected return and risk. Using fuzzy logic, managers can extract useful information and estimate expected return by using not only statistical data, but also economical and financial behaviors of the companies and their business strategies. In the formulated fuzzy portfolio model, fuzzy set theory provides the possibility of trade-off between risk and return. This is obtained by assigning a satisfaction degree between criteria and constraints. Using the formulated fuzzy portfolio model, a Genetic Algorithm (GA) is applied to find optimal values of risky securities. Numerical examples are given to demonstrate the effectiveness of proposed method.     

Genetic algorithms for outlier detection and variable selection in linear regression models

This article addresses some problems in outlier detection and variable selection in linear regression models. First, in outlier detection there are problems known as smearing and masking. Smearing means that one outlier makes another, non-outlier observation appear as an outlier, and masking that one outlier prevents another one from being detected. Detecting outliers one by one may therefore give misleading results. In this article a genetic algorithm is presented which considers different possible groupings of the data into outlier and non-outlier observations. In this way all outliers are detected at the same time. Second, it is known that outlier detection and variable selection can influence each other, and that different results may be obtained, depending on the order in which these two tasks are performed. It may therefore be useful to consider these tasks simultaneously, and a genetic algorithm for a simultaneous outlier detection and variable selection is suggested. Two real data sets are used to illustrate the algorithms, which are shown to work well. In addition, the scalability of the algorithms is considered with an experiment using generated data.I would like to thank Dr Tero Aittokallio and an anonymous referee for useful comments.     

A clustering based forecasting algorithm for multivariable fuzzy time series using linear combinations of independent variables

There are two popular types of forecasting algorithms for fuzzy time series (FTS). One is based on intervals of universal sets of independent variables and the other is based on fuzzy clustering algorithms. Clustering based FTS algorithms are preferred since role and optimal length of intervals are not clearly understood. Therefore data of each variable are individually clustered which requires higher computational time. Fuzzy Logical Relationships (FLRs) are used in existing FTS algorithms to relate input and output data. High number of clusters and FLRs are required to establish precise input/output relations which incur high computational time. This article presents a forecasting algorithm based on fuzzy clustering (CFTS) which clusters vectors of input data instead of clustering data of each variable separately and uses linear combinations of the input variables instead of the FLRs. The cluster centers handle fuzziness and ambiguity of the data and the linear parts allow the algorithm to learn more from the available information. It is shown that CFTS outperforms existing FTS algorithms with considerably lower testing error and running time.     

A distance-based fuzzy time series model for exchange rates forecasting

Fuzzy time series model has been successfully employed in predicting stock prices and foreign exchange rates. In this paper, we propose a new fuzzy time series model termed as distance-based fuzzy time series (DBFTS) to predict the exchange rate. Unlike the existing fuzzy time series models which require exact match of the fuzzy logic relationships (FLRs), the distance-based fuzzy time series model uses the distance between two FLRs in selecting prediction rules. To predict the exchange rate, a two factors distance-based fuzzy time series model is constructed. The first factor of the model is the exchange rate itself and the second factor comprises many candidate variables affecting the fluctuation of exchange rates. Using the exchange rate data released by the Central Bank of Taiwan, we conducted several experiments on exchange rate forecasting. The experiment results showed that the distance-based fuzzy time series outperformed the random walk model and the artificial neural network model in terms of mean square error.     

Interactive genetic algorithms with individual’s fuzzy fitness

Interactive genetic algorithms are effective methods to solve an optimization problem with implicit or fuzzy indices, and have been successfully applied to many real-world optimization problems in recent years. In traditional interactive genetic algorithms, many researchers adopt an accurate number to express an individual’s fitness assigned by a user. But it is difficult for this expression to reasonably reflect a user’s fuzzy and gradual cognitive to an individual. We present an interactive genetic algorithm with an individual’s fuzzy fitness in this paper. Firstly, we adopt a fuzzy number described with a Gaussian membership function to express an individual’s fitness. Then, in order to compare different individuals, we generate a fitness interval based on α-cut set, and obtain the probability of individual dominance by use of the probability of interval dominance. Finally, we determine the superior individual in tournament selection with size two based on the probability of individual dominance, and perform the subsequent evolutions. We apply the proposed algorithm to a fashion evolutionary design system, a typical optimization problem with an implicit index, and compare it with two interactive genetic algorithms, i.e., an interactive genetic algorithm with an individual’s accurate fitness and an interactive genetic algorithm with an individual’s interval fitness. The experimental results show that the proposed algorithm is advantageous in alleviating user fatigue and looking for user’s satisfactory individuals.     

Machining process sequencing with fuzzy expert system and genetic algorithms

Traditional process planning systems are usually established in a deterministic framework that can only deal with precise information. However, in a practical manufacturing environment, decision making frequently involves uncertain and imprecise information. This paper describes a fuzzy approach for solving the process selection and sequencing problem under uncertainty. The proposed approach comprises a two-stage process for machining process selection and sequencing. The two stages are called intra-feature planning and inter-feature planning, respectively. According to the feature precedence relationship of a machined part, the intra-feature planning module generates a local optimal operation sequence for each feature element. This is based on a fuzzy expert system incorporated with genetic algorithms for machining cost optimization according to the cost-tolerance relationship. Manufacturing resources such as machines, tools, and fixtures are allocated to each selected operation to form an Operation-Machine-Tool (OMT) unit in the manufacturing resources allocation module. Finally, inter-feature planning generates a global OMT sequence. A genetic algorithm with fuzzy numbers and fuzzy arithmetic is developed to solve this global sequencing problem.     

基于Hubness的类别均衡的时间序列实例选择算法

针对实例选择算法INSIGHT存在选出的实例类别分布不均衡和得分相等的实例的重要性无法区分两个问题,分别提出了改进算法。改进算法B INSIGHT1基于分治思想,通过筛选出训练集各类中最具有代表性的实例,来确保选出的实例类别分布尽可能均衡。改进算法B INSIGHT2将改进算法B INSIGHT1的单重排序改进成了双重排序,以便更有效地衡量实例的重要性。实验结果表明,在时间复杂度基本不变的前提下,所提算法在分类准确率上均优于INSIGHT算法。