Zhi Xiao

Data analysis approaches of soft sets under incomplete information

In view of the particularity of the value domains of mapping functions in soft sets, this paper presents data analysis approaches of soft sets under incomplete information. For standard soft sets, the decision value of an object with incomplete information is calculated by weighted-average of all possible choice values of the object, and the weight of each possible choice value is decided by the distribution of other objects. For fuzzy soft sets, incomplete data will be predicted based on the method of average-probability. Results of comparison show that comparing to other approaches for dealing with incomplete data, these approaches presented in this paper are preferable for reflecting actual states of incomplete data in soft sets. At last, an example is provided to illuminate the practicability and validity of the data analysis approach of soft sets under incomplete information.

Financial ratio selection for business failure prediction using soft set theory

This paper presents a novel parameter reduction method guided by soft set theory (NSS) to select financial ratios for business failure prediction (BFP). The proposed method integrates statistical logistic regression into soft set decision theory, hence takes advantages of two approaches. The procedure is applied to real data sets from Chinese listed firms. From the financial analysis statement category set and the financial ratio set considered by the previous literatures, our proposed method selects nine significant financial ratios. Among them, four ratios are newly recognized as important variables for BFP. For comparison, principal component analysis, traditional soft set theory, and rough set theory are reduction methods included in the study. The predictive ability of the selected ratios by each reduction method along with the ratios commonly used in the prior literature is evaluated by three forecasting tools support vector machine, neural network, and logistic regression. The results demonstrate superior forecasting performance of the proposed method in terms of accuracy and stability.

A method based on interval-valued fuzzy soft set for multi-attribute group decision-making problems under uncertain environment

In this paper, we develop a new method for multiple attributes group decision-making problems under uncertain environment, in which the information about attribute weights is incompletely known or completely unknown, and each maker’s decision information is expressed by an interval-valued fuzzy soft set. Moreover, this paper takes account of the decision makers’ attitude toward risk. In order to get the weight vector of the attributes, we construct the score matrix of the final fuzzy soft set. From the score matrix and the given attribute weights information, we establish an optimization model to determine the weights of attributes. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. According to these models, a method based on interval-valued fuzzy soft set, which considers the decision makers’ risk attitude under uncertain environment, is given to rank the alternatives. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

A multiple support vector machine approach to stock index forecasting with mixed frequency sampling

Abstract The independent variables commonly used to predict the stock price index usually contain data sampled at different frequencies, and simultaneously, there exist multiple outputs. However, most current researches ignore different frequencies among independent variables and multi-output issues. This paper proposes a multiple output support vector machine unrestricted mixed data sampling (MSVM-UMIDAS) approach – which can achieve multiple results for sequential points simultaneously by applying mixed frequency independent variables. We test the in-sample and out-of-sample performances of MSVM-UMIDAS for stock forecasting in terms of (t−1), (t−2) and (t−3) and then compare the performances of the proposed model with those of other models. The results indicate that our model performs better when assessed by four different measurements. Thus, our proposed model is more realistic in practice and an appropriate tool for multi-output and mixed frequency issues for stock price forecasting.

Dynamic ensemble classification for credit scoring using soft probability

A soft probability based dynamic ensemble classification method is proposed.Soft probability covers classifiers selection and combination.Selecting classifiers based on Type I and II error can minimize the risk.Combing different classifiers for the testing samples is more reasonable.Selective ensembles for credit scoring are a promising research field. In recent years, classification ensembles or multiple classifier systems have been widely applied to credit scoring, and they achieve significantly better performance than individual classifiers do. Selective ensembles, an important part of this group of systems, are a promising field of research. However, none of them considers the relative costs of Type I error and Type II error for credit scoring when selecting classifiers, which bring higher risks for the financial institutions. Moreover, earlier dynamic selective ensembles usually select and combine classifiers for each test sample dynamically based on classifiers performance in the validation set, regardless of their behaviors in the testing set. To fill the gap and overcome the limitations, we propose a new dynamic ensemble classification method for credit scoring based on soft probability. In this method, the classifiers are first selected based on their classification ability and the relative costs of Type I error and Type II error in the validation set. With the selected classifiers, we combine different classifiers for the samples in the testing set based on their classification results to get an interval probability of default by using soft probability. The proposed method is compared with some well-known individual classifiers and ensemble classification methods, including five selective ensembles, for credit scoring by using ten real-world data sets and seven performance indicators. Through these analyses and statistical tests, the experimental results demonstrate the ability and efficiency of the proposed method to improve prediction performance against the benchmark models.

A Novel Nonlinear Integrated Forecasting Model of Logistic Regression and Support Vector Machine for Business Failure Prediction with All Sample Sizes

The aim of this work was to improve the forecasting performance of business failure prediction with all sample sizes by constructing a novel nonlinear integrated forecasting model (ANIFM) of individual linear forecasting models and individual nonlinear forecasting models. First, a new variable set including internal variables and external variables was proposed. Using scatter diagrams, all variables were placed in either the linear group or the nonlinear group. We considered logistic regression (LR) as the individual linear forecasting method to deal with each linear variable, the support vector machine (SVM) as the individual nonlinear forecasting method to deal with each nonlinear variable, and the residual SVM as the integration method to integrate the forecasts of LRs and SVMs. The proposed procedure was applied to real datasets from China. For performance comparison, single LR, SVM methods, integration forecasting models based on equal weights and on neural networks, and one based on rough set and Dempster-Shafer evidence theory (D-S theory) were also included in the empirical experiment as benchmarks. The experimental results demonstrate the superior forecasting performance of the proposed ANIFM in terms of forecasting accuracy and forecasting stability, especially with small sample sizes.

Dynamic weighted ensemble classification for credit scoring using Markov Chain

As the ensemble methods achieve significantly better performances than individual models do, they have been widely applied to credit scoring. However, most of them employ a static combiner to combine base classifiers, which do not consider the base classifiers’ characters and their dynamic classification ability. Though some dynamic ensemble methods are proposed, they need to produce a large number of base classifiers or employ a fixed combiner, which limit the generality of the ensemble methods. In this paper, we propose a new dynamic weighted ensemble method for credit scoring. Markov Chain is employed to model the change of each classifier’s classification ability and build a dynamic weighted trainable combiner, which dynamically assign weights to the base classifiers for each sample in the testing set. Through eight credit data sets from the real world, the experimental study demonstrates the ability and efficiency of the dynamic weighted ensemble method to improve prediction performance against the benchmark models, including some well-known individual classifiers and dynamic ensemble methods. Moreover, the proposed method can effectively decrease the misclassification cost, which can reduce risks for the financial institutions.