Rough approximation of a preference relation by a multi-attribute stochastic dominance for determinist and stochastic evaluation problems

Let A be a set of actions evaluated by a set of attributes. Two kinds of evaluations will be considered in this paper: determinist or stochastic in relation to each attribute. The multi-attribute stochastic dominance (MSD_r) for a reduced number of attributes will be suggested to model the preferences in this kind of problem. The case of mixed data, where we have the attributes of different natures is not well known in the literature, although it is essential from a practical point of view. To apply the MSD_r the subset R of attributes from which approximation of the global preference is valid should be known. The theory of Rough Sets gives us an answer on this issue allowing us to determine a minimal subset of attributes that enables the same classification of objects as the whole set of attributes. In our approach these objects are pairs of actions. In order to represent preferential information we shall use a pairwise comparison table. This table is built for subset B⊂A described by stochastic dominance (SD) relations for particular attributes and a total order for the decision attribute given by the decision maker (DM). Using a Rough Set approach to the analysis of the subset of preference relations, a set of decision rules is obtained, and these are applied to a set A⧹B of potential actions. The Rough Set approach of looking for the reduction of the set of attributes gives us the possibility of operating with MSD_r.     

Belief Scheduler based on model failure detection in the TBM framework. Application to human activity recognition

A tool called Belief Scheduler is proposed for state sequence recognition in the Transferable Belief Model (TBM) framework. This tool makes noisy temporal belief functions smoother using a Temporal Evidential Filter (TEF). The Belief Scheduler makes belief on states smoother, separates the states (assumed to be true or false) and synchronizes them in order to infer the sequence. A criterion is also provided to assess the appropriateness between observed belief functions and a given sequence model. This criterion is based on the conflict information appearing explicitly in the TBM when combining observed belief functions with predictions. The Belief Scheduler is part of a generic architecture developed for on-line and automatic human action and activity recognition in videos of athletics taken with a moving camera. In experiments, the system is assessed on a database composed of 69 real athletics video sequences. The goal is to automatically recognize running, jumping, falling and standing-up actions as well as high jump, pole vault, triple jump and long jump activities of an athlete. A comparison with Hidden Markov Models for video classification is also provided.     

Multi-criteria classification – A new scheme for application of dominance-based decision rules

We are considering the problem of multi-criteria classification. In this problem, a set of “if … then …” decision rules is used as a preference model to classify objects evaluated by a set of criteria and regular attributes. Given a sample of classification examples, called learning data set, the rules are induced from dominance-based rough approximations of preference-ordered decision classes, according to the Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). The main question to be answered in this paper is how to classify an object using decision rules in situation where it is covered by (i) no rule, (ii) exactly one rule, (iii) several rules. The proposed classification scheme can be applied to both, learning data set (to restore the classification known from examples) and testing data set (to predict classification of new objects). A hypothetical example from the area of telecommunications is used for illustration of the proposed classification method and for a comparison with some previous proposals.     

Dynamic projection network for supervised pattern classification

This paper describes the development of the utility of a dynamic neural network known as projection network for pattern classification. It first gives the derivation of the projection network, and then describes the network architecture and analyzes properties such as equilibrium points and their stability condition. The procedures for utilizing the projection network for pattern classification are established and the benefits are discussed. The proposed classification system is then tested with well-known benchmark data sets, namely the Fisher’s iris data, the heart disease data and the credit screening data and the results are compared to other classifiers including Neural Network Rule Base (NNRB), Genetic Algorithm Rule Base (GARB), Rough Set, and C4.5 decision tree. The projection network was proven to be a viable alternative to existing methods.     

Decision functions for chain classifiers based on Bayesian networks for multi-label classification

Multi-label classification problems require each instance to be assigned a subset of a defined set of labels. This problem is equivalent to finding a multi-valued decision function that predicts a vector of binary classes. In this paper we study the decision boundaries of two widely used approaches for building multi-label classifiers, when Bayesian network-augmented naive Bayes classifiers are used as base models: Binary relevance method and chain classifiers. In particular extending previous single-label results to multi-label chain classifiers, we find polynomial expressions for the multi-valued decision functions associated with these methods. We prove upper boundings on the expressive power of both methods and we prove that chain classifiers provide a more expressive model than the binary relevance method.     

Dynamic projection network for supervised pattern classification

This paper describes the development of the utility of a dynamic neural network known as projection network for pattern classification. It first gives the derivation of the projection network, and then describes the network architecture and analyzes properties such as equilibrium points and their stability condition. The procedures for utilizing the projection network for pattern classification are established and the benefits are discussed. The proposed classification system is then tested with well-known benchmark data sets, namely the Fisher’s iris data, the heart disease data and the credit screening data and the results are compared to other classifiers including Neural Network Rule Base (NNRB), Genetic Algorithm Rule Base (GARB), Rough Set, and C4.5 decision tree. The projection network was proven to be a viable alternative to existing methods.     

Facial expression classification: An approach based on the fusion of facial deformations using the transferable belief model

A method for the classification of facial expressions from the analysis of facial deformations is presented. This classification process is based on the transferable belief model (TBM) framework. Facial expressions are related to the six universal emotions, namely Joy, Surprise, Disgust, Sadness, Anger, Fear, as well as Neutral. The proposed classifier relies on data coming from a contour segmentation technique, which extracts an expression skeleton of facial features (mouth, eyes and eyebrows) and derives simple distance coefficients from every face image of a video sequence. The characteristic distances are fed to a rule-based decision system that relies on the TBM and data fusion in order to assign a facial expression to every face image. In the proposed work, we first demonstrate the feasibility of facial expression classification with simple data (only five facial distances are considered). We also demonstrate the efficiency of TBM for the purpose of emotion classification. The TBM based classifier was compared with a Bayesian classifier working on the same data. Both classifiers were tested on three different databases.     

A survey of fuzzy decision tree classifier

Decision-tree algorithm provides one of the most popular methodologies for symbolic knowledge acquisition. The resulting knowledge, a symbolic decision tree along with a simple inference mechanism, has been praised for comprehensibility. The most comprehensible decision trees have been designed for perfect symbolic data. Over the years, additional methodologies have been investigated and proposed to deal with continuous or multi-valued data, and with missing or noisy features. Recently, with the growing popularity of fuzzy representation, some researchers have proposed to utilize fuzzy representation in decision trees to deal with similar situations. This paper presents a survey of current methods for Fuzzy Decision Tree (FDT) designment and the various existing issues. After considering potential advantages of FDT classifiers over traditional decision tree classifiers, we discuss the subjects of FDT including attribute selection criteria, inference for decision assignment and stopping criteria. To be best of our knowledge, this is the first overview of fuzzy decision tree classifier.     

区间二型模糊集效用函数和熵在风险决策中的应用

针对以区间二型模糊集(IT2FS)为信息环境的多属性决策(MADM)问题,引入IT2FS效用函数,并提出基于IT2FS效用函数,熵和风险因子的风险决策模型。首先基于截集思想提出两种IT2FS效用函数公式,有效提取了IT2FS全部信息,比以往的序值型公式更加科学有效。其次基于已提出的IT2FS三种不确定度量存在的问题提出三种新型不确定度量,并基于此三种不确定度量提出IT2FS熵公式弥补原有熵度量的不足。再次引入风险偏好因子反映决策者不同的风险态度,并改进风险偏好因子范围。构造基于效用函数,熵和风险偏好因子的风险决策模型。最后利用一个实例分析结果表明,该风险决策模型中决策者风险偏好对属性权重以及方案的排序存在影响,该决策思想对风险投资决策和风险管理决策均有一定的参考作用。     

An extended TODIM method for multiple attribute group decision‐making based on 2‐dimension uncertain linguistic Variable

The significant characteristic of the TODIM (an acronym in Portuguese of Interactive and Multiple Attribute Decision Making) method is that it can consider the bounded rationality of the decision makers. However, in the classical TODIM method, the rating of the attributes only can be used in the form of crisp numbers. Because 2‐dimension uncertain linguistic variables can easily express the fuzzy information, in this article, we extend the TODIM method to 2‐dimension uncertain linguistic information. First of all, the definition, characteristics, expectation, comparative method and distance of 2‐dimension uncertain linguistic information are introduced, and the steps of the classical TODIM method for Multiple attribute decision making (MADM) problems are presented. Second, on the basis of the classical TODIM method, the extended TODIM method is proposed to deal with MADM problems in which the attribute values are in the form of 2‐dimension uncertain linguistic variables, and detailed decision steps are given. Its significant characteristic is that it can fully consider the bounded rationality of the decision makers, which is a real action in real decision making. Finally, a numerical example is provided to verify the developed approach and its practicality and effectiveness. © 2014 Wiley Periodicals, Inc. Complexity 21: 20–30, 2016     

Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

Rough sets for pattern classification using pairwise-comparison-based tables

Rough set theory is a useful mathematical tool to deal with vagueness and uncertainty in available information. The results of a rough set approach are usually presented in the form of a set of decision rules derived from a decision table. Because using the original decision table is not the only way to implement a rough set approach, it could be interesting to investigate possible improvement in classification performance by replacing the original table with an alternative table obtained by pairwise comparisons among patterns. In this paper, a decision table based on pairwise comparisons is generated using the preference relation as in the Preference Ranking Organization Methods for Enrichment Evaluations (PROMETHEE) methods, to gauges the intensity of preference for one pattern over another pattern on each criterion before classification. The rough-set-based rule classifier (RSRC) provided by the well-known library for the Rough Set Exploration System (RSES) running under Windows as been successfully used to generate decision rules by using the pairwise-comparisons-based tables. Specifically, parameters related to the preference function on each criterion have been determined using a genetic-algorithm-based approach. Computer simulations involving several real-world data sets have revealed that of the proposed classification method performs well compared to other well-known classification methods and to RSRC using the original tables.     

Benchmarking state-of-the-art classification algorithms for credit scoring

In this paper, we study the performance of various state-of-the-art classification algorithms applied to eight real-life credit scoring data sets. Some of the data sets originate from major Benelux and UK financial institutions. Different types of classifiers are evaluated and compared. Besides the well-known classification algorithms (eg logistic regression, discriminant analysis, k-nearest neighbour, neural networks and decision trees), this study also investigates the suitability and performance of some recently proposed, advanced kernel-based classification algorithms such as support vector machines and least-squares support vector machines (LS-SVMs). The performance is assessed using the classification accuracy and the area under the receiver operating characteristic curve. Statistically significant performance differences are identified using the appropriate test statistics. It is found that both the LS-SVM and neural network classifiers yield a very good performance, but also simple classifiers such as logistic regression and linear discriminant analysis perform very well for credit scoring.     

Evaluating correct classification probability for weighted voting classifiers with plurality voting

Weighted voting classifiers (WVCs) consist of N units that each provide individual classification decisions. The entire system output is based on tallying the weighted votes for each decision and choosing the winning one (plurality voting) or one which has the total weight of supporting votes greater than some specified threshold (threshold voting). Each individual unit may abstain from voting. The entire system may also abstain from voting if no decision is ultimately winning. Existing methods of evaluating the correct classification probability (CCP) of WVCs can be applied to limited special cases of these systems (threshold voting) and impose some restrictions on their parameters. In this paper a method is suggested which allows the CCP of WVCs with both plurality and threshold voting to be exactly evaluated without imposing constraints on unit weights. The method is based on using the modified universal generating function technique.     

Exploration of a hybrid feature selection algorithm

In the Knowledge Discovery Process, classification algorithms are often used to help create models with training data that can be used to predict the classes of untested data instances. While there are several factors involved with classification algorithms that can influence classification results, such as the node splitting measures used in making decision trees, feature selection is often used as a pre-classification step when using large data sets to help eliminate irrelevant or redundant attributes in order to increase computational efficiency and possibly to increase classification accuracy. One important factor common to both feature selection as well as to classification using decision trees is attribute discretization, which is the process of dividing attribute values into a smaller number of discrete values. In this paper, we will present and explore a new hybrid approach, ChiBlur, which involves the use of concepts from both the blurring and χ²-based approaches to feature selection, as well as concepts from multi-objective optimization. We will compare this new algorithm with algorithms based on the blurring and χ²-based approaches.     

基于区间AHP与粗糙集的决策系统的排序

针对决策系统中属性值以区间数形式给出的多指标决策问题,根据区间层次分析法(IAHP)与粗糙集的特点,提出了一种合理的排序方法.在保持分类能力不变的前提下,利用粗糙集理论中的知识约简方法,删除其中不相关或不重要的知识,结合区间层次分析法计算权重进行有效的排序.最后,给出算例说明了该方法的可行性和有效性.     

Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems with uncertain linguistic information. Motivated by the ideal of Bonferroni mean and geometric Bonferroni mean, we develop two aggregation techniques called the uncertain linguistic Bonferroni mean (ULBM) operator and the uncertain linguistic geometric Bonferroni mean (ULGBM) operator for aggregating the uncertain linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the uncertain linguistic weighted Bonferroni mean (ULWBM) operator and the uncertain linguistic weighted geometric Bonferroni mean (ULWGBM) operator, based on which we develop two procedures for multiple attribute decision making under the uncertain linguistic environments. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Dominance of capacities by k-additive belief functions

In this paper we deal with the set of k-additive belief functions dominating a given capacity. We follow the line introduced by Chateauneuf and Jaffray for dominating probabilities and continued by Grabisch for general k-additive measures. First, we show that the conditions for the general k-additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid. On the other hand, we show that these conditions cannot be improved. We solve this situation by imposing additional constraints on the dominating functions. Then, we consider the more restrictive case of k-additive belief functions. In this case, a similar result with stronger conditions is proved. Although better, this result is not completely satisfactory and, as before, the conditions cannot be strengthened. However, when the initial capacity is a belief function, we find a subfamily of the set of dominating k-additive belief functions from which it is possible to derive any other dominant k-additive belief function, and such that the conditions are even more restrictive, obtaining the natural extension of the result for probabilities. Finally, we apply these results in the fields of Social Welfare Theory and Decision Under Risk.     

Multicategory classification via discrete support vector machines

Discrete support vector machines (DSVM), originally proposed for binary classification problems, have been shown to outperform other competing approaches on well-known benchmark datasets. Here we address their extension to multicategory classification, by developing three different methods. Two of them are based respectively on one-against-all and round-robin classification schemes, in which a number of binary discrimination problems are solved by means of a variant of DSVM. The third method directly addresses the multicategory classification task, by building a decision tree in which an optimal split to separate classes is derived at each node by a new extended formulation of DSVM. Computational tests on publicly available datasets are then conducted to compare the three multicategory classifiers based on DSVM with other methods, indicating that the proposed techniques achieve significantly higher accuracies. This research was partially supported by PRIN grant 2004132117.     

Learning multicriteria classification models from examples: Decision rules in continuous space

The classification problem statement of multicriteria decision analysis is to model the classification of the alternatives/actions according to the decision maker's preferences. These models are based on outranking relations, utility functions or (linear) discriminant functions. Model parameters can be given explicitly or learnt from a preclassified set of alternatives/actions.In this paper we propose a novel approach, the Continuous Decision (CD) method, to learn parameters of a discriminant function, and we also introduce its extension, the Continuous Decision Tree (CDT) method, which describes the classification more accurately.The proposed methods are results of integration of Machine Learning methods in Decision Analysis. From a Machine Learning point of view, the CDT method can be considered as an extension of the C4.5 decision tree building algorithm that handles only numeric criteria but applies more complex tests in the inner nodes of the tree. For the sake of easier interpretation, the decision trees are transformed to rules.