Marcin Szeląg

On variable consistency dominance-based rough set approaches

We consider different variants of Variable Consistency Dominance-based Rough Set Approach (VC-DRSA). These variants produce more general (extended) lower approximations than those computed by Dominance-based Rough Set Approach (DRSA), (i.e., lower approximations that are supersets of those computed by DRSA). They define lower approximations that contain objects characterized by a strong but not necessarily certain relation with approximated sets. This is achieved by introduction of parameters that control consistency of objects included in lower approximations. We show that lower approximations generalized in this way enable us to observe dependencies that remain undiscovered by DRSA. Extended lower approximations are also a better basis for rule generation. In the paper, we focus our considerations on different definitions of generalized lower approximations. We also show definitions of VC-DRSA decision rules, as well as their application to classification/sorting and ranking/choice problems.

Learning of Rule Ensembles for Multiple Attribute Ranking Problems

In this paper, we consider the multiple attribute ranking problem from a Machine Learning perspective. We propose two approaches to statistical learning of an ensemble of decision rules from decision examples provided by the Decision Maker in terms of pairwise comparisons of some objects. The first approach consists in learning a preference function defining a binary preference relation for a pair of objects. The result of application of this function on all pairs of objects to be ranked is then exploited using the Net Flow Score procedure, giving a linear ranking of objects. The second approach consists in learning a utility function for single objects. The utility function also gives a linear ranking of objects. In both approaches, the learning is based on the boosting technique. The presented approaches to Preference Learning share good properties of the decision rule preference model and have good performance in the massive-data learning problems. As Preference Learning and Multiple Attribute Decision Aiding share many concepts and methodological issues, in the introduction, we review some aspects bridging these two fields. To illustrate the two approaches proposed in this paper, we solve with them a toy example concerning the ranking of a set of cars evaluated by multiple attributes. Then, we perform a large data experiment on real data sets. The first data set concerns credit rating. Since recent research in the field of Preference Learning is motivated by the increasing role of modeling preferences in recommender systems and information retrieval, we chose two other massive data sets from this area – one comes from movie recommender system MovieLens, and the other concerns ranking of text documents from 20 Newsgroups data set.

Induction of Ordinal Classification Rules from Incomplete Data

In this paper, we consider different ways of handling missing values in ordinal classification problems with monotonicity constraints within Dominance-based Rough Set Approach (DRSA). We show how to induce classification rules in a way that has desirable properties. Our considerations are extended to an experimental comparison of the postulated rule classifier with other ordinal and non-ordinal classifiers.

Probabilistic rough set approaches to ordinal classification with monotonicity constraints

We present some probabilistic rough set approaches to ordinal classification with monotonicity constraints, where it is required that the class label of an object does not decrease when evaluation of this object on attributes improves. Probabilistic rough set approaches allow to structure the classification data prior to induction of decision rules. We apply sequential covering to induce rules that satisfy consistency constraints. These rules are then used to make predictions on a new set of objects. After discussing some interesting features of this type of reasoning about ordinal data, we perform an extensive computational experiment to show a practical value of this proposal which is compared to other well known methods.

A Novel Method for Elimination of Inconsistencies in Ordinal Classification with Monotonicity Constraints

In order to handle inconsistencies in ordinal and monotonic information systems, several relaxed versions of the Dominance-based Rough Set Approach DRSA have been proposed, e.g., VC-DRSA. These versions use special consistency measures to admit some inconsistent objects in the lower approximations. The minimal consistency level that has to be attained by objects included in the lower approximations is defined using a prior knowledge or a trial-and-error procedure. In order to avoid dependence on prior knowledge, an alternative way of handling inconsistencies is to iteratively eliminate the most inconsistent objects according to some measure until the information system becomes consistent. This idea is a base of a new method of handling inconsistencies presented in this paper and called TIPStoC. The TIPStoC algorithm is illustrated by an example from the area of telecommunication and the efficiency of the new method is proved by a computational experiment.

Ensembles of decision rules for solving binary classification problems in the presence of missing values

In this paper, we consider an algorithm that generates an ensemble of decision rules. A single rule is treated as a specific subsidiary, base classifier in the ensemble that indicates only one of the decision classes. Experimental results have shown that the ensemble of decision rules is as efficient as other machine learning methods. In this paper we concentrate on a common problem appearing in real-life data that is a presence of missing attributes values. To deal with this problem, we experimented with different approaches inspired by rough set approach to knowledge discovery. Results of those experiments are presented and discussed in the paper.

Learnability in rough set approaches

We consider learning abilities of classifiers learned from data structured by rough set approaches into lower approximations of considered sets of objects. We introduce two measures, λ and δ, that estimate attainable predictive accuracy of rough-set-based classifiers. To check the usefulness of the estimates for various types of classifiers, we perform a computational experiment on fourteen data sets. In the experiment, we use two versions of the rough-set-based rule classifier, called VC-DomLEM, and few other well known classifiers. The results show that both introduced measures are useful for an a priori identification of data sets that are hard to learn by all classifiers.

On Different Ways of Handling Inconsistencies in Ordinal Classification with Monotonicity Constraints

Ordinal classification problem with monotonicity constraints involves a monotonic relationship between the description of an object and the class to which it is assigned. An example of such a relationship is: “the higher the quality of service and the lower the price, the higher the customer satisfaction level (class)”. Violation of the monotonic relationship is considered as an inconsistency. Rough set approaches to induction of the monotonic relationships in form of decision rules handle these inconsistencies at the stage of data pre-processing. As a result, the data sufficiently consistent for rule induction are identified. In this paper, we compare two ways of handling inconsistencies. The first one consists in distinguishing objects that are not less consistent than a specified threshold from those which are less consistent. The second one involves iterative removal of the most inconsistent objects until the data set is consistent. We present results of a computational experiment, in which rule classifiers are induced from data pre-processed in the two considered ways.

Dominance-Based Rough Set Approach to Multiple Criteria Ranking with Sorting-Specific Preference Information

A novel multiple criteria decision aiding method is proposed, that delivers a recommendation characteristic for ranking problems but employs preference information typical for sorting problems. The method belongs to the category of ordinal regression methods: it starts with preference information provided by the Decision Maker (DM) in terms of decision examples, and then builds a preference model that reproduces these exemplary decisions. The ordinal regression is analogous to inductive learning of a model that is true in the closed world of data where it comes from. The sorting examples show an assignment of some alternatives to pre-defined and ordered quality classes. Although this preference information is purely ordinal, the number of quality classes separating two assigned alternatives is meaningful for an ordinal intensity of preference. Using an adaptation of the Dominance-based Rough Set Approach (DRSA), the method builds from this information a decision rule preference model. This model is then applied on a considered set of alternatives to finally rank them from the best to the worst. The decision rule preference model resulting from DRSA is able to represent the preference information about the ordinal intensity of preference without converting this information into a cardinal scale. Moreover, the decision rules can be interpreted straightforwardly by the DM, facilitating her understanding of the feedback between the preference information and the preference model. An illustrative case study performed in this paper supports this claim.

Rough Set Analysis of Classification Data with Missing Values

In this paper, we consider a rough set analysis of non-ordinal and ordinal classification data with missing attribute values. We show how this problem can be addressed by several variants of Indiscernibility-based Rough Set Approach (IRSA) and Dominance-based Rough Set Approach (DRSA). We propose some desirable properties that a rough set approach being able to handle missing attribute values should possess. Then, we analyze which of these properties are satisfied by the considered variants of IRSA and DRSA.