Dominik Ślęzak

Rough Sets, Fuzzy Sets, Data Mining, and Granulär Computing

14th International Conference, RSFDGrC 2013, Halifax, NS, Canada, October 11-14, 2013. Proceedings - Part of the Lecture Notes in Computer Science book series

Rough sets and bayes factor

We present a novel approach to understanding the concepts of the theory of rough sets in terms of the inverse probabilities derivable from data. It is related to the Bayes factor known from the Bayesian hypothesis testing methods. The proposed Rough Bayesian model (RB) does not require information about the prior and posterior probabilities in case they are not provided in a confirmable way. We discuss RB with respect to its correspondence to the original Rough Set model (RS) introduced by Pawlak and Variable Precision Rough Set model (VPRS) introduced by Ziarko. We pay a special attention on RB’s capability to deal with multi-decision problems. We also propose a method for distributed data storage relevant to computational needs of our approach.

Various approaches to reasoning with frequency based decision reducts: a survey

Various aspects of reduct approximations are discussed. In particular, we show how to use them to develop flexible tools for analysis of strongly inconsistent and/or noisy data tables. A special attention is paid to the notion of a rough membership decision reduct — a feature subset (almost) preserving the frequency based information about conditions-→decision dependencies. Approximate criteria of preserving such a kind of information under attribute reduction are considered. These criteria are specified by using distances between frequency distributions and information measures related to different ways of interpreting rough membership based knowledge.

On Algebraic Operations on Fuzzy Numbers

New definition of the fuzzy counterpart of real number is presented. An extra feature, called the orientation of the membership curve is introduced. It leads to a novel concept of an ordered fuzzy number, represented by the ordered pair of real continuous functions. Four algebraic operations on ordered fuzzy numbers are defined; they enable to avoid some drawbacks of the classical approach.

Feature selection with fuzzy decision reducts

In this paper, within the context of fuzzy rough set theory, we generalize the classical rough set framework for data-based attribute selection and reduction, based on the notion of fuzzy decision reducts. Experimental analysis confirms the potential of the approach.

On Algebraic Operations on Fuzzy Reals

Fuzzy counterpart of real numbers is investigated in order to algorithmise algebraic operations on fuzzy reals. Fuzzy membership functions satisfying conditions similar to the quasi-convexity are discussed. An extra feature, called the orientation of their graph, is added to the definition. Two operations: addition and subtraction between fuzzy numbers are proposed. They are programmed and implemented in the Delphi language for selected types of membership functions.

Granular Sets --- Foundations and Case Study of Tolerance Spaces

A novel approach to extend the notions of definability and rough set approximations in information systems with non-equivalence relations is proposed. The upper approximation is defined as set-theoretic complement of negative region of a given concept; therefore, it does not need to be definable. Fundamental properties of new approximation operators are compared with the previous ones reported in literature. The proposed idea is illustrated within tolerance approximation spaces. In particular, granulation based on maximal preclasses is considered.

Rough Set Methods for Attribute Clustering and Selection

In this study we investigate methods for attribute clustering and their possible applications to the task of computation of decision reducts from information systems. We focus on high-dimensional datasets, that is, microarray data. For this type of data, the traditional reduct construction techniques either can be extremely computationally intensive or can yield poor performance in terms of the size of the resulting reducts. We propose two reduct computation heuristics that combine the greedy search with a diverse selection of candidate attributes. Our experiments confirm that by proper grouping of similar—in some sense interchangeable—attributes, it is possible to significantly decrease computation time, as well as to increase a quality of the obtained reducts (i.e., to decrease their average size). We examine several criteria for attribute clustering, and we also identify so-called garbage clusters, which contain attributes that can be regarded as irrelevant.

Roughfication of numeric decision tables: the case study of gene expression data

We extend the standard rough set-based approach to be able to deal with huge amounts of numeric attributes versus small amount of available objects. We transform the training data using a novel way of non-parametric discretization, called roughfication (in contrast to fuzzification known from fuzzy logic). Given roughfied data, we apply standard rough set attribute reduction and then classify the testing data by voting among the obtained decision rules. Roughfication enables to search for reducts and rules in the tables with the original number of attributes and far larger number of objects. It does not require expert knowledge or any kind of parameter tuning or learning. We illustrate it by the analysis of the gene expression data, where the number of genes (attributes) is enormously large with respect to the number of experiments (objects).

Approximate Reducts and Association Rules

We consider approximate versions of fundamental notions of theories of rough sets and association rules. We analyze the complexity of searching for α-reducts, understood as subsets discerning “α-almost” objects from different decision classes, in decision tables. We present how optimal approximate association rules can be derived from data by using heuristics for searching for minimal α-reducts. NP-hardness of the problem of finding optimal approximate association rules is shown as well. It makes the results enabling the usage of rough sets algorithms to the search of association rules extremely important in view of applications.