Catálogo de publicaciones - libros

This paper extends the basic rough set formalism introduced by Pawlak [1] to a rule-based knowledge representation language, called Rough Datalog, where rough sets are represented by predicates and described by finite sets of rules. The rules allow us to express background knowledge involving rough concepts and to reason in such a knowledge base. The semantics of the new language is based on a four-valued logic, where in addition to the usual values and , we also have the values , representing uncertainty, and corresponding to the lack of information. The semantics of our language is based on a truth ordering different from the one used in the well-known Belnap logic [2, 3] and we show why Belnap logic does not properly reflect natural intuitions related to our approach. The declarative semantics and operational semantics of the language are described. Finally, the paper outlines a query language for reasoning about rough concepts.

This paper proposes an approach to representation and analysis of information systems with fuzzy attributes, which combines the variable precision fuzzy rough set (VPFRS) model with the fuzzy flow graph method. An idea of parameterized approximation of crisp and fuzzy sets is presented. A single -approximation, which is based on the notion of fuzzy rough inclusion function, can be used to express the crisp approximations in the rough set and variable precision rough set (VPRS) model. A unified form of the -approximation is particularly important for defining a consistent VPFRS model. The introduced fuzzy flow graph method enables alternative description of decision tables with fuzzy attributes. The generalized VPFRS model and fuzzy flow graphs, taken together, can be applied to determining a system of fuzzy decision rules from process data.

In the paper the accuracy of greedy algorithms with weights for construction of partial covers, reducts and decision rules is considered. Bounds on minimal weight of partial covers, reducts and decision rules based on an information on greedy algorithm work are studied. Results of experiments with software implementation of greedy algorithms are described.

It is an honor to contribute my short article to this special issue commemorating the life and work of Professor Zdzisław Pawlak. In this article I would like to discuss my encounters with the field of artificial intelligence (AI) in general, and how I see rough set theory and Professor Zdzisław Pawlak in this context. I have been fortunate to know some of the greatest scholars in the AI field. There are many of them, but if I had to choose the three I admire most, they are: Professors Zdzisław Pawlak, Lotfi Zadeh and Herbert A. Simon. There are common characteristics among all of them. Although they are the most prominent of scholars, all are frank and easy and pleasant to talk with. All are professionally active at ages where ordinary people would have long since retired.

Rough Set Theory may be considered as a formal interpretation of observation of phenomena. On one side we have objects and on the other side we have properties. This is what we call a . Observing is then the act of perceiving and then interpreting the binary relation (of satisfaction) between the two sides. Of course, the set of properties can be given a particular structure. However, from a pure ”phenomenological” point of view, a structure is given by the satisfaction relation we observe. So it is a result and not a precondition. Phenomena, in general, do not give rise to topological systems but to pre-topological systems. In particular, ”interior” and ”closure” operators are not continuous with respect to joins, so that they can ”miss” information. To obtain continuous operators we have to lift the abstraction level of Property Systems by synthesizing relations between objects and properties into systems of relations between objects and objects. Such relations are based on the notion of a that is carried by an item. This way we can also account for , that is, systems in which we have attributes instead of properties and items are evaluated by means of attribute values. But in order to apply our mathematical machinery to Attribute Systems we have to transform them into Property Systems in an appropriate manner.

Rough sets, the notion introduced by Zdzisław Pawlak in early 80’s and developed subsequently by many researchers, have proved their usefulness in many problems of Approximate Reasoning, Data Mining, Decision Making. Inducing knowledge from data tables with data in either symbolic or numeric form, rests on computations of dependencies among groups of attributes, and it is a well–developed part of the rough set theory.

Recently, some works have been devoted to problems of concept learning in humane sciences via rough sets. This problem is distinct as to its nature from learning from data, as it does involve a dialogue between the teacher and the pupil in order to explain the meaning of a concept whose meaning is subjective, vague and often initially obscure, through a series of interchanges, corrections of inappropriate choices, explanations of reasons for corrections, finally reaching a point, where the pupil has mastered enough knowledge of the subject to be able in future to solve related problems fairly satisfactorily.

We propose here an approach to the problem of learning concepts in humane sciences based on the notion of a conjugate system; it is a family of information systems, organized by means of certain requirements in order to allow a group of students and a teacher to analyze a common universe ofobjects and to correct faulty choices of attribute value in order to reach a more correct understanding of the concept.

The problem of incomplete data in the data mining is well known. In the literature many solutions to deal with missing values in various knowledge discovery tasks were presented and discussed. In the area of association rules the problem was presented mainly in the context of relational data. However, the methods proposed for incomplete relational database can not be easily adapted to incomplete transactional data. In this paper we introduce postulates of a statistically justified approach to discovering rules from incomplete transactional data and present the new approach to this problem, satisfying the postulates.

Problems of using elements of rough sets theory and rule induction to create efficient classifiers are discussed. In the last decade many researches attempted to increase a classification accuracy by combining several classifiers into integrated systems. The main aim of this paper is to summarize the author’s own experience with applying one of his rule induction algorithm, called MODLEM, in the framework of different combined classifiers, namely, the bagging, –classifier and the combiner aggregation. We also discuss how rough approximations are applied in rule induction. The results of carried out experiments have shown that the MODLEM algorithm can be efficiently used within the framework of considered combined classifiers.

Pawlak introduced approximation spaces in his seminal work on rough sets more than two decades ago. In this paper, we show that approximation spaces are basic structures for knowledge discovery from multi-relational data. The utility of approximation spaces as fundamental objects constructed for concept approximation is emphasized. Examples of basic concepts are given throughout this paper to illustrate how approximation spaces can be beneficially used in many settings. The contribution of this paper is the presentation of an approximation space-based framework for doing research in various forms of knowledge discovery in multi relational data.

In many domains the data objects are described in terms of a large number of features (e.g. microarray experiments, or spectral characterizations of organic and inorganic samples). A pipelined approach using two clustering algorithms in combination with Rough Sets is investigated for the purpose of discovering important combinations of attributes in high dimensional data. The Leader and several k-means algorithms are used as fast procedures for attribute set simplification of the information systems presented to the rough sets algorithms. The data described in terms of these fewer features are then discretized with respect to the decision attribute according to different rough set based schemes. From them, the reducts and their derived rules are extracted, which are applied to test data in order to evaluate the resulting classification accuracy in crossvalidation experiments. The data mining process is implemented within a high throughput distributed computing environment. Nonlinear transformation of attribute subsets preserving the similarity structure of the data were also investigated. Their classification ability, and that of subsets of attributes obtained after the mining process were described in terms of analytic functions obtained by genetic programming (gene expression programming), and simplified using computer algebra systems. Visual data mining techniques using virtual reality were used for inspecting results. An exploration of this approach (using Leukemia, Colon cancer and Breast cancer gene expression data) was conducted in a series of experiments. They led to small subsets of genes with high discrimination power.