Fundamenta Informaticae - Volume 27, issue 2-3

Authors: Slowiński, Roman | Stefanowski, Jerzy

Article Type: Research Article

Abstract: Rough set theory refers to classification of objects described by well-defined values of qualitative and quantitative attributes. The values of attributes defined for each pair [object, attribute], called descriptors, are assumed to be unique and precise. In practice, however, these attribute values may be neither unique nor precise, i.e. they can be uncertain. We are distinguishing four types of uncertainty affecting values of attributes: uncertain discretization of quantitative attributes, imprecision of values of numerical attributes, unknown (missing) values of attributes, multiple values possible for one pair [object, attribute]. We propose a special way of modelling the first three types of …uncertainty using fuzzy sets, which boils them down to the fourth type, called shortly, multiple descriptors. Thus, the generalization of the rough set approach consists in handling the case of multiple descriptors for both condition and decision attributes. The generalization preserves all characteristic features of the rough set approach while enabling reasoning about uncertain data. This capacity is illustrated by a simple example. Show more

Keywords: Rough sets, uncertain descriptors, fuzzy sets, approximate reasoning

DOI: 10.3233/FI-1996-272310

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 229-243, 1996

Authors: Skowron, Andrzej | Stepaniuk, Jaroslaw

Article Type: Research Article

Abstract: We generalize the notion of an approximation space introduced in [8]. In tolerance approximation spaces we define the lower and upper set approximations. We investigate some attribute reduction problems for tolerance approximation spaces determined by tolerance information systems. The tolerance relation defined by the so called uncertainty function or the positive region of a given partition of objects have been chosen as invariants in the attribute reduction process. We obtain the solutions of the reduction problems by applying boolean reasoning [1]. The solutions are represented by tolerance reducts and relative tolerance reducts.

DOI: 10.3233/FI-1996-272311

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 245-253, 1996

Authors: Skowron, Andrzej | Polkowski, Lech

Article Type: Research Article

Abstract: We propose a method called analytical morphology for data filtering. The method was created on the basis of some ideas of rough set theory and mathematical morphology. Mathematical morphology makes an essential use of geometric structure of objects while the aim of our method is to provide tools for data filtering when there is no directly available geometric structure in the data set.

DOI: 10.3233/FI-1996-272312

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 255-271, 1996

Authors: Tsumoto, Shusaku | Tanaka, Hiroshi

Article Type: Research Article

Abstract: In order to acquire knowledge from databases, there have been proposed several methods of inductive learning, such as ID3 family and AQ family. These methods are applied to discover meaningful knowledge from large databases, and their usefulness is ensured. However, since there has been no formal approach proposed to treat these methods, efficiency of each method is only compared empirically. In this paper, we introduce matroid theory and rough sets to construct a common framework for empirical machine learning methods which induce the combination of attribute-value pairs from databases. Combination of the concepts of rough sets and matroid theory gives …us an excellent set-theoretical framework and enables us to understand the differences and the similarities between these methods clearly. In this paper, we compare three classical methods, AQ, Pawlak's Consistent Rules and ID3. The results show that there exist the differences in algebraic structure between the former two and the latter and that this causes the differences between AQ and ID3. Show more

DOI: 10.3233/FI-1996-272313

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 273-288, 1996

Authors: Yao, Y.Y. | Li, Xining

Article Type: Research Article

Abstract: In the rough-set model, a set is represented by a pair of ordinary sets called the lower and upper approximations. In the interval-set model, a pair of sets is referred to as the lower and upper bounds which define a family of sets. A significant difference between these models lies in the definition and interpretation of their extended set-theoretic operators. The operators in the rough-set model are not truth-functional, while the operators in the interval-set model are truth-functional. Within the framework of possible-worlds analysis, we show that the rough-set model corresponds to the modal logic system S5 , while the …interval-set model corresponds to Kleene's three-valued logic system K3 . It is argued that these two models extend set theory in the same manner as the logic systems S5 and K3 extend standard propositional logic. Their relationships to probabilistic reasoning are also examined. Show more

DOI: 10.3233/FI-1996-272314

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 289-298, 1996

Authors: Zytkow, Jan M.

Article Type: Research Article

Abstract: We define the problem of empirical search for knowledge by interaction with a setup experiment, and we present a solution implemented in the FAHRENHEIT discovery system. FAHRENHEIT autonomously explores multi-dimensional empirical spaces of numerical parameters, making experiments, generalizing them into empirical equations, finding the scope of applications for each equation, and setting new discovery goals, until it reaches the empirically complete theory. It turns out that a small number of generic goals and a small number of data structures, when combined recursively, can lead to complex discovery processes and to the discovery of complex theories. We present FAHRENHEIT's knowledge representation …and the ways in which the discovery mechanism interacts with the emerging knowledge. Brief descriptions of several real-world applications demonstrate the system's discovery potential. Show more

DOI: 10.3233/FI-1996-272315

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 299-318, 1996