Fundamenta Informaticae - Volume 27, issue 2-3

Authors: Skowron, Andrzej | Ziarko, Wojciech

Article Type: Other

DOI: 10.3233/FI-1996-272316

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 101-102, 1996

Authors: Pawlak, Zdzislaw

Article Type: Research Article

Abstract: The paper explores the concepts of approximate relations and functions in the framework of the theory of rough sets. The difficulties with the application of the idea of rough relation to general rough function definition are discussed. The definition of rough function for the domain of real numbers is introduced and its properties are investigated in detail including the generalization of the standard notion of function continuity known in the theory of real functions.

DOI: 10.3233/FI-1996-272301

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 103-108, 1996

Authors: Bryniarski, Edward

Article Type: Research Article

Abstract: In the paper we present a formal description of rough sets within the framework of the generalized set theory, which is interpreted in the set approximation theory. The rough sets are interpreted as approximations, which are defined by means of the Pawlak's rough sets.

DOI: 10.3233/FI-1996-272302

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 109-136, 1996

Authors: Lin, T.Y. | Liu, Qing

Article Type: Research Article

Abstract: Earlier the authors have shown that rough sets can be characterized by six topological properties. In this paper, a new formal logic system based on such axioms is proposed. It will be called First-Order Logic for Rough Approximation or simply Rough Logic. The axiom schemas of rough logic turn out to be the same as those of the modal logic S5 . In other words, topological and modal logic considerations led to the same conclusion. So rough logic must have captured the intrinsic meaning of approximate reasoning However, their interpretations are different. To reflect the differences in semantics, possible worlds …are renamed as observable worlds. Each observable world represents a different rough observation of the actual world. Rough logic also provides a frame work for approximation. It integrates imperfect observations (observable worlds) into an approximation of actual world. Any good approximation theory should have a convergence theorem-its details are deferred to next paper. A sample theorem is as follows: If there is a convergent sequence of rough observations (namely, equivalence relations), then the corresponding rough models converge to the Tarskian model of first-order classical logic. Show more

DOI: 10.3233/FI-1996-272303

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 137-153, 1996

Authors: Katzberg, Jack David | Ziarko, Wojciech

Article Type: Research Article

Abstract: We present a generalization of the original idea of rough sets as introduced by Pawlak. The generalization, called the Variable Precision Rough Sets Model with Asymmetric Bounds, is aimed at modeling decision situations characterized by uncertain information expressed in terms of probability distributions estimated form frequency distributions observed in empirical data. The model presented is a direct extension of the previous concept, the Variable Precision Rough Sets Model. The properties of the extended model are investigated and compared to the original model. Also, a real life problem of identifying the factors which most affect the likelihoods of specified events in …the steel industry is discussed in the context of this theory. Show more

DOI: 10.3233/FI-1996-272304

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 155-168, 1996

Authors: Kent, Robert E.

Article Type: Research Article

Abstract: The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak [10] with the theory of Formal Concept Analysis pioneered by Rudolf Wille [11]. The central notion in this paper of a rough formal concept combines in a natural fashion the two notions of rough set and formal concept — to use a slogan: “rough set + formal concept = rough formal concept”. This paper is an extension of the paper [5] presented at the international workshop on Rough Sets and …Knowledge Discovery (RSKD'93). A related paper [8] using distributed constraints provides a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis, and Entity-Relationship database modeling. A follow-up paper [9] will extend rough concept analysis from formal contexts to distributed constraints. Show more

DOI: 10.3233/FI-1996-272305

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 169-181, 1996

Authors: Kryszkiewicz, Marzena | Rybinski, Henryk

Article Type: Research Article

Abstract: A set-theoretical approach to finding reducts of composed information systems is presented. It is shown how the search space can be represented in form of a pair of boundaries. It is also shown, how reducts of composing information systems can be used to reduce the search space of the composed system. Presented solutions are implied directly from the properties of composed monotonic Boolean functions.

DOI: 10.3233/FI-1996-272306

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 183-195, 1996

Authors: Moshkov, Mikhail

Article Type: Research Article

Abstract: We investigate decision trees for decision tables. We present upper and lower bounds on the minimal decision tree depth. Some bounds are expressed by parameters of decision rule systems constructed for decision tables.

Keywords: decision table, decision rule, decision tree, depth, bounds

DOI: 10.3233/FI-1996-272307

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 197-203, 1996

Authors: Pagliani, Piero

Article Type: Research Article

Abstract: Any Rough Sets System induced by an Approximation Space can be given several logic-algebraic interpretations. In this paper a Rough Sets System is investigated as a finite semi-simple Nelson algebra whose structure is inherently described using the properties of the underlying Approximation Space. Moreover some of the most characterizing features of Rough Sets Systems are derived from this interpretation in logic-algebraic terms. Particularly the logic-algebraic structure given to the Rough Sets System, qua a Nelson algebra is equipped by a weak negation and a strong negation, and, since it is a finite distributive lattice, it can be regarded also as …a Heyting algebra equipped by its own pseudocomplementation. Moreover the weak Nelson negation reveals to be a dual pseudocomplementation in the lattice of Rough Sets. In this way we are able, for instance, to recover the well-known fact that Rough Sets Systems are double Stone algebras, and to exploit both their properties and the general properties of Nelson algebras in order to analyse the notions of ”definable set” and ”rough top (bottom) equality” in Approximation Spaces. Show more

DOI: 10.3233/FI-1996-272308

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 205-219, 1996

Authors: Pomykala, Janusz | De Haas, Erik

Article Type: Research Article

Abstract: In this article we present a framework in which we can reason about damaged or lost information. As a basis of reasoning about information we use the notion of ’information system’ of Pawlak [1]. Furthermore this article presents introductory considerations for analyzing information systems using tools of category theory.

DOI: 10.3233/FI-1996-272309

Citation: Fundamenta Informaticae, vol. 27, no. 2-3, pp. 221-227, 1996