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1
Content available remote Automated Comparative Study of Some Generalized Rough Approximations
Grabowski Adam
Fundamenta Informaticae
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2021
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Vol. 179, nr 2
165--182
EN
The paper contains some remarks on building automated counterpart of a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to arbitrary binary relation. Our focus was on translating rationality postulates for such operators by means of the Mizar system – the software and the database which allows for expressing and checking mathematical knowledge for the logical correctness. The main objective was the formal (and machine-checked) proof of Theorem 4.1 from A. Gomolińska’s paper “A Comparative Study of Some Generalized Rough Approximations ”, hence the present title. We provide also the discussion on how to make the presentation more efficient to reuse the reasoning techniques of the Mizar verifier.
2
Content available remote Neighborhood Systems : Rough Set Approximations and Definability
Syau Y.-R., Lin E.-B., Liau C.-J.
Fundamenta Informaticae
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2018
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Vol. 159, nr 4
429--450
EN
The notions of approximation and definability in classical rough set theory and their generalizations have received much attention. In this paper, we study such generalizations from the perspective of neighborhood systems. We introduce four different types of definability, called interior definability, closure definability, interior-closure (IC) definability, and weak IC definability respectively. We also point out the relationship between IC definability and other types of definability for some special kinds of neighborhood systems. Several examples are presented to illustrate the concepts introduced in this paper.
3
Content available remote On Graded Nearness of Sets
Gomolińska A., Wolski M.
Fundamenta Informaticae
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2012
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Vol. 119, nr 3/4
301-317
EN
In this article we present three inclusion functions which characterise the nearness relation between finite sets of objects defined in line with J. F. Peters, A. Skowron, and J. Stepaniuk [26]. By means of these functions we extend the notion of nearness to the graded case where one can measure the degree to which one set is near to another one.
4
Content available remote Rough Approximations in Varieties of Regular Languages
Martin G., Steinby M.
Fundamenta Informaticae
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2011
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Vol. 112, nr 4
281-303
EN
We study approximations of regular languages bymembers of a given variety L of regular languages. These are upper or lower approximations in the sense of Pawlak’s rough set theory with respect to congruences belonging to the variety of congruences corresponding to L. In particular, we consider the closest upper and lower approximations in L. In so-called principal varieties these always exist, and we present algorithms for finding them, but for other varieties the situation is more complex. Although we consider just Eilenberg’s +-varieties, the general ideas apply also to other types of varieties of languages. Our work may also be viewed as an approach to the characterizable inference problem in which a language of a certain kind is to be inferred from a given sample.
5
Content available remote A Logic-Algebraic Approach to Graded Inclusion
Gomolińska A.
Fundamenta Informaticae
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2011
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Vol. 109, nr 3
265-279
EN
In this article we continue searching for functions which might be used as measures of inclusion of information granules in information granules. Starting with a 3-valued logic having an adequate logical matrix, we show how to derive a corresponding graded inclusion function. We report on the results of examination of several best known 3-valued logics in this respect. We also give some basic properties of the inclusion functions obtained.
6
Content available remote On the Structure of Rough Approximations
Järvinen J.
Fundamenta Informaticae
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2002
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Vol. 53, nr 2
135-153
EN
We study rough approximations based on indiscernibility relations which are not necessarily reflexive, symmetric or transitive. For this, we define in a lattice-theoretical setting two maps which mimic the rough approximation operators and note that this setting is suitable also for other operators based on binary relations. Properties of the ordered sets of the upper and the lower approximations of the elements of an atomic Boolean lattice are studied.
7
Content available remote A Comparative Study of Some Generalized Rough Approximations
Gomolińska A.
Fundamenta Informaticae
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2002
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Vol. 51, nr 1,2
103-119
EN
In this paper we focus upon a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to any binary reflexive relation. We aim at finding the best of several candidates for generalized rough approximation mappings, where both definability of sets by elementary granules of information as well as the issue of distinction among positive, negative, and border regions of a set are taken into account.
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