Fundamenta Informaticae - Volume 115, issue 4

Authors: Kryszkiewicz, Marzena | Obiedkov, Sergei | Raś, Zbigniew W.

Article Type: Other

DOI: 10.3233/FI-2012-654

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. i-ii, 2012

Authors: Pankratieva, Vera V. | Kuznetsov, Sergei O.

Article Type: Research Article

Abstract: Relationships between proto-fuzzy concepts, crisply generated fuzzy concepts, and pattern structures are considered. It is shown that proto-fuzzy concepts are closely related to crisply generated fuzzy concepts in the sense that the mappings involved in the definitions coincide for crisp subsets of attributes. Moreover, a proto-fuzzy concept determines a crisp subset of attributes, which generates a (crisply generated) fuzzy concept. However, the reverse is true only in part: given a crisp subset of attributes, one can find a proto-fuzzy concept whose intent includes (but not necessarily coincides with) the given subset of attributes. Interval pattern concepts are shown to be …related to crisply generated formal concepts. In particular, every crisply closed subset of objects is an extent of an interval pattern concept. Also, we establish some properties of the collection of formal concepts for a given fuzzy context. Show more

Keywords: proto-fuzzy concepts, crisply generated fuzzy concepts, pattern structures, interval pattern concepts

DOI: 10.3233/FI-2012-655

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 265-277, 2012

Authors: Belohlavek, Radim | Konecny, Jan

Article Type: Research Article

Abstract: We present results regarding row and column spaces of matrices whose entries are elements of residuated lattices. In particular, we define the notions of a row and column space for matrices over residuated lattices, provide connections to concept lattices and other structures associated to such matrices, and show several properties of the row and column spaces, including properties that relate the row and column spaces to Schein ranks of matrices over residuated lattices. Among the properties is a characterization of matrices whose row (column) spaces are isomorphic. In addition, we present observations on the relationships between results established in Boolean …matrix theory on one hand and formal concept analysis on the other hand. Show more

Keywords: graded matrix, formal concept analysis, morphism

DOI: 10.3233/FI-2012-656

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 279-295, 2012

Authors: Krídlo, Ondrej | Krajči, Stanislav | Ojeda-Aciego, Manuel

Article Type: Research Article

Abstract: An L-fuzzy generalization of the so-called Chu correspondences between formal contexts forms a category called L-ChuCors. In this work, we show that this category naturally embeds ChuCors and prove that it is *ast;-autonomous. We also focus on the direct product of two L-fuzzy contexts, which is defined with the help of a binary operation, essentially a disjunction, on a lattice of truth-values L.

DOI: 10.3233/FI-2012-657

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 297-325, 2012

Authors: Dolques, Xavier | Huchard, Marianne | Nebut, Clémentine | Reitz, Philippe

Article Type: Research Article

Abstract: Use case diagrams appear early within a UML-based development, structured over the concepts of actors and use cases to capture user requirements of an application. Good modeling practices suggest that use case diagrams should be simple and easy-to-read, two goals that can be achieved by introducing relevant generalizations of actors and use cases. The approach presented in this paper allows, using Formal Concept Analysis and one of its variants, Relational Concept Analysis, to refactor a use case diagram as a whole in order to make it clearer while respecting the semantics of the original diagram. The relevancy of this approach …has been confirmed by its implementation as a tool and the results obtained from its application on several representative diagrams. Show more

Keywords: Formal Concept Analysis, UML use case diagrams

DOI: 10.3233/FI-2012-658

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 327-356, 2012

Authors: Missaoui, Rokia | Nourine, Lhouari | Renaud, Yoan

Article Type: Research Article

Abstract: The objective of this article is to define an approach towards generating implications with (or without) negation when only a formal context K = (G, M, I) is provided. To that end, we define a two-step procedure which first (i) computes implications whose premise is a key in the context K | $\tilde{\rm K}$ representing the apposition of the context K and its complementary $\tilde{\rm K}$ with attributes in $\tilde{\rm M}$ (negative attributes), and then (ii) uses an inference axiom we have defined to produce the whole set of implications.

Keywords: Formal concept analysis, implication, negation, key, inference system

DOI: 10.3233/FI-2012-659

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 357-375, 2012

Authors: Revenko, Artem | Kuznetsov, Sergei O.

Article Type: Research Article

Abstract: An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Example functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration is run on contexts where objects are functions and attributes are 16 function properties. Minimal implication bases are presented. The list of proved implications is presented and discussed.

Keywords: Properties of Functions, Attribute Exploration, Implication Basis

DOI: 10.3233/FI-2012-660

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 377-394, 2012

Authors: Krajca, Petr | Outrata, Jan | Vychodil, Vilem

Article Type: Research Article

Abstract: We present a novel approach to compute formal concepts of formal context. In terms of operations with Boolean matrices, the presented algorithm computes all maximal rectangles of the input Boolean matrix which are full of 1s. The algorithm combines basic ideas of previous approaches with our recent observations on the influence of attribute permutations and attribute sorting on the number of formal concepts which are computed multiple times. As a result, we present algorithm which computes formal concepts by successive context reduction and attribute sorting. We prove its soundness, discuss its complexity and efficiency, and show that it outperforms other …algorithms from the CbO family in terms of substantially lower numbers of formal concepts which are computed multiple times. Show more

DOI: 10.3233/FI-2012-661

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 395-417, 2012

Article Type: Other

Citation: Fundamenta Informaticae, vol. 115, no. 4, pp. 419-420, 2012