Fundamenta Informaticae - Volume 148, issue 1-2

Authors: Ciucci, Davide | Ślęzak, Dominik | Wolski, Marcin

Article Type: Other

DOI: 10.3233/FI-2016-1419

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. v-vi, 2016

Authors: Rauch, Jan

Article Type: Research Article

Abstract: Association rules are introduced as general relations of two general Boolean attributes derived from columns of an analysed data matrix. Expressive power of such association rules makes possible to use various items of domain knowledge in data mining. Each particular item of domain knowledge is mapped to a set of simple association rules. Simple association rules together with their logical consequences are understood as a set of consequences of a given item of domain knowledge. Such sets of consequences are used when interpreting results of a data mining procedure. Logical deduction plays a crucial role in this approach. New results …on related deduction rules are presented. Show more

Keywords: data mining, association rules, formalization of CRISP-DM, domain knowledge, logical calculus of association rules

DOI: 10.3233/FI-2016-1420

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 1-33, 2016

Authors: Nowak-Brzezińska, Agnieszka

Article Type: Research Article

Abstract: Rule-based knowledge bases are constantly increasing in volume, thus the knowledge stored as a set of rules is getting progressively more complex and when rules are not organized into any structure, the system is inefficient. The aim of this paper is to improve the performance of mining knowledge bases by modification of both their structure and inference algorithms, which in author’s opinion, lead to improve the efficiency of the inference process. The good performance of this approach is shown through an extensive experimental study carried out on a collection of real knowledge bases. Experiments prove that rules partition enables reducing …significantly the percentage of the knowledge base analysed during the inference process. It was also proved that the form of the group’s representative plays an important role in the efficiency of the inference process. Show more

Keywords: rough set theory, rules clustering, knowledge bases, inference algorithms, rules mining

DOI: 10.3233/FI-2016-1421

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 35-50, 2016

Authors: Napierala, Krystyna | Stefanowski, Jerzy

Article Type: Research Article

Abstract: Rule-based classifiers constructed from imbalanced data fail to correctly classify instances from the minority class. Solutions to this problem should deal with data and algorithmic difficulty factors. The new algorithm BRACID addresses these factors more comprehensively than other proposals. The experimental evaluation of classification abilities of BRACID shows that it significantly outperforms other rule approaches specialized for imbalanced data. However, it may generate too high a number of rules, which hinder the human interpretation of the discovered rules. Thus, the method for post-processing of BRACID rules is presented. It aims at selecting rules characterized by high supports, in particular for …the minority class, and covering diversified subsets of examples. Experimental studies confirm its usefulness. Show more

Keywords: Rule induction, class imbalances, interpretability of rules, filtering of rules

DOI: 10.3233/FI-2016-1422

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 51-64, 2016

Authors: Kryszkiewicz, Marzena

Article Type: Research Article

Abstract: In this paper, we propose an ACBC-evaluation formula, which delivers a flexible way of formulating different kinds of criteria for association and decision rules. We prove that rules with minimal antecedents that fulfill ACBC-evaluation formulae are key generators, which are patterns of a special type. We also show that a number of types of rough set approximations of decision classes can be expressed based on ACBC-evaluation formulae. We prove that decision rules preserving respective approximations of decision classes are rules that satisfy an ACBC-evaluation formula and that antecedents of such optimal decision rules are key generators, too. A number of …properties related to particular measures of association rules and key generators are derived. Show more

DOI: 10.3233/FI-2016-1423

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 65-85, 2016

Authors: Zielosko, Beata

Article Type: Research Article

Abstract: In the paper, an application of dynamic programming approach to global optimization of approximate association rules relative to coverage and length is presented. It is an extension of the dynamic programming approach to optimization of decision rules to inconsistent tables. Experimental results with data sets from UCI Machine Learning Repository are included.

Keywords: Rough sets, association rules, decision rules, length, coverage, dynamic programming

DOI: 10.3233/FI-2016-1424

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 87-105, 2016

Authors: Kopczyński, Maciej | Grześ, Tomasz | Stepaniuk, Jarosław

Article Type: Research Article

Abstract: In this paper we propose a combination of capabilities of the FPGA based device and PC computer for rough sets based data processing resulting in generating decision rules. Presented architecture has been tested on the exemplary datasets. Obtained results confirm the significant acceleration of the computation time using hardware supporting rough set operations in comparison to software implementation.

DOI: 10.3233/FI-2016-1425

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 107-122, 2016

Authors: Chakraborty, Mihir K.

Article Type: Research Article

Abstract: This paper is concerned with some issues connected with the foundations of rough set theory. Particularly the problem of definition of a rough set is discussed.

Keywords: rough set, granulation, vagueness, indiscernibility

DOI: 10.3233/FI-2016-1426

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 123-132, 2016

Authors: Maji, Pradipta | Mandal, Ankita

Article Type: Research Article

Abstract: One of the main problems in real life omics data analysis is how to extract relevant and non-redundant features from high dimensional multimodal data sets. In general, supervised regularized canonical correlation analysis (SRCCA) plays an important role in extracting new features from multimodal omics data sets. However, the existing SRCCA optimizes regularization parameters based on the quality of first pair of canonical variables only using standard feature evaluation indices. In this regard, this paper introduces a new SRCCA algorithm, integrating judiciously the merits of SRCCA and rough hypercuboid approach, to extract relevant and non-redundant features in approximation spaces from multimodal …omics data sets. The proposed method optimizes regularization parameters of the SRCCA based on the quality of a set of pairs of canonical variables using rough hypercuboid approach. While the rough hypercuboid approach provides an efficient way to calculate the degree of dependency of class labels on feature set in approximation spaces, the merit of SRCCA helps in extracting non-redundant features from multimodal data sets. The effectiveness of the proposed approach, along with a comparison with related existing approaches, is demonstrated on several real life data sets. Show more

Keywords: Multimodal data analysis, canonical correlation analysis, feature extraction, rough sets, rough hypercuboid approach

DOI: 10.3233/FI-2016-1427

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 133-155, 2016

Authors: Wolski, Marcin | Gomolińska, Anna

Article Type: Research Article

Abstract: The paper studies the rough granular computing paradigm within the conceptual settings of multi-modal logic. The main idea is to express a generalised approximation space (U ; I ; κ ), where U is the universe of objects, I is an uncertainty function, and κ is a rough inclusion function, in terms of binary relations, and then to consider the corresponding modal operators. The new modal structure obtained in this way is rich enough to define closure and interior operators corresponding to the classical rough approximation operators and their well-known uni-modal generalisations. In contrast to the standard …modal interpretation of rough set approximations, in the new settings one can directly deal with information granules and their properties, which is crucial for granular computing paradigm. More precisely, we are provided with means of describing features of objects and information granules, as well as inclusion degrees between granules. Show more

Keywords: rough granular computing, generalised approximation space, modal logic, rough inclusion, topological space, Frechet (V)space

DOI: 10.3233/FI-2016-1428

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 157-172, 2016

Authors: More, Anuj Kumar | Banerjee, Mohua

Article Type: Research Article

Abstract: Rough sets are investigated from the viewpoint of topos theory. Two categories RSC and ROUGH of rough sets and a subcategory ξ -RSC are focussed upon. It is shown that RSC and ROUGH are equivalent. Generalizations RSC (𝒞) and ξ -RSC(𝒞) are proposed over an arbitrary topos 𝒞. RSC(𝒞) is shown to be a quasitopos, while ξ -RSC(𝒞) forms a topos in the special case when 𝒞 is Boolean. An example of RSC(𝒞) is given, through which one is able to define monoid actions on rough sets. Next, the algebra of strong subobjects of an …object in RSC is studied using the notion of relative rough complementation. A class of contrapositionally complemented ‘c . ∨ c .’ lattices is obtained as a result, from the object class of RSC . Moreover, it is shown that such a class can also be obtained if the construction is generalized over an arbitrary Boolean algebra. Show more

Keywords: Rough sets, Elementary Topos, Quasitopos, Lattices with Complementation

DOI: 10.3233/FI-2016-1429

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 173-190, 2016

Authors: Düntsch, Ivo | Orłowska, Ewa | Wang, Hui

Article Type: Research Article

Abstract: In previous work we have presented a class of algebras enhanced with two contact relations representing rough set style approximations of a spatial contact relation. In this paper, we develop a class of relational systems which is mutually interpretable with that class of algebras, and we consider a relational logic whose semantics is determined by those relational systems. For this relational logic we construct a proof system in the spirit of Rasiowa-Sikorski, and we outline the proofs of its soundness and completeness.

DOI: 10.3233/FI-2016-1430

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 191-206, 2016

Authors: Chiaselotti, Giampiero | Ciucci, Davide | Gentile, Tommaso | Infusino, Federico

Article Type: Research Article

Abstract: We introduce and study new generalizations of some rough set tools. Namely, the extended core, the generalized discernibility function, the discernibility space and the maximum partitioner. All these concepts where firstly introduced during the application of rough set theory to graphs, here we show that they have an interesting and useful interpretation also in the general setting. Indeed, among other results, we prove that reducts can be computed in incremental polynomial time, we give some conditions in order that a partition coincides with an indiscernibility partition of a given information table and we give the conditions such that a discernibility …matrix corresponds to an information table. Show more

DOI: 10.3233/FI-2016-1431

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 207-227, 2016

Authors: Pancerz, Krzysztof

Article Type: Research Article

Abstract: The main goal of the paper is to show the idea of incorporating paradigmatic and syntagmatic relations into processing data stored in information tables using rough set methods. Input data, in a tabular form, are used in many machine learning and computational intelligence methods and algorithms, among others, those based on rough set theory. Additional knowledge about semantic relations (both paradigmatic and syntagmatic) can be considered as a useful context affecting data classification or clustering.

Keywords: information systems, rough sets, ontological graphs, semantic relations, paradigmatic relations, syntagmatic relations

DOI: 10.3233/FI-2016-1432

Citation: Fundamenta Informaticae, vol. 148, no. 1-2, pp. 229-242, 2016