Fundamenta Informaticae - Volume 97, issue 4

Authors: Düntsch, Ivo | Pratt-Hartmann, Ian

Article Type: Research Article

Abstract: An arithmetic circuit is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest subalgebra of the complex algebra of the semiring of natural numbers. In the present paper we investigate the algebraic structure of complex algebras of natural numbers and make some observations regarding the complexity of various theories of such …algebras. Show more

DOI: 10.3233/FI-2009-206

Citation: Fundamenta Informaticae, vol. 97, no. 4, pp. 347-367, 2009

Authors: Kieu, The Duc | Chang, Chin-Chen

Article Type: Research Article

Abstract: The advances of network technologies and digital devices facilitate users to exchange multimedia data over the public networks. However, this also raises significant concerns about how to protect sensitive multimedia data from being illegally copied and unauthorized modifications. Thus, this paper proposes a fragile watermarking method to detect illegitimate alterations of the watermarked data. The proposed method embeds a grayscale watermark image into a grayscale cover image in a block-by-block manner by using discrete …Fourier transform. Experimental results show that the proposedmethod can successfully and exactly detect and localize any tampered regions of the watermarked image. Show more

Keywords: Information hiding, watermarking, Fourier transform

DOI: 10.3233/FI-2009-207

Citation: Fundamenta Informaticae, vol. 97, no. 4, pp. 369-379, 2009

Authors: Suresh, Kaushik | Kundu, Debarati | Ghosh, Sayan | Das, Swagatam | Abraham, Ajith

Article Type: Research Article

Abstract: The article considers the task of fuzzy clustering in a multi-objective optimization (MO) framework. It compares the relative performance of four recently developedmulti-objective variants of Differential Evolution (DE) on over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to …the problem specifications. A real-coded representation for the candidates is used for DE. A comparative study of four DE variants with two most well-known MO clustering techniques, namely the NSGA II (Non Dominated Sorting GA) and MOCK (Multi- Objective Clustering with an unknown number of clusters K) is also undertaken. Experimental results reported for six artificial and four real life datasets (including a microarray dataset of budding yeast) of varying range of complexities indicates that DE can serve as a promising algorithm for devising MO clustering techniques. Show more

Keywords: Differential Evolution, Multi-objective optimization, Fuzzy clustering, Micro-array data clustering

DOI: 10.3233/FI-2009-208

Citation: Fundamenta Informaticae, vol. 97, no. 4, pp. 381-403, 2009

Authors: Vitória, Aida | Małuszyński, Jan | Szałas, Andrzej

Article Type: Research Article

Abstract: We present a language for defining paraconsistent rough sets and reasoning about them. Our framework relates and brings together two major fields: rough sets [23] and paraconsistent logic programming [9]. To model inconsistent and incomplete information we use a four-valued logic. The language discussed in this paper is based on ideas of our previous work [21,32,22] developing a four-valued framework for rough sets. In this approach membership function, set containment and set operations are four-valued, where …logical values are t (true), f (false), i (inconsistent) and u (unknown). We investigate properties of paraconsistent rough sets as well as develop a paraconsistent rule language, providing basic computational machinery for our approach. Show more

Keywords: approximate reasoning, rough sets, paraconsistent reasoning, four-valued logics

DOI: 10.3233/FI-2009-209

Citation: Fundamenta Informaticae, vol. 97, no. 4, pp. 405-438, 2009

Authors: Winkowski, Józef

Article Type: Research Article

Abstract: The paper is the second part of two-part paper that contributeswith a concept of a process, with operations allowing to define complex processes in terms of their components, with the respective algebras, and with the idea of using the formal tools thus obtained to describe the behaviours of concurrent systems. In the first part a universal model of a process have been introduced and operations on processes have been defined. A process is viewed as a …model of a run of a system (discrete, continuous, or of a mixed type). A process may have an initial state (a source), a final state (a target), or both. A process can be represented by a partially ordered multiset. Processes of which one is a continuation of the other can be composed sequentially. Independent processes, can be composed in parallel. Processes may be prefixes, i.e. independent components of initial segments of other processes. It has been shown that processes in a universe of objects and operations on such processes form a partial algebra, called algebra of processes, that is a specific partial category with respect to the sequential composition, and a specific partial monoid with respect to the parallel composition. In the second part the properties of algebras of processes described in the first part are regarded as axioms defining a class of abstract partial algebras, called behaviour-oriented algebras, and properties of such algebras are investigated. In particular, it is shown how some of the behaviour-oriented algebras can be represented as algebras of processes, and how to use them to describe phenomena with states and processes provided with specific structures. Show more

Keywords: Process, state, sequential composition, parallel composition, category, partial category, partial monoid, independence, structure, behaviour, random behaviour

DOI: 10.3233/FI-2009-210

Citation: Fundamenta Informaticae, vol. 97, no. 4, pp. 439-470, 2009

Authors: Zhang, Zhiming

Article Type: Research Article

Abstract: Given a widespread interest in rough sets as being applied to various tasks of data analysis it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. This paper proposes an interval-valued intuitionistic fuzzy rough model by means of integrating the classical Pawlak rough set theory with the interval-valued intuitionistic fuzzy set theory. Firstly, some concepts and properties of interval-valued intuitionistic fuzzy set and …interval-valued intuitionistic fuzzy relation are introduced. Secondly, a pair of lower and upper interval-valued intuitionistic fuzzy rough approximation operators induced from an interval-valued intuitionistic fuzzy relation is defined, and some properties of approximation operators are investigated in detail. Furthermore, by introducing cut sets of interval-valued intuitionistic fuzzy sets, classical representations of interval-valued intuitionistic fuzzy rough approximation operators are presented. Finally, the connections between special interval-valued intuitionistic fuzzy relations and interval-valued intuitionistic fuzzy rough approximation operators are constructed, and the relationships of this model and the others rough set models are also examined. Show more

Keywords: Rough sets, interval-valued intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy relations, interval-valued intuitionistic fuzzy rough sets, knowledge reduction

DOI: 10.3233/FI-2009-211

Citation: Fundamenta Informaticae, vol. 97, no. 4, pp. 471-498, 2009