Andrzej Skowron

Transactions on rough sets XVII

Three-Valued Logics, Uncertainty Management and Rough Sets.- Standard Errors of Indices in Rough Set Data Analysis.- Proximity System: A Description-Based System for Quantifying the Nearness or Apartness of Visual Rough Sets.- Rough Sets and Matroids.- An Efficient Approach for Fuzzy Decision Reduct Computation.- Rough Sets in Economy and Finance.- Algorithms for Similarity Relation Learning from High Dimensional Data.

Zdzisław pawlak commemorating his life and work

Zdzislaw Pawlak will be remembered as a great human being with exceptional humility, wit and kindness as well as an extraordinarily innovative researcher with exceptional stature. His research contributions have had far-reaching implications inasmuch as his works are fundamental in establishing new perspectives for scientific research in a wide spectrum of fields.

Preface: pattern recognition and mining

Natural computing, also called natural computation, refers to understanding computational processes observed in nature, and human-designed computing inspired by nature. It encompasses three classes of methods, namely, those that are inspired by the nature to develop novel problem-solving techniques; those that are used for modeling natural phenomena based on the use of computers; and those that employ natural materials such as molecules to compute with use of discovered models of relevant natural phenomena. Our understanding of nature, as well as the essence of computation, is enhanced if complex natural phenomena are analyzed in terms of computational processes. Characteristic for human-designed computing inspired by nature is the metaphorical use of concepts, principles, and mechanisms underlying natural systems. The processes occurring in nature can be viewed as different kinds of information processing. Self-assembly, selfreproduction, self-evolution, granulation, gene regulation networks, protein–protein interaction networks, active and passive biological transport networks, and gene assembly in unicellular organisms are some of the examples of such processes. Understanding the universe itself from the information processing point of view and engineering of semi-synthetic organisms are some efforts to understand biological systems. The most established classical nature-inspired models of computation are cellular automata, neural computation, evolutionary computation and granular computation. More recent computational systems abstracted from natural processes include artificial life, swarm intelligence, artificial immune systems, membrane computing, DNA computing, molecular computing, quantum computing, fractal geometry, and amorphous computing, among others. In fact, all major methods and algorithms are nature-inspired metaheuristic algorithms. Granulation is a process, among others, that is abstracted from natural phenomena. Granulation is inherent in human thinking and reasoning process. Granular computing (GrC) is a problem solving paradigm where computation and operations are performed on information granules, and it is based on the realization that precision is sometimes expensive and not very meaningful in modelling and controlling complex systems. This framework can be modeled with principles of neural networks, fuzzy sets and rough sets, both in isolation and integration, among other theories. GrC has been proven to be effective in intelligent information processing and data mining, and has a strong promise for Big data analysis. To reflect the current trends in the domain of natural computing and its application, this special issue of Natural Computing (Springer) on Pattern Recognition and Mining has been brought out. The issue contains nine contributory papers, six selected from those presented in 5th International Conference on Pattern Recognition and Machine Intelligence (PReMI 2013) and three out of a call for P. Maji (&) Machine Intelligence Unit, Indian Statistical Institute, Kolkata, India e-mail: pmaji@isical.ac.in

Transactions on Rough Sets XX

Feature selecting is considered as one of the most important pre-process methods in machine learning, data mining and bioinformatics. By applying pre-process techniques, we can defy the curse of dimensionality by reducing computational and storage costs, facilitate data understanding and visualization, and diminish training and testing times, leading to overall performance improvement, especially when dealing with large datasets. Correlation feature selection method uses a conventional merit to evaluate different feature subsets. In this paper, we propose a new merit by adapting and employing of correlation feature selection in conjunction with fuzzy-rough feature selection, to improve the effectiveness and quality of the conventional methods. It also outperforms the newly introduced gradient boosted feature selection, by selecting more relevant and less redundant features. The two-step experimental results show the applicability and efficiency of our proposed method over some well known and mostly used datasets, as well as newly introduced ones, especially from the UCI collection with various sizes from small to large numbers of features and samples.

Transactions on Rough Sets XIX

A Uniform Framework for Rough Approximations Based on Generalized Quantifiers.- PRE and Variable Precision Models in Rough Set Data Analysis.- Three Approaches to Deal with Tests for Inconsistent Decision Tables - Comparative Study.- Searching for Reductive Attributes in Decision Tables.- Sequential Optimization of c-Decision Rules Relative to Length, Coverage and Number of Misclassifications.- Toward Qualitative Assessment of Rough Sets in Terms of Decision Attribute Values in Simple Decision Systems over Ontological Graphs.- Predicting the Presence of Serious Coronary Artery Disease Based on 24 Hour Holter ECG Monitoring.- Interface of Rough Set Systems and Modal Logics: A Survey.- A Semantic Text Retrieval for Indonesian Using Tolerance Rough Sets Models.- Some Transportation Problems Under Uncertain Environments.

Generalized Quantifiers in the Context of Rough Set Semantics

Looking back to Prof. Zadeh’s paradigm of Computing with Words (CWW) [28, 29, 30], one can notice that the initial attempt of such an endeavour was to set up a basic vocabulary of linguistic words, and fix their semantics based on fuzzy sets. Then a grammar was proposed to generate compound linguistic expressions based on the primitive ones, and simultaneously based on the semantic interpretations of those basic linguistic expressions a general scheme for the semantics of the rest of linguistic expressions were proposed. Sentences involving linguistic quantifiers and vague predicates constitute a fragment of natural language. In this paper, we choose this fragment of the natural language, and explore the semantics from the perspective of rough sets [13, 14, 16, 17, 18, 21]. We fix a set of basic crisp quantifiers, mainly of proportional kind. A set of vague quantifiers are proposed to lie in a close vicinity of those crisp quantifiers in the sense that a particular vague quantifier can be visualized as a blurred, may be called rough, image of a set of crisp quantifiers. Address for correspondence: Institute of Mathematics, University of Warsaw, 02 Banacha, 02-097 Warsaw, Poland ∗This work has been carried out during the ERCIM Alain Benseossan fellowship. †This work was partially supported by the Polish National Science Centre (NCN) grants DEC-2011/01/D/ST6/06981, DEC2012/05/B/ST6/03215, DEC-2013/09/B/ST6/01568 as well as by the Polish National Centre for Research and Development (NCBiR) under the grant O ROB/0010/03/001. 214 S. Dutta and A. Skowron / Generalized Quantifiers with Rough Set Semantics Semantics of the rest of the vague quantifiers can be obtained based on the subjective perception of the interrelations among the (vague) quantifiers.

Transactions on Rough Sets XVIII

A rough intuitionistic fuzzy set is the result of approximation of an intuitionistic fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough intuitionistic fuzzy sets. We first show that a reflexive crisp rough approximation space can induce an intuitionistic fuzzy Alexandrov space. It is proved that the lower and upper rough intuitionistic fuzzy approximation operators are, respectively, an intuitionistic fuzzy interior operator and an intuitionistic fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. We then verify that a similarity crisp approximation space can produce an intuitionistic fuzzy clopen topological space. We further examine sufficient and necessary conditions that an intuitionistic fuzzy interior (closure, respectively) operator derived from an intuitionistic fuzzy topological space can associate with a reflexive and transitive crisp relation such that the induced lower (upper, respectively) rough intuitionistic fuzzy approximation operator is exactly the intuitionistic fuzzy interior (closure, respectively) operator.