# Andrzej SkowronUniversity of Warsaw | UW · Institute of Mathematics

Andrzej Skowron

Professor

## About

526

Publications

43,504

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19,993

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Citations since 2017

## Publications

Publications (526)

This paper is an attempt to present some grounds that a change is needed in the way of viewing mathematical tools, such as fuzzy sets, rough sets, in the context of classifying and approximating concepts pertaining to the real physical complex phenomenon. The paper argues in favour of developing models going beyond the pure mathematical manifold. T...

This paper is a continuation of our earlier works in establishing the need for introducing Interactive Granular Computing (IGrC) in developing Intelligent Systems (IS’s) and/or Decision Support Systems (DSS’s) dealing with complex phenomena. Among several crucial points, this paper argues in favour of the necessity to provide tools for learning mod...

The problem of understanding intelligence is treated, by some prominent researchers, as the greatest problem of this century. In this article we justify that a decision support systems to be intelligent there is a need for developing new reasoning tools which can take into account the significance of the processes of sensory measurement, experience...

The original article can be found online.

We discuss an approach of concept approximation based on judgment rather than on partial containment of sets only. This approach seems to be much more general than the traditional one. However, it requires developing some new logical tools for reasoning based on judgment, which is often expressed in natural language.

This paper is an attempt to show how dialogue between a system and a user is important to design a robust system which can learn a user’s perspective and revise its knowledge base through interactions. The dialogue is crucial in order to better respond to a given query of a user. The problems, where dialogues can play a role, are discussed from two...

In this paper we have proposed a variation of Barwise and Seligman's proposal for information flow among a distributed network of agents by bringing in a notion of belief structure and a notion of graded inference. In their proposal, belief profile of an agent has played an important role as it is explicitly mentioned in the principles of informati...

In the original publication, the Acknowledgments was published incorrectly. The correct Acknowledgments is provided in this Correction.

Introduction of rough sets by Professor Zdzisław Pawlak has completed 35 years. The theory has already attracted the attention of many researchers and practitioners, who have contributed essentially to its development, from all over the world. The methods, developed based on rough set theory alone or in combination with other approaches, found appl...

This paper aims to discuss about the reasons behind the wide applicability of the rough set approach in real-life projects. The rough set-based approximations of (vague) concepts is one among the most central notions, available in the literature, for dealing with imperfect data and/or information. Moreover, as the approach based on rough sets is di...

This paper proposes an interpretation of characterizing required condition and desired condition of an user, that is a bipolar query, from the perspective of rough set semantics with an additional feature of learning the user’s need through dialogue.

This is a biogram of Professor Helena Rasiowa (1917–1994) one of the leading representatives of logicians from Warsaw. She was not only the great scientist but also the great human being. Rasiowa influenced numerous researchers from all over the world, especially by her results in algebraic logic, as well as by her great contribution for the mathem...

We discuss the rough set approach to approximation of vague concepts. There are already published several papers on rough sets and vague concepts staring from the seminal papers by Zdzisław Pawlak. However, only a few of them are discussing the relationships of rough sets with the sorites paradox. This paper contains a continuation of discussion on...

In Chapter “Challenges of Real-Scale Production with Smart Dynamic Casting”, low-resolution Figure 4 is replaced with high resolution, Figure 5 is replaced with new figure and Figure 6 and the graph near are positioned as per the standard.

The acknowledgement section of this paper originally referred to grant DEC-2013/09/B/ST6/01568. The reference to this grant has been removed from the acknowledgement section at the request of one of the authors.

In this chapter our attempt is to point out different ways of addressing different perspectives of understanding a vague concept from the angle of rough set semantics. In this attempt, we propose to depart from the closed way of presenting information table characterizing a vague concept with respect to a closed sample of objects, a fixed set of at...

The acknowledgement section of this paper originally referred to grant DEC-2013/09/B/ST6/01568. The reference to this grant has been removed from the acknowledgement section at the request of one of the authors.

The acknowledgement section of this paper originally referred to grant DEC-2013/09/B/ST6/01568. The reference to this grant has been removed from the acknowledgement section at the request of one of the authors.

We present an extension of logical structures, called interactive logical structures, for reasoning about interactive computations performed by Intelligent Systems or Complex Adaptive Systems. Reasoning based on such structures is called adaptive judgment and it goes beyond deduction, induction, and abduction. An extension of logical structures, ba...

A decision tree with verifying cuts, called V-tree, uses additional knowledge encoded in many attributes to classify new objects. The purpose of the verifying cuts is to confirm the correctness of the partitioning of tree nodes based on the (semi)-optimal cut determined by a greedy approach. The confirmation may be relevant because for some new obj...

In this paper we take an attempt to depart from the closed way of presenting information table characterizing a vague concept with respect to a closed sample of objects, a fixed set of attributes, and a static time point. The aim is rather to have an interactive information system which is open to incorporate new information based on the interactio...

In this paper, we incorporate the concepts of evidence theory and variable precision rough set model (VP-model) to examine inconsistent decision tables. For the decision classes in a given decision table, we point out the relationship between approximation degree of dependency and the belief functions. We also introduce the notion of weakly discern...

In this chapter we propose a departure from classical notion of information systems. We propose to bring in the background of agent’s interaction with physical reality in arriving at a specific information system. The proposals for generalizing the notion of information systems are made from two aspects. In the first aspect, we talk about incorpora...

In this chapter we begin from rough set rudiments. Next we outline applications of rough sets in pattern recognition. This chapter covers partially the material presented in the chapter [272] published in 2001 in the book [184] and also includes information on development of the rough set based methods in pattern recognition published after 2001.

Nowadays efficient methods for dealing with Big Data are urgently needed for many real-life applications. Big Data is often distributed over networks of agents involved in complex interactions. Decision support for users, to solve problems using Big Data, requires to develop relevant computation models for the agents as well as methods for incorpor...

In several papers we have discussed a computing model, called the Interactive Granular Computing (IGrC), for interactive computations on complex granules. In this paper, we compare two models of computing, namely the Turing model and the IGrC model.

Development of methods for Wisdom Web of Things (W2T) should be based on foundations of computations performed in the complex environments of W2T. We discuss some characteristic features of decision making processes over W2T. First of all the decisions in W2T are very often made by different agents on the basis of complex vague concepts and relatio...

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to...

We discuss an approach to modeling of computations performed by Complex Adaptive Systems (CAS) based on Interactive Granular Computing (IGrC).

Decision support in solving problems related to complex systems requires relevant computation models for the agents as well as methods for incorporating reasoning over computations performed by agents. Agents are performing computations on complex objects (e.g., (behavioral) patterns, classifiers, clusters, structural objects, sets of rules, aggreg...

Granular computing (GrC) is a domain of science aiming at modeling computations and reasoning that deals with imprecision, vagueness, and incompleteness of information. Computations in GrC are performed on granules that are obtained as a result of information granulation. Principal issues in GrC concern processes of representation, construction, tr...

Looking back to Prof. Zadeh's paradigm of Computing withWords (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 sim...

Big data has a role in its promising usefulness in many fields, such as commerce and business, biology, medicine, public administration, material science, and cognition in human brain. The objective of big data is to develop complex procedure running over large-scale enormous-sized data repositories for extracting useful knowledge hidden there in a...

Understanding the nature of interactions is regarded as one of the biggest challenges in projects related to complex adaptive systems. We discuss foundations for interactive computations in interactive intelligent systems (IIS), developed in the Wistech program and used for modeling complex systems. We emphasize the key role of risk management in p...

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 phenomen...

This volume of the TRS presents extensions of papers from the 2012 Workshop on Rough Set Applications.

We discuss an approach for dealingwith uncertainty in complex intelligent systems. The approach is based on interactive computations over complex objects called here complex granules (c-granules, for short). C-granules are defined relative to a given agent. Any c-granule of a given agent specifies a perceived structure of local environment of physi...

Granular Computing (GrC) is a domain of science aiming at modeling computations and reasoning that deals with imprecision, vagueness and incompleteness of information. Computations in GrC are performed on granules which are obtained as a result of information granulation. Principal issues in GrC concern processes of representation, construction, tr...

Building on our diverse research traditions in studying reasoning, language and communication, the Polish School of Argumentation integrates different disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Crafting methodological program and establishing organisational in...

Information granules (infogranules, for short) are widely discussed in the literature. In particular, let us mention here the rough granular computing approach based on the rough set approach and its combination with other approaches to soft computing. However, the issues related to interactions of infogranules with the physical world and to percep...

Volume XVII of the Transactions on Rough Sets (TRS) is a continuation of a
number of research streams that have grown out of the seminal work of Zdzis�law
Pawlak during the first decade of the twenty-first century. The research streams
represented in the papers cover both the theory and applications of rough, fuzzy,
and near sets as well as their c...

Information granules (infogranules, for short) are widely discussed in the literature. In particular, let us mention here the rough granular computing approach based on the rough set approach and its combination with other approaches to soft computing. However, the issues related to interactions of infogranules with the physical world and to percep...

This volume of the TRS presents articles on 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 Compu...

We discuss an approach for dealing with uncertainty in complex systems. The approach is based on interactive computations over complex objects called here complex granules c-granules, for short. Any c-granule consists of a physical part and a mental part linked in a special way. We begin from the rough set approach and next we move toward interacti...

This volume of Transactions on Rough Sets (TRS) in LNCS 8449 calls attention to research streams begun by Zdzislaw Pawlak during his lifetime. These research streams include topological structures emanating from rough sets, feature selection and attribute reduction, rough neural computing, rough fuzzy analysis and various forms of clustering.

We prove the recent result of Liu and Zhu [1] and discuss some consequences of that and related facts for the development of rough set theory.

This article introduces a new method of a decision tree construction. Such decision tree is constructed with the usage of additional cuts that are used for a verification of cuts in tree nodes during the classification of objects. The presented approach allows the use of additional knowledge contained in the attributes which could be eliminated usi...

We discuss how to support commanders at the fire ground. We present a risk management framework for modelling the fire phenomena and for communicating with firefighters. We claim that appropriate derivation, selection and representation of information is the crucial aspect of decision support, as it may improve the commander's perception.

Understanding of interactions is the critical issue of complex systems. Interactions in physical world are represented by information granules. We propose to model complex systems by interactive intelligent systems (IIS) created by societies of agents. Computations in IIS are based on complex granules (c-granules, for short). Adaptive judgement all...

In the development of rough set theory and applications, one can distinguish three main stages. While the first period was based on the assumption that objects are perceived by means of partial information represented by attributes, in the second period it was assumed that information about the approximated concepts is partial too. Approximation sp...

Volume XVI of the TRS includes extensions of papers from RSK 2011, held in Banff, Alberta, Canada in October 2011 and published in Lecture Notes in Artificial Intelligence 6954. In addition to 8 regular papers, this volume includes a Ph.D. thesis on approximation of sets based partial covering by Z.E.Csajbok.

The problem considered in this paper is how to describe and compare visual objects. The
solution to this problem stems from a consideration of nearness relations in two different forms of
Efremovi˘c proximity spaces. In this paper, the visual objects are picture elements in digital images.
In particular, this problem is solved in terms of the appli...

This volume introduces paradigms for machine learning that tend to emerge from nature studies.

It is a privilege for the author to be involved in composing a book chapter in the anthology devoted to the life and scientific occupation of Professor Zdzislaw Pawlak. The author made a personal acquaintance with the outstanding scientist Professor Pawlak and still remembers him as a warm and gentle human being. Professor Pawlak’s theory of rough...

The problem considered is how to construct classifiers for approximation of complex concepts on the basis of experimental data sets and domain knowledge that are mainly represented by concept ontology. The approach presented in this chapter to solving this problem is based on the rough set theory methods. Rough set theory introduced by Zdzisław Paw...

Rough set theory, proposed by Professor Zdzisław Pawlak in 1982 [163, 165, 166, 169], can be seen as a new mathematical approach to dealing with imperfect knowledge, in particular with vague concepts. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information (data, knowle...

In the development of rough set theory and applications, one can distinguish three main stages. At the beginning, the researchers concentrated on descriptive properties such as reducts of information systems preserving indiscernibility relations or description of concepts or classifications. Next, they moved to applications of rough sets in machine...

Test Theory (TT) was created by Yablonskii and Chegis in the middle of fifties of the last century as a tool for analysis of problems connected with control and diagnosis of faults in circuits. The first short paper [75] was published in 1955, and the principal paper [10] - in 1958. In 1966 Dmitriev, Zhuravlev and Krendelev [16] adapted test approa...

Logical analysis of data (LAD) is a data analysis methodology which combines ideas and concepts from optimization, combinatorics and Boolean functions. The idea of LAD was first described by Peter L. Hammer in a lecture given in 1986 at the International Conference on Multi-attribute Decision Making via OR-based Expert Systems [41] and was later ex...

This chapter is dedicated to the memory of Professor Zdzisław Pawlak, founder of the Polish school of Artificial Intelligence and one of the pioneers in Computer Engineering and Computer Science with worldwide influence.
To capture the spirit of Professor Pawlak’s creative genius, this chapter contains testimonies of many collaborators, colleagues...

Glossary Definition of the Subject Introduction Approximation Spaces Rough Sets Dimensionality Reduction Summary Future Directions Acknowledgments Bibliography

We discuss the role of interactions in the modeling of perception processes. Interactive information systems, introduced in this paper, play the important role in this modeling. Moreover, the proposed approach opens a new research direction in rough set theory. In this approach, partial information about the environment used for the approximation o...

The risk management is of the great importance for the success of behaviors of individuals, groups, societies, as well as the whole civilization. The aim of this paper is to present a step toward building risk management systems based on computational models for interactive systems. Computations in such systems are performed in an integrated distri...

Rough separability in topology is discussed by its connections with pseudometric spaces and rough sets. Pseudometric spaces are presented from the point of view of their connections with approximation spaces. A special way of determining equivalence relations by pseudometric spaces is considered and open sets in pseudometric spaces are studied. Inv...

We consider several issues related to reasoning about changes in systems interacting with the environment by sensors. In particular, we discuss challenging problems of reasoning about changes in hierarchical modeling and approximation of transition functions or trajectories. This paper can also be treated as a step toward developing rough calculus.

We discuss the motivation for investigations on rough calculus and some steps toward development of rough calculus based on the rough set approach. In particular, we introduce rough derivatives represented by dynamic granules.

Diverse attempts are being made to develop new computers, machines and systems that could act not only autonomously, but also in an increasingly intelligent, perceptual and cognitive manner. This paper discusses some of the educational challenges stemming from this emerging modelling and design paradigm, including teaching appropriate subjects to u...

The results reported in this paper create a step toward the rough set-based foundations of data mining and machine learning. The approach is based on calculi of approximation spaces. In this paper, we present the summarization and extension of our results obtained since 2003 when we started investigations on foundations of approximation of partiall...

We present the architecture of the system aimed at search and synthesis of information within document repositories originating
from different sources, with documents provided not necessarily in the same format and the same level of detail. The system
is expected to provide domain knowledge interfaces enabling the internally implemented algorithms...

Volume XV of the TRS offers a number of research streams that have grown out of the seminal work by Zdzislaw Pawlak during the first decade of the twenty-first century. These research streams include a rough set approach in machine learning (A. Janusz), multi-valued near set theory (M.E. Abd El-Monsef, H.M. Abu-Donia, and E.A. Marei), a rough-near...

This paper is devoted to a nearness relation in an Efremovič- proximity space. The basic approach is to consider the nearness of the upper and lower approximation of a set introduced by Z. Pawlak during the early 1980s as a foundation for rough sets. Two forms of nearness relations are considered, namely, a spatial EF- And a descriptive EF-relation...

The aim of this paper is to present a step toward building computational models for interactive systems. Such computations are performed in an integrated distributed environments on objects of different kinds of complexity, called here as information granules. The computations are progressing by interactions among information granules and physical...

We present a general scheme of interaction and we discuss the role of interactions in modeling of perception processes. We use information systems as a starting point for perception modeling, i.e., modeling of the process of understanding of sensory measurements. The novelty of the paper is an attempt to present the perception process by means of i...

In recent years, a rapid growth of interest in rough set theory, fuzzy set theory, and their hybridization and applications has been witnessed worldwide. In this chapter, the basic concepts of rough/fuzzy computing are presented. The role of rough/fuzzy computing in the development of Wisdom Technology (Wistech) is also emphasized.

We present an architecture aimed at semantic search and synthesis of information acquired from the document repositories. The proposed framework is expected to provide domain knowledge interfaces enabling the internally implemented algorithms to identify relationships between documents, researchers, institutions, as well as concepts extracted from...

In our previous papers, we investigated rough approximations of functions. These approximations are different than considered by Professor Zdzisław Pawlak [13,14]. In particular, our approach allows us to overcome the drawback of the exiting approach that the lower approximations of functions are usually empty. In this paper, we emphasize a possibl...

In this paper we discuss the importance of information systems in modeling interactive computations performed on (complex)
granules and propose a formal approach to interactive computations based on information systems. The basic concepts of information
systems and rough sets are interpreted in the framework of interactive computations. We also sho...

Some of the research papers studying rough sets and fuzzy sets in natural computing (NC) are presented. The paper 'Approximation of sets based on partial covering', by Zoltán Csajbók, proposes a possible generalization of approximations of sets relying on the partial covering of the universe of discourse. 'Fuzzy Rough Granular Neural Networks, Fuzz...

Solving complex real-life problems requires new approximate reasoning methods based on new computing paradigms. One such recently
emerging computing paradigm is Rough-Granular Computing (Pedrycz et al. 2008, Stepaniuk 2008) (RGC, in short). The RGC methods
have been successfully applied for solving complex problems in areas such as identification o...

We discuss the problem of measuring the quality of decision support (classification) system that involves granularity based on rough set concepts. We put forward the proposal for such quality measure in the case when the underlying granular system is based on rough sets and makes use of approximation spaces. We introduce the notion of approximation...

Volume XIV of the TRS includes extensions of papers presented at the 12th Int. Conf. on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, IIT Delhi, India, published in LNAI 5908. The contents of this special issue refer to both rough set-based theory and practice.

Volume XIII of the TRS is a special issue containing extensions of papers from RSCTC 2008.

Computations in Rough-Granular Computing (RGC) are performed on (information) granules. The rough set approach is used in RGC for inducing granules approximating other granules about which imperfect knowledge is given only. For modeling of complex systems, it is important to extend the RGC approach to Interactive Rough-Granular Computing (IRGC) bas...

## Projects

Project (1)