Building Granular Systems - from Concepts to Applications

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, transformation and evaluation of granules. It also requires aligning with some of the fundamental computational issues concerning, e.g., interaction and adaptation. The paper outlines the current status of GrC and provides the general overview of the process of building granular solutions to challenges posed by various real-life problems involving granularity. It discusses the steps that lead from raw data and imprecise/vague specification towards a complete, useful application of granular paradigm.

[1]  Janusz Kacprzyk,et al.  Computing with Words in Information/Intelligent Systems 1 , 1999 .

[2]  Lotfi A. Zadeh,et al.  Computing with Words - Principal Concepts and Ideas , 2012, Studies in Fuzziness and Soft Computing.

[3]  Chen Wei-min.  Rough Set Theory and Granular Computing , 2006 .

[4]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[5]  Witold Pedrycz,et al.  Information granularity, big data, and computational intelligence , 2015 .

[6]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[7]  Andrzej Skowron,et al.  Rough Mereological Calculi of Granules: A Rough Set Approach To Computation , 2001, Comput. Intell..

[8]  J. Stepaniuk.  Rough – Granular Computing in Knowledge Discovery and Data Mining , 2008 .

[9]  Andrzej Skowron,et al.  Rough-Neural Computing: Techniques for Computing with Words , 2004, Cognitive Technologies.

[10]  Witold Pedrycz,et al.  The Principle of Justifiable Granularity and an Optimization of Information Granularity Allocation as Fundamentals of Granular Computing , 2011, J. Inf. Process. Syst..

[11]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[12]  Witold Pedrycz,et al.  Knowledge-based clustering - from data to information granules , 2007 .

[13]  Tsau Young Lin,et al.  Data Mining and Machine Oriented Modeling: A Granular Computing Approach , 2000, Applied Intelligence.

[14]  Dominik Slezak,et al.  Stable rule extraction and decision making in rough non-deterministic information analysis , 2011, Int. J. Hybrid Intell. Syst..

[15]  Andrzej Bargiela,et al.  Human-Centric Information Processing Through Granular Modelling , 2009, Human-Centric Information Processing Through Granular Modelling.

[16]  Gordon P. Baker,et al.  Wittgenstein : understanding and meaning , 1980 .

[17]  Andrzej Skowron,et al.  Function Approximation and Quality Measures in Rough-Granular Systems , 2011, Fundam. Informaticae.

[18]  Hiroshi Sakai,et al.  Apriori-Based Rule Generation in Incomplete Information Databases and Non-Deterministic Information Systems , 2014, Fundam. Informaticae.

[19]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[20]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[21]  R. Keefe.  Theories of vagueness , 2000 .

[22]  Sergei O. Kuznetsov,et al.  Relations between Proto-fuzzy concepts, Crisply Generated Fuzzy Concepts, and Interval Pattern Structures , 2010, CLA.

[23]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[24]  Witold Pedrycz,et al.  Granular Computing - The Emerging Paradigm , 2007 .

[25]  Ling Zhang,et al.  Quotient Space Based Problem Solving: A Theoretical Foundation of Granular Computing , 2014 .

[26]  Witold Pedrycz,et al.  Granular computing: an introduction , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[27]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .

[28]  Andrzej Skowron,et al.  Rudiments of rough sets , 2007, Inf. Sci..

[29]  Piotr Synak,et al.  Two Database Related Interpretations of Rough Approximations: Data Organization and Query Execution , 2013, Fundam. Informaticae.

[30]  Andrzej Skowron,et al.  From Sensory Data to Decision Making: A Perspective on Supporting a Fire Commander , 2013, 2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT).

[31]  Witold Pedrycz,et al.  Granular Computing: At the Junction of Rough Sets and Fuzzy Sets , 2008 .

[32]  JingTao Yao,et al.  Novel Developments in Granular Computing: Applications for Advanced Human Reasoning and Soft Computation , 2010 .

[33]  Yiyu Yao,et al.  Granular Computing , 2008 .

[34]  Witold Pedrycz,et al.  Knowledge-Based Clustering , 2005 .

[35]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[36]  W. Pedrycz,et al.  Granular computing and intelligent systems : design with information granules of higher order and higher type , 2011 .

[37]  Lotfi A. Zadeh,et al.  Generalized theory of uncertainty (GTU) - principal concepts and ideas , 2006, Comput. Stat. Data Anal..

[38]  Andrzej Skowron,et al.  Calculi of Approximation Spaces , 2006, Fundam. Informaticae.

[39]  Witold Pedrycz,et al.  Granular Computing: Analysis and Design of Intelligent Systems , 2013 .

[40]  Andrzej Skowron,et al.  Rough-Fuzzy Hybridization: A New Trend in Decision Making , 1999 .

[41]  Witold Pedrycz,et al.  From fuzzy sets to shadowed sets: Interpretation and computing , 2009, Int. J. Intell. Syst..

[42]  Witold Pedrycz,et al.  The Puzzle of Granular Computing , 2008, Studies in Computational Intelligence.

[43]  Lech Polkowski,et al.  Granular Computing in Decision Approximation - An Application of Rough Mereology , 2015, Intelligent Systems Reference Library.