The Principle of Justifiable Granularity and an Optimization of Information Granularity Allocation as Fundamentals of Granular Computing

  • Pedrycz, Witold (Department of Electrical & Computer Engineering University of Alberta, Edmonton Canada and Systems Research Institute of the Polish Academy of Sciences Warsaw)
  • Received : 2011.05.20
  • Accepted : 2011.08.08
  • Published : 2011.09.30


Granular Computing has emerged as a unified and coherent framework of designing, processing, and interpretation of information granules. Information granules are formalized within various frameworks such as sets (interval mathematics), fuzzy sets, rough sets, shadowed sets, probabilities (probability density functions), to name several the most visible approaches. In spite of the apparent diversity of the existing formalisms, there are some underlying commonalities articulated in terms of the fundamentals, algorithmic developments and ensuing application domains. In this study, we introduce two pivotal concepts: a principle of justifiable granularity and a method of an optimal information allocation where information granularity is regarded as an important design asset. We show that these two concepts are relevant to various formal setups of information granularity and offer constructs supporting the design of information granules and their processing. A suite of applied studies is focused on knowledge management in which case we identify several key categories of schemes present there.


Information Granularity;Principle of Justifiable Granularity;Knowledge Management;Optimal Granularity Allocation


  1. L.A. Zadeh, "Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic", Fuzzy Sets and Systems, 90, 1997, 111-117.
  2. B. Apolloni, S. Bassis, D. Malchiodi, W. Pedrycz, "Interpolating support information granules", Neurocomputing, 71, 13-15, 2008, 2433-2445.
  3. A.Bargiela, W. Pedrycz, Granular Computing: An Introduction, Kluwer Academic Publishers, Dordrecht, 2003.
  4. A. Bargiela, W. Pedrycz (eds.), Human-Centric Information Processing Through Granular Modelling, Springer -Verlag, Heidelberg, 2009.
  5. A. Bargiela, W. Pedrycz, "Granular mappings", IEEE Transactions on Systems, Man, and Cybernetics-part A, 35, 2, 2005, 292-297.
  6. A. Bargiela, W. Pedrycz, "A model of granular data: a design problem with the Tchebyschev FCM", Soft Computing, 9, 2005,155-163.
  7. A. Bargiela, W. Pedrycz, "Toward a theory of Granular Computing for human-centered information processing", IEEE Transactions on Fuzzy Systems, 16, 2, 2008, 320-330.
  8. J.C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, N. York, 1981.
  9. S. Calegari, D. Ciucci, "Granular computing applied to ontologies", Int. Journal of Approximate Reasoning, 51, 4, 2010, 391-409.
  10. K. Hirota, "Concepts of probabilistic sets", Fuzzy Sets and Systems, 5, 1, 1981, 31-46.
  11. K. Hirota, W. Pedrycz, "Characterization of fuzzy clustering algorithms in terms of entropy of probabilistic sets", Pattern Recognition Letters, 2, 4, 1984, 213-216.
  12. Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning about Data, System Theory, Kluwer Academic Publishers, Dordrecht, 1991.
  13. Z. Pawlak, "Rough sets and fuzzy sets", Fuzzy Sets and Systems, 17, 1, 1985, 99-102.
  14. Z. Pawlak, "A. Skowron, Rudiments of rough sets", Information Sciences, 177, 1, 1 2007, 3-27.
  15. Z. Pawlak, "A. Skowron, Rough sets: Some extensions", Information Sciences, 177, 1, 2007, 28-40.
  16. W. Pedrycz, F. Gomide, Fuzzy Systems Engineering: Toward Human-Centric Computing, John Wiley, Hoboken, NJ, 2007.
  17. W. Pedrycz, "Shadowed sets: representing and processing fuzzy sets", IEEE Trans. on Systems, Man, and Cybernetics, Part B, 28, 1998, 103-109.
  18. W. Pedrycz, M. Song, "Analytic Hierarchy Process (AHP) in group decision making and its optimization with an allocation of information granularity", IEEE Trans.on Fuzzy Systems, 2011, to appear.
  19. W. Pedrycz, Shadowed sets: bridging fuzzy and rough sets, In: Rough Fuzzy Hybridization. A New Trend in Decision-Making, S.K. Pal, A. Skowron, (eds.), Springer Verlag, Singapore, 1999, 179-199.
  20. W. Pedrycz, Interpretation of clusters in the framework of shadowed sets, Pattern Recognition Letters, 26, 15, 2005, 2439-2449.
  21. W. Pedrycz, K. Hirota, "A consensus-driven clustering", Pattern Recognition Letters, 29, 2008, 1333-1343.
  22. W. Pedrycz, P. Rai, "Collaborative clustering with the use of Fuzzy C-Means and its quantification", Fuzzy Sets and Systems, 159, 18, 2008, 2399-2427.
  23. W. Pedrycz, "The design of cognitive maps: A study in synergy of granular computing and evolutionary optimization", Expert Systems with Applications, 37, 10, 2010, 7288-7294.
  24. Y. Qian, J. Liang, Y. Yao, C. Dang, "MGRS: A multi-granulation rough set", Information Sciences, 180, 6, 2010, 949-970.
  25. T. L. Saaty, "How to handle dependence with the analytic hierarchy process", Mathematical Modelling, 9, 1987, 369-376.
  26. D. Slezak, "Degrees of conditional (in)dependence: A framework for approximate Bayesian networks and examples related to the rough set-based feature selection", Information Sciences, 179, 3, 2009, 197-209.
  27. R. W. Swiniarski, A. Skowron, "Rough set methods in feature selection and recognition", Pattern Recognition Letters, 24, 6, 2003, 833-849.
  28. W-Z. Wu, Y. Leung, Theory and applications of granular labeled partitions in multi-scale decision tables, Information Sciences, In Press, Available online 10 May, 2011.
  29. L.A. Zadeh, "From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions", IEEE Trans. on Circuits and Systems, 45, 1999, 105-119.
  30. X. Zhang, Y. Yao, H. Yu, "Rough implication operator based on strong topological rough algebras", Information Sciences, 180, 19, 2010, 3764-3780.

Cited by

  1. Design of granular interval-valued information granules with the use of the principle of justifiable granularity and their applications to system modeling of higher type vol.20, pp.6, 2016,
  2. A method for constructing the Composite Indicator of business cycles based on information granulation and Dynamic Time Warping vol.101, 2016,
  3. Fuzzy numbers from raw discrete data using linear regression vol.233, 2013,
  4. A triarchic theory of granular computing vol.1, pp.2, 2016,
  5. From Principal Curves to Granular Principal Curves vol.44, pp.6, 2014,
  6. A multi-objective evolutionary method for learning granularities based on fuzzy discretization to improve the accuracy-complexity trade-off of fuzzy rule-based classification systems: D-MOFARC algorithm vol.24, 2014,
  7. Development of granular models through the design of a granular output spaces vol.134, 2017,
  8. A neurofuzzy algorithm for learning from complex granules vol.1, pp.4, 2016,
  9. Hybrid Learning for General Type-2 TSK Fuzzy Logic Systems vol.10, pp.3, 2017,
  10. Granular modeling and computing approaches for intelligent analysis of non-geometric data vol.27, 2015,
  11. Calibrating level set approach by granular computing in computed tomography abdominal organs segmentation vol.49, 2016,
  12. Granular computing: from granularity optimization to multi-granularity joint problem solving vol.2, pp.3, 2017,
  13. Building consensus in group decision making with an allocation of information granularity vol.255, 2014,
  14. Multi-attribute Group Decision-Making Method Based on Cloud Distance Operators With Linguistic Information vol.19, pp.4, 2017,
  15. Hierarchical description of uncertain information vol.268, 2014,
  16. The uncertainty of probabilistic rough sets in multi-granulation spaces vol.77, 2016,
  17. Group Decision Making in Linguistic Contexts: An Information Granulation Approach vol.91, 2016,
  18. A method based on PSO and granular computing of linguistic information to solve group decision making problems defined in heterogeneous contexts vol.230, pp.3, 2013,
  19. Classification of Type-2 Fuzzy Sets Represented as Sequences of Vertical Slices vol.24, pp.5, 2016,
  20. Information granules in image histogram analysis 2017,
  21. Data Representation Based on Interval-Sets for Anomaly Detection in Time Series vol.6, pp.2169-3536, 2018,