Abstract
Information granules are conceptual entities using which experimental data are conveniently described and in the sequel their processing is realized at the higher level of abstraction. The central problem is concerned with the design of information granules. We advocate that a principle of justifiable granularity can be used as a sound vehicle to construct information granules so that they are (i) experimentally justifiable and (ii) semantically sound. We elaborate on the algorithmic details when forming information granules of type-1 and type-2. It is also stressed that the construction of information granule realized in this way follows a general paradigm of elevation of type of information granule, say numeric data (regarded as information granules of type-0) give rise to information granule of type-1 while experimental evidence coming as information granules of type-1 leads to the emergence of a single information granule of type-2. We discuss their direct applications to the area of system modeling, in particular showing how type-n information granules are used in the augmentation of numeric models.
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References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Hwang, C., Rhee, F.C.H.: Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-means. IEEE Trans. Fuzzy Syst. 15(12), 107–120 (2007)
Jin, Y.: Fuzzy modeling of high-dimensional systems: complexity reduction and interpretability improvement. IEEE Trans. Fuzzy Syst. 8, 212–221 (2000)
Johansen, T.A., Babuska, R.: Multiobjective identification of Takagi-Sugeno fuzzy models. IEEE Trans. Fuzzy Syst. 11, 847–860 (2003)
Lai, J.Z.C., Juan, E.Y.T., Lai, F.J.C.: Rough clustering using generalized fuzzy clustering algorithm. Pattern Recogn. 46(9), 2538–2547 (2013)
Li, F., Ye, M., Chen, X.: An extension to rough c-means clustering based on decision-theoretic rough sets model. Int. J. Approx. Reason. 55(1), 116–129 (2014)
Pawlak, Z.: Rough sets. Int. J. Inf. Comput. Sci. 11, 341–356 (1982)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordecht (1991)
Pedrycz, W.: Granular computing - the emerging paradigm. J. Uncertain Syst. 1(1), 38–61 (2007)
Pedrycz, W.: Granular Computing: Analysis and Design of Intelligent Systems. CRC Press/Francis Taylor, Boca Raton (2013)
Pedrycz, W., Bargiela, A.: An optimization of allocation of information granularity in the interpretation of data structures: toward granular fuzzy clustering. IEEE Trans. Syst. Man Cybern. Part B 42, 582–590 (2012)
Pedrycz, W., Homenda, W.: Building the fundamentals of granular computing: a principle of justifiable granularity. Appl. Soft Comput. 13, 4209–4218 (2013)
Pedrycz, W.: Knowledge-Based Fuzzy Clustering. Wiley, New York (2005)
Pedrycz, W., de Oliveira, J.V.: A development of fuzzy encoding and decoding through fuzzy clustering. IEEE Trans. Instrum. Meas. 57(4), 829–837 (2008)
Pedrycz, W.: Shadowed sets: representing and processing fuzzy sets. IEEE Trans. Syst. Man Cybern. Part B 28, 103–109 (1998)
Yager, R.R.: Ordinal measures of specificity. Int. J. Gen. Syst. 17, 57–72 (1990)
Xu, R., Wunsch II, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645–678 (2005)
Yao, J.T., Vasilakos, A.V., Pedrycz, W.: Granular computing: perspectives and challenges. IEEE Trans. Cybern. 43(6), 1977–1989 (2013)
Wang, W.N., Zhang, Y.J.: On fuzzy cluster validity indices. Fuzzy Sets Syst. 158(19), 2095–2117 (2007)
Zadeh, L.A.: Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90, 111–117 (1997)
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Support from the Canada Research Chair (CRC) and Natural Sciences and Engineering Research Council (NSERC) is gratefully acknowledged.
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Pedrycz, W. (2017). Algorithmic Developments of Information Granules of Higher Type and Higher Order and Their Applications. In: Petrosino, A., Loia, V., Pedrycz, W. (eds) Fuzzy Logic and Soft Computing Applications. WILF 2016. Lecture Notes in Computer Science(), vol 10147. Springer, Cham. https://doi.org/10.1007/978-3-319-52962-2_2
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DOI: https://doi.org/10.1007/978-3-319-52962-2_2
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