Granular Encoding-Decoding for the Design of Granular Architectures
Witold Pedrycz
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Keywords: Encoding-decoding, Embedding, Granular Computing, Reconstruction error, Fuzzy cognitive maps.,
Abstract :
Fuzzy constructs (models) interact with numeric entities. This communication is realized through mechanisms of encoding and decoding. Encoding realizes a representation of input data through a collection of information granules and, as such, can be viewed as a nonlinear transformation of the original numeric entity to some internal (granular) format. The decoding is carried out in the opposite direction: the result at the level of information granules is brought back to the numeric entity. This study provides a unified view of the functionalities and design of these mechanisms by studying their components information granules. The optimization concerns a minimization of loss functions guided by criteria of minimal reconstruction error and a retention of semantics of the codebooks (landmarks) encountered in the encoding and decoding procedures. The role of triangular fuzzy sets is discussed along with associated learning mechanisms. Illustrative applications to hierarchical models and fuzzy cognitive maps are covered.
[1] Moral JMA, Castiello C, Magdalena L, Mencar C. Explainable Fuzzy Systems. Springer; 2021.
[2] Pedrycz W, Rocha AF. Fuzzy-set based models of neurons and knowledge-based networks. IEEE Transactions on Fuzzy Systems. 1993; 1(4): 254-266. DOI: https://doi.org/10.1109/91.251926
[3] Zadeh LA. Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems. 1997; 90(2): 111-127. DOI: https://doi.org/10.1016/S0165- 0114(97)00077-8
[4] Zadeh LA. From computing with numbers to computing with words. From manipulation of measurements to manipulation of perceptions. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1999; 46(1): 105-119. DOI: https://doi.org/10.1109/81.739259
[5] Pedrycz W. Granular computing for data analytics: A manifesto of human-centric computing. IEEE/CAA Journal of Automatica Sinica. 2018; 5(6): 1025-1034. DOI:
https://doi.org/10.1109/JAS.2018.7511213
[6] Qin J, Martnez L, Pedrycz W, Ma X, Liang Y. An overview of granular computing in decisionmaking: Extensions, applications, and challenges. Information Fusion. 2023; 98: 101833. DOI: https://doi.org/10.1016/j.inffus.2023.101833
[7] Zhu X, Pedrycz W, Li Z. Granular encoders and decoders: A study in processing information granules. IEEE Transactions on Fuzzy Systems. 2017; 25(5): DOI: https://doi.org/10.1109/TFUZZ.2016.2598366
[8] Nadaraya EA. On estimating regression. Theory of Probability & Its Applications. 1964; 9(1): 141-142. DOI: https://doi.org/10.1137/1109020
[9] Watson GS. Smooth regression analysis. Sankhy: The Indian Journal of Statistics, Series A(1961-2002). 1964; 26(4): 359-372.
[10] Pedrycz W, Wang X. Designing fuzzy sets with the use of the parametric principle of justifiable granularity. IEEE Transactions on Fuzzy Systems. 2016; 24(2): 489-496. DOI:
https://doi.org/10.1109/TFUZZ.2015.2453393
[11] Li W, Zhai S, Xu W, Pedrycz W, Qian Y, Ding W, Zhan T. Feature selection approach based on improved fuzzy c-means with principle of refined justifiable granularity. IEEE Transactions on Fuzzy Systems. 2023; 31(7): 2112-2126. DOI: https://doi.org/10.1109/TFUZZ.2022.3217377
[12] Shan D, Lu W, Yang J. Interval granular fuzzy models: Concepts and development. IEEE Access. 2019; 7: 24140-24153. DOI: https://doi.org/10.1109/ACCESS.2019.2899830
[13] Shi W, Karastoyanova D, Ma Y, Huang Y, Zhang G. Clustering-based granular representation of time series with application to collective anomaly detection. IEEE Transactions on Instrumentation and Measurement. 2023; 72: 2530612. DOI: https://doi.org/10.1109/TIM.2023.3325521
[14] Zhang R, Xu K, Zhu S, Xing M, Quan Y. Modeling of number of sources detection under nonideal conditions based on fuzzy information granulation. IEEE Transactions on Aerospace and Electronic Systems. 2023; 59(2): 1749-1757. DOI: https://doi.org/10.1109/TAES.2022.3204925
[15] Brcena JLC, Ducange P, Marcelloni F, Renda A. Increasing trust in AI through privacy preservation and model explainability: Federated learning of fuzzy Regression trees. Information Fusion. 2025; 113: 102598. DOI: https://doi.org/10.1016/j.inffus.2024.102598
[16] Hu F, Deng Z, Wang G, Xie Z, Choi KS, Wang S. Graph fuzzy system for the whole graph prediction: Concepts, models, and algorithms. IEEE Transactions on Fuzzy Systems. 2024; 32(3): 1383-1398. DOI: https://doi.org/10.1109/TFUZZ.2023.3325458
[17] Axelrod R. Structure of Decision: The Cognitive Maps of Political Elites. Princeton University Press; 2015.
[18] Kosko B. Fuzzy cognitive maps. International Journal of Man-Machine Studies. 1986; 24(1): 65-75. DOI: https://doi.org/10.1016/S0020-7373(86)80040-2
[19] Pedrycz W. The design of cognitive maps: A study in synergy of granular computing and evolutionary optimization. Expert systems with applications. 2010; 37(10): 7288-7294. DOI: https://doi.org/10.1016/j.eswa.2010.03.006
[20] Su SF, Chen MC, Hsueh YC. A novel fuzzy modeling structure-decomposed fuzzy system. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2017; 47(8): 2311-2317. DOI: https://doi.org/10.1109/TSMC.2017.2657557
[21] Kamthan S, Singh H. Hierarchical fuzzy logic for multi-input multi-output systems. IEEE Access. 2020; 8: 206966-206981. DOI: https://doi.org/10.1109/ACCESS.2020.3037901
[22] Zhang Y, Wang G, Huang X, Ding W. TSK fuzzy system fusion at sensitivity-ensemblelevel for imbalanced data classification. Information Fusion. 2023; 92: 350-362. DOI:
https://doi.org/10.1016/j.inffus.2022.12.014
[23] Zhang Y, Wang G, Zhou T, Huang X, Lam S, Sheng J, Choi KS, Cai J, Ding W. Takagi-Sugeno-Kang fuzzy system fusion: A survey at hierarchical, wide and stacked levels. Information Fusion. 2024; 101: 101977. DOI: https://doi.org/10.1016/j.inffus.2023.101977
