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Granular Computing

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01.03.2016 | Original Paper

Granular computing, computational intelligence, and the analysis of non-geometric input spaces

verfasst von: Lorenzo Livi, Alireza Sadeghian

Erschienen in: Granular Computing | Ausgabe 1/2016

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Abstract

Data granulation emerged as an important paradigm in modeling and computing with uncertainty, exploiting information granules as the main mathematical constructs involved in the context of granular computing. In this paper, we comment on the importance of data granulation in computational intelligence methods. Toward this aim, we discuss also the peculiar aspects related to the analysis of non-geometric patterns, which have recently attracted considerable attention by researchers. As a conclusion, we elaborate over the fundamental, conceptual problems underlying the process of data granulation, which drive the quest for a sound theory of granular computing.

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Ali MI, Davvaz B, Shabir M (2013) Some properties of generalized rough sets. Inf Sci 224:170–179. doi:10.1016/j.ins.2012.10.026 CrossRefMathSciNetMATH

Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96. doi:10.1016/S0165-0114(86)80034-3 CrossRefMathSciNetMATH

Bargiela A, Pedrycz W (2008) Toward a theory of granular computing for human-centered information processing. IEEE Trans Fuzzy Syst 16(2):320–330. doi:10.1109/TFUZZ.2007.905912 CrossRef

Bianchi FM, Livi L, Rizzi A (2015) Two density-based k-means initialization algorithms for non-metric data clustering. Pattern Anal Appl, pp 1–19. doi:10.1007/s10044-014-0440-4

Bicego M, Murino V, Figueiredo MAT (2004) Similarity-based classification of sequences using hidden Markov models. Pattern Recogn 37(12):2281–2291. doi:10.1016/j.patcog.2004.04.005 CrossRef

Biglarbegian M, Melek WW, Mendel JM (2010) On the stability of interval type-2 TSK fuzzy logic control systems. IEEE Trans Syst Man Cybern Part B Cybern 40(3):798–818. doi:10.1109/TSMCB.2009.2029986 CrossRef

Bonissone PP (1997) Soft computing: the convergence of emerging reasoning technologies. Soft Comput 1(1):6–18. doi:10.1007/s005000050002 CrossRefMathSciNet

Bronevich A, Klir GJ (2010) Measures of uncertainty for imprecise probabilities: an axiomatic approach. Int J Approx Reason 51(4):365–390. doi:10.1016/j.ijar.2009.11.003 CrossRefMathSciNetMATH

Brun L, Saggese A, Vento M (2014) Dynamic scene understanding for behavior analysis based on string kernels. IEEE Trans Circuits Syst Video Technol 24(10):1669–1681. doi:10.1109/TCSVT.2014.2302521 CrossRef

Bunke H, Riesen K (2011) Recent advances in graph-based pattern recognition with applications in document analysis. Pattern Recogn 44(5):1057–1067. doi:10.1016/j.patcog.2010.11.015 CrossRefMATH

Ceroni A, Costa F, Frasconi P (2007) Classification of small molecules by two-and three-dimensional decomposition kernels. Bioinformatics 23(16):2038–2045. doi:10.1093/bioinformatics/btm298 CrossRef

Chen Y, Wu K, Chen X, Tang C, Zhu Q (2014) An entropy-based uncertainty measurement approach in neighborhood systems. Inf Sci 279:239–250. doi:10.1016/j.ins.2014.03.117 CrossRefMathSciNet

Chen S-M, Chang C-H (2015) A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci 291:96–114. doi:10.1016/j.ins.2014.07.033 CrossRefMathSciNet

Chen S-M, Tanuwijaya K (2011) Fuzzy forecasting based on high-order fuzzy logical relationships and automatic clustering techniques. Expert Syst Appl 38(12):15425–15437. doi:10.1016/j.eswa.2011.06.019 CrossRef

Dai J, Tian H (2013) Entropy measures and granularity measures for set-valued information systems. Inf Sci 240:72–82. doi:10.1016/j.ins.2013.03.045 CrossRefMathSciNet

Ding S, Jia H, Chen J, Jin F (2014) Granular neural networks. Artif Intell Rev 41(3):373–384. doi:10.1007/s10462-012-9313-7 CrossRef

Engelbrecht AP (2007) Computational intelligence: an introduction. Wiley, HobokenCrossRef

Fischer A, Suen CY, Frinken V, Riesen K, Bunke H (2015) Approximation of graph edit distance based on Hausdorff matching. Pattern Recogn 48(2):331–343. doi:10.1016/j.patcog.2014.07.015 CrossRef

Foithong S, Pinngern O, Attachoo B (2012) Feature subset selection wrapper based on mutual information and rough sets. Expert Syst Appl 39(1):574–584. doi:10.1016/j.eswa.2011.07.048 CrossRef

Ganivada A, Dutta S, Pal SK (2011) Fuzzy rough granular neural networks, fuzzy granules, and classification. Theor Comput Sci 412(42):5834–5853. doi:10.1016/j.tcs.2011.05.038 CrossRefMathSciNetMATH

Gaxiola F, Melin P, Valdez F, Castillo O (2014) Interval type-2 fuzzy weight adjustment for backpropagation neural networks with application in time series prediction. Inf Sci 260:1–14. doi:10.1016/j.ins.2013.11.006 CrossRefMathSciNet

Guevara J, Hirata R, Canu S (2014) Positive definite kernel functions on fuzzy sets. In: Proceedings of the IEEE international conference on fuzzy systems, Beijing, China, pp 439–446. doi:10.1109/FUZZ-IEEE.2014.6891628

Ha M, Yang Y, Wang C (2013) A new support vector machine based on type-2 fuzzy samples. Soft Comput 17(11):2065–2074. doi:10.1007/s00500-013-1122-7 CrossRef

Han J, Lin TY (2010) Granular computing: models and applications. Int J Intell Syst 25(2):111–117. doi:10.1002/int.20390 MathSciNet

Haykin S (2007) Neural networks: a comprehensive foundation. Prentice Hall PTR, Upper Saddle River

Huang B, Zhuang YL, Li HX (2013) Information granulation and uncertainty measures in interval-valued intuitionistic fuzzy information systems. Eur J Oper Res 231(1):162–170. doi:10.1016/j.ejor.2013.05.006 CrossRefMathSciNet

Huarng K, Yu H-K (2005) A type 2 fuzzy time series model for stock index forecasting. Phys A Stat Mech Appl 353:445–462. doi:10.1016/j.physa.2004.11.070 CrossRef

Izakian H, Pedrycz W, Jamal I (2015) Fuzzy clustering of time series data using dynamic time warping distance. Eng Appl Artif Intell 39:235–244. doi:10.1016/j.engappai.2014.12.015 CrossRef

Kahraman C, Ertay T, Büyüközkan G (2006) A fuzzy optimization model for QFD planning process using analytic network approach. Eur J Oper Res 171(2):390–411. doi:10.1016/j.ejor.2004.09.016 CrossRefMATH

Klir GJ (1995) Principles of uncertainty: what are they? Why do we need them? Fuzzy Sets Syst 74(1):15–31. doi:10.1016/0165-0114(95)00032-G CrossRef

Klir GJ (2006) Uncertainty and information: foundations of generalized information theory. Wiley-Interscience, Hoboken

Lange M, Biehl M, Villmann T (2015) Non-Euclidean principal component analysis by hebbian learning. Neurocomputing 147:107–119. doi:10.1016/j.neucom.2013.11.049 CrossRef

Liang RH, Liao JH (2007) A fuzzy-optimization approach for generation scheduling with wind and solar energy systems. IEEE Trans Power Syst 22(4):1665–1674. doi:10.1109/TPWRS.2007.907527 CrossRef

Linda O, Manic M (2012) General type-2 fuzzy c-means algorithm for uncertain fuzzy clustering. IEEE Trans Fuzzy Syst 20(5):883–897. doi:10.1109/TFUZZ.2012.2187453 CrossRef

Liu P, Li H (2004) Fuzzy neural network theory and application. World Scientific, SingaporeMATH

Livi L, Rizzi A, Sadeghian A (2014) Optimized dissimilarity space embedding for labeled graphs. Inf Sci 266:47–64. doi:10.1016/j.ins.2014.01.005 CrossRefMathSciNet

Livi L, Tahayori H, Sadeghian A, Rizzi A (2014) Distinguishability of interval type-2 fuzzy sets data by analyzing upper and lower membership functions. Appl Soft Comput 17:79–89. doi:10.1016/j.asoc.2013.12.020 CrossRef

Livi L, Rizzi A, Sadeghian A (2015) Granular modeling and computing approaches for intelligent analysis of non-geometric data. Appl Soft Comput 27:567–574. doi:10.1016/j.asoc.2014.08.072 CrossRef

Livi L, Giuliani A, Sadeghian A (2015) Characterization of graphs for protein structure modeling and recognition of solubility. Curr Bioinform. arXiv:1407.8033

Livi L, Rizzi A (2015) Modeling the uncertainty of a set of graphs using higher-order fuzzy sets. In: Sadeghian A, Tahayori H (eds) Frontiers of higher order fuzzy sets, pp 131–146. Springer, New York. doi:10.1007/978-1-4614-3442-9_7

Livi L, Rizzi A (2013) The graph matching problem. Pattern Anal Appl 16(3):253–283. doi:10.1007/s10044-012-0284-8 CrossRefMathSciNetMATH

Livi L, Sadeghian A (2015) Data granulation by the principles of uncertainty. Pattern Recogn Lett. doi:10.1016/j.patrec.2015.04.008

Livi L, Sadeghian A, Pedrycz W (2015) Entropic one-class classifiers. IEEE Trans Neural Netw Learn Syst. doi:10.1109/TNNLS.2015.2418332

Livi L, Tahayori H, Sadeghian A, Rizzi A (2013) Aggregating \(\alpha \)-planes for type-2 fuzzy set matching. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, pp 860–865. doi:10.1109/IFSA-NAFIPS.2013.6608513

Melin P, Castillo O (2013) A review on the applications of type-2 fuzzy logic in classification and pattern recognition. Expert Syst Appl 40(13):5413–5423. doi:10.1016/j.eswa.2013.03.020 CrossRef

Mendel JM (2014) General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans Fuzzy Syst 22(5):1162–1182. doi:10.1109/TFUZZ.2013.2286414 CrossRefMathSciNet

Montes I, Pal NR, Janis V, Montes S (2015) Divergence measures for intuitionistic fuzzy sets. IEEE Trans Fuzzy Syst 23(2):444–456. doi:10.1109/TFUZZ.2014.2315654 CrossRef

Morales-González A, Acosta-Mendoza N, Gago-Alonso A, García-Reyes EB, Medina-Pagola JE (2014) A new proposal for graph-based image classification using frequent approximate subgraphs. Pattern Recogn 47(1):169–177. doi:10.1016/j.patcog.2013.07.004 CrossRef

Nauck D, Klawonn F, Kruse R (1997) Foundations of neuro-fuzzy systems. Wiley, New York

Oh S-K, Kim W-D, Pedrycz W, Seo K (2014) Fuzzy radial basis function neural networks with information granulation and its parallel genetic optimization. Fuzzy Sets Syst 237:96–117. doi:10.1016/j.fss.2013.08.011 CrossRefMathSciNet

Pagola M, Lopez-Molina C, Fernandez J, Barrenechea E, Bustince H (2013) Interval type-2 fuzzy sets constructed from several membership functions: application to the fuzzy thresholding algorithm. IEEE Trans Fuzzy Syst 21(2):230–244. doi:10.1109/TFUZZ.2012.2209885 CrossRef

Pawlak Z (1982) Rough Sets. Int J Comput Inf Sci 11:341–356CrossRefMathSciNetMATH

Pedrycz W (1998) Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern Part B Cybern 28(1):103–109. doi:10.1109/3477.658584 CrossRef

Pedrycz W, Skowron A, Kreinovich V (2008) Handbook of granular computing. Wiley, New YorkCrossRef

Pedrycz W (2011) Information granules and their use in schemes of knowledge management. Sci Iran 18(3):602–610. doi:10.1016/j.scient.2011.04.013 CrossRefMathSciNet

Pedrycz W (2013) Granular computing: analysis and design of intelligent systems. Taylor & Francis Group, AbingdonCrossRef

Pedrycz W (2014) Allocation of information granularity in optimization and decision-making models: towards building the foundations of Granular Computing. Eur J Oper Res 232(1):137–145. doi:10.1016/j.ejor.2012.03.038 CrossRefMathSciNet

Pedrycz W, Succi G, Sillitti A, Iljazi J (2015) Data description: a general framework of information granules. Knowl Based Syst 80:98–108. doi:10.1016/j.knosys.2014.12.030 CrossRef

Pedrycz W, Bargiela A (2012) An optimization of allocation of information granularity in the interpretation of data structures: toward granular fuzzy clustering. IEEE Trans Syst Man Cybern Part B Cybern 42(3):582–590. doi:10.1109/TSMCB.2011.2170067 CrossRef

Pedrycz W, Chen S-M (2014) Information granularity, big data, and computational intelligence, vol 8. Springer International Publishing, Cham

Pedrycz W, Homenda W (2013) Building the fundamentals of granular computing: a principle of justifiable granularity. Appl Soft Comput 13(10):4209–4218. doi:10.1016/j.asoc.2013.06.017 CrossRef

Pȩkalska E, Duin RPW (2005) The dissimilarity representation for pattern recognition: foundations and applications. World Scientific, Singapore

Qian Y, Liang J, Dang C (2010) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern Part A Syst Hum 40(2):420–431. doi:10.1109/TSMCA.2009.2035436 CrossRef

Qian Y, Zhang H, Li F, Hu Q, Liang J (2014) Set-based granular computing: a lattice model. Int J Approx Reason 55(3):834–852. doi:10.1016/j.ijar.2013.11.001 CrossRefMathSciNet

Qian Y, Li Y, Liang J, Lin G, Dang C (2015) Fuzzy granular structure distance. IEEE Trans Fuzzy Syst PP(99):1. doi:10.1109/TFUZZ.2015.2417893

Rizzi A, Livi L, Tahayori H, Sadeghian A (2013) Matching general type-2 fuzzy sets by comparing the vertical slices. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, pp 866–871. Edmonton. doi:10.1109/IFSA-NAFIPS.2013.6608514

Rossi L, Torsello A, Hancock ER (2015) Unfolding kernel embeddings of graphs: enhancing class separation through manifold learning. Pattern Recogn 48(11):3357–3370. doi:10.1016/j.patcog.2015.03.018 CrossRef

Rupp M, Schneider G (2010) Graph kernels for molecular similarity. Mol Inf 29(4):266–273. doi:10.1002/minf.200900080 CrossRef

Sadeghian A, Lavers JD (2011) Dynamic reconstruction of nonlinear v-i characteristic in electric arc furnaces using adaptive neuro-fuzzy rule-based networks. Appl Soft Comput 11(1):1448–1456. doi:10.1016/j.asoc.2010.04.016 CrossRef

Sainath TN, Kingsbury B, Saon G, Soltau H, Mohamed A-R, Dahl G, Ramabhadran B (2014) Deep convolutional neural networks for large-scale speech tasks. Neural Netw 64:39–48. doi:10.1016/j.neunet.2014.08.005

Salehi S, Selamat A, Fujita H (2015) Systematic mapping study on granular computing. Knowl Based Syst 80:78–97. doi:10.1016/j.knosys.2015.02.018 CrossRef

Schleif F-M (2014) Generic probabilistic prototype based classification of vectorial and proximity data. Neurocomputing 154:208–216. doi:10.1016/j.neucom.2014.12.002 CrossRef

Schölkopf B, Smola AJ (2002) Learning with kernels: support vector machines, regularization, optimization, and beyond. MIT Press, Cambridge

Serratosa F, Cortés X, Solé-Ribalta A (2013) Component retrieval based on a database of graphs for hand-written electronic-scheme digitalisation. Expert Syst Appl 40(7):2493–2502CrossRef

Song M, Pedrycz W (2013) Granular neural networks: concepts and development schemes. IEEE Trans Neural Netw Learn Syst 24(4):542–553. doi:10.1109/TNNLS.2013.2237787 CrossRef

Soto J, Melin P, Castillo O (2014) Time series prediction using ensembles of ANFIS models with genetic optimization of interval type-2 and type-1 fuzzy integrators. Int J Hybrid Intell Syst 11(3):211–226. doi:10.3233/HIS-140196

Swiniarski RW, Skowron A (2003) Rough set methods in feature selection and recognition. Pattern Recogn Lett 24(6):833–849. doi:10.1016/S0167-8655(02)00196-4 CrossRefMATH

Tahayori H, Livi L, Sadeghian A, Rizzi A (2015) Interval type-2 fuzzy set reconstruction based on fuzzy information-theoretic kernels. IEEE Trans Fuzzy Syst 23(4):1014–1029. doi:10.1109/TFUZZ.2014.2336673 CrossRef

Tang X-Q, Zhu P (2013) Hierarchical clustering problems and analysis of fuzzy proximity relation on granular space. IEEE Trans Fuzzy Syst 21(5):814–824. doi:10.1109/TFUZZ.2012.2230176 CrossRef

Thangavel K, Pethalakshmi A (2009) Dimensionality reduction based on rough set theory: a review. Appl Soft Comput 9(1):1–12. doi:10.1016/j.asoc.2008.05.006 CrossRef

Theodoridis S, Koutroumbas K (2008) Pattern Recognition, 4th edn. Elsevier/Academic Press, Waltham

Wagner C, Miller S, Garibaldi JM, Anderson DT, Havens TC (2015) From interval-valued data to general type-2 fuzzy sets. IEEE Trans Fuzzy Syst 23(2):248–269. doi:10.1109/TFUZZ.2014.2310734 CrossRef

Wagner C, Hagras H (2010) Toward general type-2 fuzzy logic systems based on zslices. IEEE Trans Fuzzy Syst 18(4):637–660. doi:10.1109/TFUZZ.2010.2045386 CrossRef

Wang S, Pedrycz W (2014a) Robust granular optimization: a structured approach for optimization under integrated uncertainty. IEEE Trans Fuzzy Syst. doi:10.1109/TFUZZ.2014.2360941

Wang S, Watada J, Pedrycz W (2014b) Granular robust Mean-CVaR feedstock flow planning for waste-to-energy systems under integrated uncertainty. IEEE Trans Cybern 44(10):1846–1857. doi:10.1109/TCYB.2013.2296500

White D, Wilson RC (2010) Generative models for chemical structures. J Chem Inf Model 50(7):1257–1274. doi:10.1021/ci9004089 CrossRef

Wu G-D, Zhu Z-W (2014) An enhanced discriminability recurrent fuzzy neural network for temporal classification problems. Fuzzy Sets Syst 237:47–62. doi:10.1016/j.fss.2013.05.007 CrossRefMathSciNet

Yao JT, Vasilakos AV, Pedrycz W (2013) Granular computing: perspectives and challenges. IEEE Trans Cybern 43(6):1977–1989. doi:10.1109/TSMCC.2012.2236648 CrossRef

Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353. doi:10.1016/S0019-9958(65)90241-X CrossRefMathSciNetMATH

Zhai D, Mendel JM (2011) Uncertainty measures for general type-2 fuzzy sets. Inf Sci 181(3):503–518. doi:10.1016/j.ins.2010.09.020 CrossRefMathSciNetMATH

Zhang YQ, Jin B, Tang Y (2008) Granular neural networks with evolutionary interval learning. IEEE Trans Fuzzy Syst 16(2):309–319CrossRef

Zhao T, Xiao J, Li Y, Deng X (2014) A new approach to similarity and inclusion measures between general type-2 fuzzy sets. Soft Comput 18(4):809–823. doi:10.1007/s00500-013-1101-z CrossRef

Zhou S-M, Garibaldi JM, John RI, Chiclana F (2009) On constructing parsimonious type-2 fuzzy logic systems via influential rule selection. IEEE Trans Fuzzy Syst 17(3):654–667. doi:10.1109/TFUZZ.2008.928597 CrossRef

Zhu P, Wen Q (2012) Information-theoretic measures associated with rough set approximations. Inf Sci 212:33–43. doi:10.1016/j.ins.2012.05.014 CrossRefMathSciNetMATH

Titel: Granular computing, computational intelligence, and the analysis of non-geometric input spaces
verfasst von: Lorenzo Livi
Alireza Sadeghian
Publikationsdatum: 01.03.2016
Verlag: Springer International Publishing
Erschienen in: Granular Computing / Ausgabe 1/2016
Print ISSN: 2364-4966
Elektronische ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-015-0003-0

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