The Lattice Computing (LC) Paradigm

The notion of Cyber-Physical Systems (CPSs) has been introduced to account for technical devices with both sensing and reasoning abilities including a varying degree of autonomous behaviour. There is a need for supporting CPSs by mathematical models that involve both sensory data and cognitive data towards improving CPSs effectiveness during their interaction with humans. However, a widely acceptable mathematical modelling framework is currently missing. In the aforementioned context, the Lattice Computing (LC) paradigm is proposed for mathematical modelling in CPS applications based on lattice theory by unifying rigorously numerical data and non-numerical data; the latter data include (lattice ordered) logic values, sets, symbols, graphs and other. More specifically, the “cyber” components of a CPS involve nonnumerical data, whereas the “physical” components of a CPS involve numerical data. A promising advantage of LC is its capacity to compute with semantics represented by a lattice (partial) order relation.

[1]  Vassilis G. Kaburlasos,et al.  Induction of formal concepts by lattice computing techniques for tunable classification , 2014 .

[2]  Vassilios Petridis,et al.  Clustering and Classification in Structured Data Domains Using Fuzzy Lattice Neurocomputing (FLN) , 2001, IEEE Trans. Knowl. Data Eng..

[3]  Vassilis G. Kaburlasos,et al.  WINkNN: Windowed Intervals’ Number kNN Classifier for Efficient Time-Series Applications , 2020, Mathematics.

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

[5]  Pericles A. Mitkas,et al.  Fuzzy lattice reasoning (FLR) classifier and its application for ambient ozone estimation , 2007, Int. J. Approx. Reason..

[6]  Athanasios Kehagias,et al.  A Comparison of Word- and Sense-Based Text Categorization Using Several Classification Algorithms , 2003, Journal of Intelligent Information Systems.

[7]  Eleni Vrochidou,et al.  Social Robots for Pedagogical Rehabilitation , 2019, Advances in Systems Analysis, Software Engineering, and High Performance Computing.

[8]  L. Beran,et al.  [Formal concept analysis]. , 1996, Casopis lekaru ceskych.

[9]  Vassilis G. Kaburlasos,et al.  Special issue: Information engineering applications based on lattices , 2011, Inf. Sci..

[10]  Vassilis G. Kaburlasos,et al.  Unified Analysis and Design of ART/SOM Neural Networks and Fuzzy Inference Systems Based on Lattice Theory , 2007, IWANN.

[11]  Vassilis G. Kaburlasos,et al.  Fuzzy Lattice Reasoning for Brain Signal Classification , 2020, J. Univers. Comput. Sci..

[12]  Vassilis G. Kaburlasos,et al.  Neural/Fuzzy Computing Based on Lattice Theory , 2009, Encyclopedia of Artificial Intelligence.

[13]  George A. Papakostas,et al.  Intervals' Numbers (INs) interpolation/extrapolation , 2013, 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[14]  Dimitrios Serpanos,et al.  The Cyber-Physical Systems Revolution , 2018, Computer.

[15]  Vassilis G. Kaburlasos.  Adaptive resonance theory with supervised learning and large database applications , 1992 .

[16]  Athanasios Kehagias,et al.  Novel fuzzy inference system (FIS) analysis and design based on lattice theory. Part I: Working principles , 2006, Int. J. Gen. Syst..

[17]  J. Goguen.  L-fuzzy sets , 1967 .

[18]  George A. Papakostas,et al.  Learning Distributions of Image Features by Interactive Fuzzy Lattice Reasoning in Pattern Recognition Applications , 2015, IEEE Computational Intelligence Magazine.

[19]  Eleni Vrochidou,et al.  Time Series Classification in Cyber-Physical System Applications by Intervals’ Numbers Techniques , 2019, 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[20]  Yi Liu,et al.  Toward a Synergy of a Lattice Implication Algebra with Fuzzy Lattice Reasoning - A Lattice Computing Approach , 2016 .

[21]  Athanasios Kehagias,et al.  Novel Fuzzy Inference System (FIS) Analysis and Design Based on Lattice Theory , 2007, IEEE Transactions on Fuzzy Systems.

[22]  Peter N. Brett,et al.  Estimation of the stapes-bone thickness in the stapedotomy surgical procedure using a machine-learning technique , 1999, IEEE Transactions on Information Technology in Biomedicine.

[23]  Peter Sussner,et al.  Decomposition of Gray-Scale Morphological Templates Using the Rank Method , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  George A. Papakostas,et al.  Lattice Computing Extension of the FAM Neural Classifier for Human Facial Expression Recognition , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Vassilis G. Kaburlasos,et al.  A granular extension of the fuzzy-ARTMAP (FAM) neural classifier based on fuzzy lattice reasoning (FLR) , 2009, Neurocomputing.

[26]  Vassilis G. Kaburlasos,et al.  A Lattice-Computing ensemble for reasoning based on formal fusion of disparate data types, and an industrial dispensing application , 2014, Inf. Fusion.

[27]  Peter Sussner,et al.  Extreme learning machine for a new hybrid morphological/linear perceptron , 2019, Neural Networks.

[28]  X. Meng,et al.  Fuzzy C-Means on Metric Lattice , 2020, Automatic Control and Computer Sciences.

[29]  Gerhard X. Ritter,et al.  Lattice algebra approach to single-neuron computation , 2003, IEEE Trans. Neural Networks.

[30]  Vassilios Petridis,et al.  FINkNN: A Fuzzy Interval Number k-Nearest Neighbor Classifier for Prediction of Sugar Production from Populations of Samples , 2003, J. Mach. Learn. Res..

[31]  Athanasios Kehagias,et al.  Fuzzy Inference System (FIS) Extensions Based on the Lattice Theory , 2014, IEEE Transactions on Fuzzy Systems.

[32]  Vassilis G. Kaburlasos.  FINs: lattice theoretic tools for improving prediction of sugar production from populations of measurements , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  Vassilis G. Kaburlasos,et al.  Granular self-organizing map (grSOM) for structure identification , 2006, Neural Networks.

[34]  Gerhard X. Ritter,et al.  Towards a Unified Modeling and Knowledge-Representation Based on Lattice Theory: Computational Intelligence and Soft Computing Applications (Studies in Computational Intelligence) (Kaburlasos, V.G.; 2006) [book review] , 2007 .

[35]  Vassilios Petridis,et al.  Fuzzy lattice neural network (FLNN): a hybrid model for learning , 1998, IEEE Trans. Neural Networks.

[36]  Vassilios Petridis,et al.  Fuzzy Lattice Neurocomputing (FLN) models , 2000, Neural Networks.

[37]  Vassilis G. Kaburlasos,et al.  Piecewise-linear approximation of non-linear models based on probabilistically/possibilistically interpreted intervals' numbers (INs) , 2010, Inf. Sci..