Neural/Fuzzy Computing Based on Lattice Theory

Computational Intelligence (CI) consists of an evolving collection of methodologies often inspired from nature (Bonissone, Chen, Goebel & Khedkar, 1999, Fogel, 1999, Pedrycz, 1998). Two popular methodologies of CI include neural networks and fuzzy systems. Lately, a unification was proposed in CI, at a “data level”, based on lattice theory (Kaburlasos, 2006). More specifically, it was shown that several types of data including vectors of (fuzzy) numbers, (fuzzy) sets, 1D/2D (real) functions, graphs/trees, (strings of) symbols, etc. are partially(lattice)-ordered. In conclusion, a unified cross-fertilization was proposed for knowledge representation and modeling based on lattice theory with emphasis on clustering, classification, and regression applications (Kaburlasos, 2006). Of particular interest in practice is the totally-ordered lattice (R,≤) of real numbers, which has emerged historically from the conventional measurement process of successive comparisons. It is known that (R,≤) gives rise to a hierarchy of lattices including the lattice (F,≤) of fuzzy interval numbers, or FINs for short (Papadakis & Kaburlasos, 2007). This article shows extensions of two popular neural networks, i.e. fuzzy-ARTMAP (Carpenter, Grossberg, Markuzon, Reynolds & Rosen 1992) and self-organizing map (Kohonen, 1995), as well as an extension of conventional fuzzy inference systems (Mamdani & Assilian, 1975), based on FINs. Advantages of the aforementioned extensions include both a capacity to rigorously deal with nonnumeric input data and a capacity to introduce tunable nonlinearities. Rule induction is yet another advantage.

[1]  Ana Carolina Salgado,et al.  Retrieving Specific Domain Information from the Web Through Ontologies , 2006, Int. J. Intell. Inf. Technol..

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

[3]  Abdelmajid Ben Hamadou,et al.  Extending a Conceptual Modeling Language For Adaptive Web Applications , 2008, Int. J. Intell. Inf. Technol..

[4]  Piero P. Bonissone,et al.  Hybrid soft computing systems: industrial and commercial applications , 1999, Proc. IEEE.

[5]  Clarence N. W. Tan,et al.  Artificial Neural Networks in Financial Trading , 2005, Encyclopedia of Information Science and Technology.

[6]  Vassilis G. Kaburlasos,et al.  INDUCTION OF CLASSIFICATION RULES FROM HISTOGRAMS , 2007 .

[7]  Claus Rautenstrauch,et al.  A Case Study on Forecasting of the Return of Scrapped Products through Simulation and Fuzzy Reasoning , 2002 .

[8]  Kaoru Hirota,et al.  Parallel and Multistage Fuzzy Inference Based on Families of alpha-level sets , 1998, Inf. Sci..

[9]  Vassilis G. Kaburlasos,et al.  Granular Auto-regressive Moving Average (grARMA) Model for Predicting a Distribution from Other Distributions. Real-world Applications , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[10]  B. Z. Vulikh,et al.  Introduction to the Theory of Partially Ordered Spaces , 1967 .

[11]  Vijayan Sugumaran,et al.  Methodological Advancements in Intelligent Information Technologies: Evolutionary Trends , 2009 .

[12]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[13]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[14]  Cristiano Castelfranchi,et al.  Behavioral Implicit Communication (BIC): Communicating with Smart Environments , 2010, Int. J. Ambient Comput. Intell..

[15]  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..

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

[17]  Stephen Grossberg,et al.  Fuzzy ARTMAP: A neural network architecture for incremental supervised learning of analog multidimensional maps , 1992, IEEE Trans. Neural Networks.

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

[19]  Michael Lawo,et al.  IT-ASSIST: Towards Usable Applications for Elderly People , 2011, Int. J. Ambient Comput. Intell..

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

[21]  Atiq Islam,et al.  CNS Tumor Prediction Using Gene Expression Data Part II , 2009, Encyclopedia of Artificial Intelligence.

[22]  Vijayan Sugumaran.  Intelligent Information Technologies: Concepts, Methodologies, Tools and Applications , 2007 .

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

[24]  Vijayan Sugumaran.  Intelligent support systems : knowledge management , 2002 .

[25]  Alejandro Pazos Sierra,et al.  Encyclopedia of Artificial Intelligence , 2008 .

[26]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[27]  V. Sugumaran.  The Inaugural Issue of the International Journal of Intelligent Information Technologies , 2005 .

[28]  Kiyohiko Uehara,et al.  Fuzzy inference based on families of α-level sets , 1993, IEEE Trans. Fuzzy Syst..