Fundamentals and applications of fuzzy morphological associative memories

Orientador: Peter SussnerTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Uma Memória Associativa (AM, Associative Memory) é um modelo projetado para armazenar pares de entrada e saída. Sobretudo, uma AM deve ser capaz de recordar uma sida desejada ao mesmo após a apresentação de uma versão incompleta ou destorcida de um padrão de entrada. Essa tese de doutorado discute as Memórias Associativas Morfológicas Nebulosas (FMAMs, Fuzzi Morphological Associative Memories), uma classe de memórias associativas elaboradas para armazenar padrões nebulosas cujos neurÔnios realizam operações elementares da morfologia matemática, i.e., dilatação, erosão, anti-dilatação e anti-erosão. É verificado que os principais modelos de Memória Associativa Nebulosa (FAM, Fuzzy Associative Memory) pertencem à classe das FMAMs. Essa tese introduz as Memórias Associativas Nebulosas Implicativas (IFAMs, Implicative Fuzzy Associative Memories) e suas versões duas com respeito à negação e adjunção. Uma IFAM é uma FMAM onde os pares de entrada e saída são armazenados usando o armazenamento nebuloso implicativo. No armazenamento nebuloso implicativo, os pesos sinápticos. Resultados sobre a fase de armazenamento faz IFAMs e das IFAMs duas são apresentados. Em particular, são demonstrados teoremas sobre a convergência, capacidade de armazenamento, tolerância à ruído e pontos fixos das IFAMs e das IFAMs duais para o caso autoassoplos e resultados teóricos. Finalmente, são apresentadas duas aplicações das FMAMs em problemas de previsão de séries temporais. O primeiro problema trata da previsão da mão-de-obra requerida em industrias metalúrgicas enquanto que a segunda aplicação refere-se a previsão da vazão média mensal da usina hidrelétrica de FurnasAbstract: Associative memories (AMs) are models that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. This thesis discusses fuzzy morphological associative memories (FMAMs), a general class of AMs designed to store fuzzy patterns and described by fuzzy neural networks. Each neuron of a FMAM model performs an elementary operation of mathematical morphology such as dilation, erosion, anti-dilation, and anti-erosion. We show that the most widely known models of fuzzy associative memories (FAMs) belong to the FMAM class. This thesis introduces the implicative fuzzy associative memories (IFAMs) and their dual versions with respect to negation and adjunction. An IFAM is a FMAM model where the patterns are stored by means of implicative fuzzy learning. Specifically, in implicative fuzzy learning, the synaptic weights are given by the minimum of the implication of pre- and postsynaptic activations. We present results concerning the recall and storing phase of IFAM and the dual IFAM models. In particular, we present theorems concerning the convergence, the storage capacity, the noise tolerance, and the fixed points of the IFAM and dual IFAM models in the auto-associative case. We compare the IFAMs with several others FAM models by means of theoretical results and examples. Finally, we present two applications of FMAM models in problems of time-series prediction. The first problem concerns the engineering manpower requirement in steel manufacturing industry while the second refers to the stream flow prediction of a large hydroelectric plant, namely FurnasDoutoradoDoutor em Matemática Aplicad

Complete lattice projection autoassociative memories

Orientador: Marcos Eduardo Ribeiro do Valle MesquitaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: A capacidade do cérebro humano de armazenar e recordar informações por associação tem inspirado o desenvolvimento de modelos matemáticos referidos na literatura como memórias associativas. Em primeiro lugar, esta tese apresenta um conjunto de memórias autoassociativas (AMs) que pertecem à ampla classe das memórias morfológicas autoassociativas (AMMs). Especificamente, as memórias morfológicas autoassociativas de projeção max-plus e min-plus (max-plus e min-plus PAMMs), bem como suas composições, são introduzidas nesta tese. Tais modelos podem ser vistos como versões não distribuídas das AMMs propostas por Ritter e Sussner. Em suma, a max-plus PAMM produz a maior combinação max-plus das memórias fundamentais que é menor ou igual ao padrão de entrada. Dualmente, a min-plus PAMM projeta o padrão de entrada no conjunto de todas combinações min-plus. Em segundo, no contexto da teoria dos conjuntos fuzzy, esta tese propõe novas memórias autoassociativas fuzzy, referidas como classe das max-C e min-D FPAMMs. Uma FPAMM representa uma rede neural morfológica fuzzy com uma camada oculta de neurônios que é concebida para o armazenamento e recordação de conjuntos fuzzy ou vetores num hipercubo. Experimentos computacionais relacionados à classificação de padrões e reconhecimento de faces indicam possíveis aplicações dos novos modelos acima mencionadosAbstract: The human brain¿s ability to store and recall information by association has inspired the development various mathematical models referred to in the literature as associative memories. Firstly, this thesis presents a set of autoassociative memories (AMs) that belong to the broad class of autoassociative morphological memories (AMMs). Specifically, the max-plus and min-plus projection autoassociative morphological memories (max-plus and min-plus PAMMs), as well as their compositions, are introduced in this thesis. These models are non-distributed versions of the AMM models developed by Ritter and Sussner. Briefly, the max-plus PAMM yields the largest max-plus combination of the stored vectors which is less than or equal to the input pattern. Dually, the min-plus PAMM projects the input pattern into the set of all min-plus combinations. In second, in the context of fuzzy set theory, this thesis proposes new fuzzy autoassociative memories mentioned as class of the max-C and min-D FPAMMs. A FPAMM represents a fuzzy morphological neural network with a hidden layer of neurons that is designed for the storage and retrieval of fuzzy sets or vectors on a hypercube. Computational experiments concerning pattern classification and face recognition indicate possible applications of the aforementioned new AM modelsDoutoradoMatematica AplicadaDoutor em Matemática AplicadaCAPE

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

A comparative study on associative memories with emphasis on morphological associative memories

Orientador: Peter SussnerDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Memórias associativas neurais são modelos do fenômeno biológico que permite o armazenamento de padrões e a recordação destes apos a apresentação de uma versão ruidosa ou incompleta de um padrão armazenado. Existem vários modelos de memórias associativas neurais na literatura, entretanto, existem poucos trabalhos comparando as varias propostas. Nesta dissertação comparamos sistematicamente o desempenho dos modelos mais influentes de memórias associativas neurais encontrados na literatura. Esta comparação está baseada nos seguintes critérios: capacidade de armazenamento, distribuição da informação nos pesos sinápticos, raio da bacia de atração, memórias espúrias e esforço computacional. Especial ênfase dado para as memórias associativas morfológicas cuja fundamentação matemática encontra-se na morfologia matemática e na álgebra de imagensAbstract: Associative neural memories are models of biological phenomena that allow for the storage of pattern associations and the retrieval of the desired output pattern upon presentation of a possibly noisy or incomplete version of an input pattern. There are several models of neural associative memories in the literature, however, there are few works relating them. In this thesis, we present a systematic comparison of the performances of some of the most widely known models of neural associative memories. This comparison is based on the following criteria: storage capacity, distribution of the information over the synaptic weights, basin of attraction, number of spurious memories, and computational effort. The thesis places a special emphasis on morphological associative memories whose mathematical foundations lie in mathematical morphology and image algebraMestradoMatematica AplicadaMestre em Matemática Aplicad

Fuzzy Neural Networks

Práce je věnována fuzzy neuronovým sítím. Protože se jedná o techniku kombinování fuzzy logiky s neuronovými sítěmi pro řešení nejrůznějších úloh z oblasti umělé inteligence, řízení či strojového učení, teoretická část práce se nejprve zabývá neuronovými sítěmi a fuzzy logikou odděleně. Po vysvětlení nezbytných základů je zbytek teoretické části zaměřen převážně na teorii fuzzy neuronových sítí, jejich klasifikaci a použití v praxi. Na základě popsané teorie jsou navrhnuty a implementovány fuzzy asociativní paměti, jejichž cílem je řešit úlohu klasifikace a úlohu z oblasti řízení. Na závěr jsou výsledné implementace a jejich výsledky zhodnoceny a porovnány s jinými přístupy k řešení zvolených úloh.This thesis focuses on fuzzy neural networks. The combination of the fuzzy logic and artificial neural networks leads to the development of more robust systems. These systems are used in various field of the research, such as artificial intelligence, machine learning and control theory. First, we provide a quick overview of underlying neural networks and fuzzy systems to explain fundamental ideas that form the basis of the fields, and follow with the introduction of the fuzzy neural network theory, classification and application. Then we describe a design and a realization of the fuzzy associative memory, as an example of these systems. Finally, we benchmark the realization using the pattern recognition and control tasks. The results are evaluated and compared against existing systems.

Metaphor as a device for understanding cognitive concepts

The paper addresses metaphor as a cognitive-semantic device which is able to reveal intuitive mechanisms of the thinking process, thus filling the gaps in the sphere of logically objective human knowledge and opening the possibility to describe abstract concepts of the human mind in terms. This paper substantiates the principal possibility of conceptual modeling of the metaphorization process and describes its baseline algorithm, identifies complex metaphors and establishes the cognitive-semantic features of their functioning. The main conclusion of the reasoning confirms the hypothesis that different image schemes have different strength of heuristic potential, which determines the fullness of metaphorical descriptions of concepts