<p>Doktorska disertacija izučava primenu fazi operacija, prvenstveno agregacionih operatora na funkcije rastojanja i metrike. Originalan doprinos teze je u konstrukciji novih funkcija rastojanja i metrika primenom agregacionih operatora na neke polazne funkcije rastojanja i metrike. Za neke tipove agregacionih operatora i polaznih funkcija rastojanja i metrika su ispitane osobine ovako konstruisanih funkcija rastojanja i metrika. Za neke od njih su ispitane performanse pri primeni u segmentaciji slike &bdquo;Fuzzy c-means&ldquo; algoritmom.</p> / <p>This thesis studies application of fuzzy operations, especially aggregation operators, on distance functions and metrics. The contribution of the thesis is construction of new distance functions and metrics by application of aggregation operators on some basic distance functions and metrics. For some types of aggregation operators and basic distance functions and metrics, properties of distance functions and metrics constructed in this way are analyzed. For some of them, performances in application in Fuzzy c-means algorithm are analyzed.</p>

We present two Swarm Intelligence based approaches for data clustering. The first algorithm, Fuzzy Ants, presented in this thesis clusters data without the initial knowledge of the number of clusters. It is a two stage algorithm. In the first stage the ants cluster data to initially create raw clusters which are refined using the Fuzzy C Means algorithm. Initially, the ants move the individual objects to form heaps. The centroids of these heaps are redefined by the Fuzzy C Means algorithm. In the second stage the objects obtained from the Fuzzy C Means algorithm are hardened according to the maximum membership criteria to form new heaps. These new heaps are then moved by the ants. The final clusters formed are refined by using the Fuzzy C Means algorithm. Results from experiments with 13 datasets show that the partitions produced are competitive with those from FCM. The second algorithm, Fuzzy ant clustering with centroids, is also a two stage algorithm, it requires an initial knowledge of the number of clusters in the data. In the first stage of the algorithm ants move the cluster centers in feature space. The cluster centers found by the ants are evaluated using a reformulated Fuzzy C Means criterion. In the second stage the best cluster centers found are used as the initial cluster centers for the Fuzzy C Means algorithm. Results on 18 datasets show that the partitions found by FCM using the ant initialization are better than those from randomly initialized FCM. Hard C Means was also used in the second stage and the partitions from the ant algorithm are better than from randomly initialized Hard C Means. The Fuzzy Ants algorithm is a novel method to find the number of clusters in the data and also provides good initializations for the FCM and HCM algorithms. We performed sensitivity analysis on the controlling parameters and found the Fuzzy Ants algorithm to be very sensitive to the Tcreateforheap parameter. The FCM and HCM algorithms, with random initializations can get stuck in a bad extrema, the Fuzzy ant clustering with centroids algorithm successfully avoids these bad extremas.

Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / Este trabalho apresenta um método para reconhecimento do padrão na biodisponibilidade do ferro, através da interação com substâncias que auxiliam a absorção como vitamina C e vitamina A e nutrientes inibidores como cálcio, fitato, oxalato, tanino e cafeína. Os dados foram obtidos através de inquérito alimentar, almoço e jantar, em crianças de 2 a 5 anos da única Creche Municipal de Paraty-RJ entre 2007 e 2008. A Análise de Componentes Principais (ACP) foi aplicada na seleção dos nutrientes e utilizou-se o Algoritmo Fuzzy C-Means (FCM) para criar os agrupamentos classificados de acordo com a biodisponibilidade do ferro. Uma análise de sensibilidade foi desenvolvida na tentativa de buscar quantidades limítrofes de cálcio a serem consumidas nas refeições. A ACP mostrou que no almoço os nutrientes que explicavam melhor a variabilidade do modelo foram ferro, vitamina C, fitato e oxalato, enquanto no jantar o cálcio se mostrou eficaz na determinação da variabilidade do modelo devido ao elevado consumo de leite e derivados. Para o almoço, a aplicação do FCM na interação dos nutrientes, notou-se que a ingestão de vitamina C foi determinante na classificação dos grupos. No jantar, a classificação de grupos foi determinada pela quantidade de ferro heme na interação com o cálcio. Na análise de sensibilidade realizada no almoço e no jantar, duas iterações do algoritmo determinaram a interferência total do cálcio na biodisponibilidade do ferro. / This dissertation presents a method for pattern recognition on the bioavailability of iron, through interaction with substances that help the absorption such as vitamin C and vitamin A and inhibitors as calcium, phytate, oxalate, tannin and caffeine. The database was obtained through dietary, lunch and dinner, in children 2-5 years in the Municipal Nursery of Paraty - Rio de Janeiro, between 2007 and 2008. The Principal Component Analysis (PCA) was applied in the selection of nutrients and used the Fuzzy C-Means Algorithm (FCM) to create the groups classified according to the bioavailability of iron. A sensitivity analysis was developed in an attempt to find neighboring amounts of calcium being consumed at meals. The PCA showed that at lunch the nutrients that best explained the variability of the model were iron, vitamin C, phytate and oxalate, while at dinner the calcium was effective in determining the variability of the model due to high consumption of dairy products. For lunch, the application of FCM in the interaction of nutrients, it was noted that the intake of vitamin C was decisive in the classification of groups. At dinner, the classification of groups was determined by the amount of iron in the interaction with calcium. In the sensitivity analysis performed for lunch and dinner, two iterations of the algorithm determined the total interference of calcium on iron bioavailability.

Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro / Este trabalho apresenta um método para reconhecimento do padrão na biodisponibilidade do ferro, através da interação com substâncias que auxiliam a absorção como vitamina C e vitamina A e nutrientes inibidores como cálcio, fitato, oxalato, tanino e cafeína. Os dados foram obtidos através de inquérito alimentar, almoço e jantar, em crianças de 2 a 5 anos da única Creche Municipal de Paraty-RJ entre 2007 e 2008. A Análise de Componentes Principais (ACP) foi aplicada na seleção dos nutrientes e utilizou-se o Algoritmo Fuzzy C-Means (FCM) para criar os agrupamentos classificados de acordo com a biodisponibilidade do ferro. Uma análise de sensibilidade foi desenvolvida na tentativa de buscar quantidades limítrofes de cálcio a serem consumidas nas refeições. A ACP mostrou que no almoço os nutrientes que explicavam melhor a variabilidade do modelo foram ferro, vitamina C, fitato e oxalato, enquanto no jantar o cálcio se mostrou eficaz na determinação da variabilidade do modelo devido ao elevado consumo de leite e derivados. Para o almoço, a aplicação do FCM na interação dos nutrientes, notou-se que a ingestão de vitamina C foi determinante na classificação dos grupos. No jantar, a classificação de grupos foi determinada pela quantidade de ferro heme na interação com o cálcio. Na análise de sensibilidade realizada no almoço e no jantar, duas iterações do algoritmo determinaram a interferência total do cálcio na biodisponibilidade do ferro. / This dissertation presents a method for pattern recognition on the bioavailability of iron, through interaction with substances that help the absorption such as vitamin C and vitamin A and inhibitors as calcium, phytate, oxalate, tannin and caffeine. The database was obtained through dietary, lunch and dinner, in children 2-5 years in the Municipal Nursery of Paraty - Rio de Janeiro, between 2007 and 2008. The Principal Component Analysis (PCA) was applied in the selection of nutrients and used the Fuzzy C-Means Algorithm (FCM) to create the groups classified according to the bioavailability of iron. A sensitivity analysis was developed in an attempt to find neighboring amounts of calcium being consumed at meals. The PCA showed that at lunch the nutrients that best explained the variability of the model were iron, vitamin C, phytate and oxalate, while at dinner the calcium was effective in determining the variability of the model due to high consumption of dairy products. For lunch, the application of FCM in the interaction of nutrients, it was noted that the intake of vitamin C was decisive in the classification of groups. At dinner, the classification of groups was determined by the amount of iron in the interaction with calcium. In the sensitivity analysis performed for lunch and dinner, two iterations of the algorithm determined the total interference of calcium on iron bioavailability.