Discriminative learning is challenging when examples are setsof local image features, and the sets vary in cardinality and lackany sort of meaningful ordering. Kernel-based classificationmethods can learn complex decision boundaries, but a kernelsimilarity measure for unordered set inputs must somehow solve forcorrespondences -- generally a computationally expensive task thatbecomes impractical for large set sizes. We present a new fastkernel function which maps unordered feature sets tomulti-resolution histograms and computes a weighted histogramintersection in this space. This ``pyramid match" computation islinear in the number of features, and it implicitly findscorrespondences based on the finest resolution histogram cell wherea matched pair first appears. Since the kernel does not penalize thepresence of extra features, it is robust to clutter. We show thekernel function is positive-definite, making it valid for use inlearning algorithms whose optimal solutions are guaranteed only forMercer kernels. We demonstrate our algorithm on object recognitiontasks and show it to be dramatically faster than currentapproaches.

An important trend in fuzzy group theory in recent years has been the notion of classification of fuzzy subgroups using a suitable equivalence relation. In this dissertation, we have successfully used the natural equivalence relation defined by Murali and Makamba in [81] and a natural fuzzy isomorphism to classify fuzzy subgroups of some finite abelian p-groups of rank three of the form Zpn + Zp + Zp for any fixed prime integer p and any positive integer n. This was achieved through the usage of a suitable technique of enumerating distinct fuzzy subgroups and non-isomorphic fuzzy subgroups of G. We commence by giving a brief discussion on the theory of fuzzy sets and fuzzy subgroups from the perspective of group theory through to the theory of sets, leading us to establish a linkage among these theories. We have also shown in this dissertation that the converse of theorem 3.1 proposed by Das in [24] is incorrect by giving a counter example and restate the theorem. We have then reviewed and enriched the study conducted by Ngcibi in [94] by characterising the non-isomorphic fuzzy subgroups in that study. We have also developed a formula to compute the crisp subgroups of the under-studied group and provide its proof. Furthermore, we have compared the equivalence relation under which the classification problem is based with various versions of equivalence studied in the literature. We managed to use this counting technique to obtain explicit formulae for the number of maximal chains, distinct fuzzy subgroups, non-isomorphic maximal chains and non-isomorphic fuzzy subgroups of these groups and their proofs are provided.

We study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the group of homeomorphisms of Cantor space. In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we study vigorous subgroups of H[sub]c. A subgroup G of H[sub]c is vigorous if for any non-empty clopen set A with proper non-empty clopen subsets B and C there exists g ∈ G with supp(g) ⊑ A and Bg ⊆ C. It is a corollary of the main theorem of Chapter 3 that all finitely generated simple vigorous subgroups of H[sub]c are in fact 2-generated. We show the family of finitely generated, simple, vigorous subgroups of H[sub]c is closed under several natural constructions. In Chapter 4 we use a generalised notion of word and the tight completion construction from [13] to construct a family of subgroups of H[sub]c which generalise Thompson's group V . We give necessary conditions for these groups to be finitely generated and simple. Of these we show which are vigorous. Finally we give some examples.

Made available in DSpace on 2016-01-13T13:27:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-07-08. Added 1 bitstream(s) on 2016-01-13T13:31:37Z : No. of bitstreams: 1 000855574.pdf: 806510 bytes, checksum: 5165b6086fbf8e4db7aeff948269d0e3 (MD5) / Neste trabalho são apresentadas algumas de nições básicas da Teoria de Conjuntos Fuzzy e alguns exemplos teóricos que, na maioria dos textos, são deixados como exercí- cio para o leitor. Dessa forma, pretende-se que o texto que mais didático e completo, podendo ser aproveitado para cursos introdutórios da teoria. Algumas aplicações, voltadas para a área de Geologia, também são apresentadas. Destacamos a proposta de modelagem realizada utilizando-se informações geofísicas [1] e um sistema baseado em regras fuzzy para o estudo de locais na região de Rio Claro (São Paulo - Brasil) que são mais propícios para se perfurar poços com boas vazões / This work presents some basic de nitions of fuzzy set theory and some theoretical examples that in most of the texts are left as an exercise for the reader. Thus, it is intended that the text is more didactic, complete and can be used to introductory courses theory . Some applications, focused on the Geology eld, are also presented. Highlight the proposed modeling performed using geophysical [1] and a system based on fuzzy rules for study sites in Rio Claro region (São Paulo - Brazil) that are more conducive to drill wells with good flow

The main results of this dissertation are various algorithms related to partially ordered sets. The dissertation basically consists of two parts. The first part treats algorithms that generate ideals of partially ordered sets. The second part concerns the generation of partially ordered sets themselves. First, we present two algorithms for listing ideals of a forest poset. These algorithms generate ideals in a Gray Code manner, that is, consecutive ideals differ by exactly one element. Both algorithms use storage O(n), where n is the number of elements in the poset. The first algorithm traverses, at each phase, the current ideal being listed and runs in time O(nN), where N is the number of ideals of the poset. The second algorithm mimics the first but eliminates the traversal and runs in time O(N). This algorithm has the property that the amount of computation between successive ideals is O(1). Secondly, we give orderly algorithms for constructing acyclic digraphs, acyclic transitive digraphs, finite topologies and finite topologies and finite lattices. For the first time we show that the number of finite lattices on 11, 12, and 13 elements are 37622, 262775, and 2018442, respectively, and the number of finite topologies on 8 and 9 elements are 35979 and 363083, respectively. We also describe orderly algorithms for generating k-colored graphs. We present, in particular, an algorithm for generating connected bicolorable graphs. We also prove some properties of a canonic matrix which might be generally useful for improving the efficiency of orderly algorithms. / Graduate

Orientador: Renata Zotin Gomes de Oliveira / Banca: Magda da Silva Peixoto / Banca: Laécio Carvalho de Barros / Resumo: Neste trabalho são apresentadas algumas de nições básicas da Teoria de Conjuntos Fuzzy e alguns exemplos teóricos que, na maioria dos textos, são deixados como exercí- cio para o leitor. Dessa forma, pretende-se que o texto que mais didático e completo, podendo ser aproveitado para cursos introdutórios da teoria. Algumas aplicações, voltadas para a área de Geologia, também são apresentadas. Destacamos a proposta de modelagem realizada utilizando-se informações geofísicas [1] e um sistema baseado em regras fuzzy para o estudo de locais na região de Rio Claro (São Paulo - Brasil) que são mais propícios para se perfurar poços com boas vazões / Abstract: This work presents some basic de nitions of fuzzy set theory and some theoretical examples that in most of the texts are left as an exercise for the reader. Thus, it is intended that the text is more didactic, complete and can be used to introductory courses theory . Some applications, focused on the Geology eld, are also presented. Highlight the proposed modeling performed using geophysical [1] and a system based on fuzzy rules for study sites in Rio Claro region (São Paulo - Brazil) that are more conducive to drill wells with good flow / Mestre

A new class of functions, called somewhat e-continuous functions, has been defined and studied by making use of e-open sets. Characterizations and properties of somewhat e-continuous functions are presented.

No description available.

Magister Commercii - MCom / With the transition to a democratic society, one of the challenges to emerge was to provide economic freedoms for all – that is, freedom from isolation, freedom from powerlessness, freedom from hunger, and freedom from poverty. Fighting poverty has always been high on the agenda of the democratic government since the transition. Numerous measures and policies were instituted aimed at reducing poverty. Researchers initiated serious efforts to try and understand the nature and extent of poverty, through various studies being conducted. Many of these studies focused only on money-metric measures, despite the fact that poverty is a multidimensional concept. What has resulted are various poverty-measurement methods producing different results on the extent of poverty. In addition, certain aspects of these money-metric approaches have serious shortcomings. The fuzzy sets approach addresses many of these shortcomings, as it is a multidimensional approach. Few studies have used this approach to measure poverty in South Africa. This thesis plans to use this method to analyse poverty levels and trends in South Africa, focusing on multidimensional, non-money-metric poverty. Data from Census 1996, Census 2001 and Community Survey 2007 will be used for the study. From the results of the analysis it was established that there is some divergence in the findings of money-metric approaches and those of fuzzy sets. A key result to emerge is the difference in poverty trends over the period 1996 – 2007. Most studies reviewed in Chapter Three that used the money-metric approach showed that poverty trends were upward in the 1990s, before a downward trend took place in the 2000s. This took place irrespective of the survey data used. The non-money-metric poverty trends derived in this chapter, however, show a continuous downward trend over the period. The overall mean deprivation in South Africa has declined since 1996. For people residing in provinces such as Limpopo, the Eastern Cape and KwaZulu-Natal, they are more likely to be poor under the fuzzy sets approach. This may be an indication of inadequate service delivery and the extent to which recent government measures to address poverty have been successful or not. In terms of race, blacks still have the highest mean deprivation, but enjoyed the biggest decline of mean deprivation between 1996 and 2007. Finally, mean deprivation for female-headed households in South Africa was also higher than for male-headed households over the period.

For a fuzzy uniform space, the notion of a Cauchy prefilter, a precompact fuzzy set, a complete fuzzy set and a bounded fuzzy set are defined in such a way that these notions are good extensions of the corresponding notions for a uniform space. A theory of fuzzy uniform spaces is developed which generalises the theory of uniform spaces.