What is a Fuzzy Bi-implication?

In order to make this document self-contained, we first present all the necessary theory as a background. Then we study several definitions that extended the classic bi-implication in to the domain of well stablished fuzzy logics, namely, into the [0; 1] interval. Those approaches of the fuzzy bi-implication can be summarized as follows: two axiomatized definitions, which we proved that represent the same class of functions, four defining standard (two of them proposed by us), which varied by the number of different compound operators and what restrictions they had to satisfy. We proved that those defining standard represent only two classes of functions, having one as a proper subclass of the other, yet being both a subclass of the class represented by the axiomatized definitions. Since those three clases satisfy some contraints that we judge unnecessary, we proposed a new defining standard free of those restrictions and that represents a class of functions that intersects with the class represented by the axiomatized definitions. By this dissertation we are aiming to settle the groundwork for future research on this operator.

On fuzzy ideals and fuzzy filters of fuzzy lattices

In the literature there are several proposals of fuzzi cation of lattices and ideals concepts. Chon in (Korean J. Math 17 (2009), No. 4, 361-374), using the notion of fuzzy order relation de ned by Zadeh, introduced a new notion of fuzzy lattice and studied the level sets of fuzzy lattices, but did not de ne a notion of fuzzy ideals for this type of fuzzy lattice. In this thesis, using the fuzzy lattices de ned by Chon, we de ne fuzzy homomorphism between fuzzy lattices, the operations of product, collapsed sum, lifting, opposite, interval and intuitionistic on bounded fuzzy lattices. They are conceived as extensions of their analogous operations on the classical theory by using this de nition of fuzzy lattices and introduce new results from these operators. In addition, we de ne ideals and lters of fuzzy lattices and concepts in the same way as in their characterization in terms of level and support sets. One of the results found here is the connection among ideals, supports and level sets. The reader will also nd the de nition of some kinds of ideals and lters as well as some results with respect to the intersection among their families. Moreover, we introduce a new notion of fuzzy ideals and fuzzy lters for fuzzy lattices de ned by Chon. We de ne types of fuzzy ideals and fuzzy lters that generalize usual types of ideals and lters of lattices, such as principal ideals, proper ideals, prime ideals and maximal ideals. The main idea is verifying that analogous properties in the classical theory on lattices are maintained in this new theory of fuzzy ideals. We also de ne, a fuzzy homomorphism h from fuzzy lattices L and M and prove some results involving fuzzy homomorphism and fuzzy ideals as if h is a fuzzy monomorphism and the fuzzy image of a fuzzy set ~h(I) is a fuzzy ideal, then I is a fuzzy ideal. Similarly, we prove for proper, prime and maximal fuzzy ideals. Finally, we prove that h is a fuzzy homomorphism from fuzzy lattices L into M if the inverse image of all principal fuzzy ideals of M is a fuzzy ideal of L. Lastly, we introduce the notion of -ideals and - lters of fuzzy lattices and characterize it by using its support and its level set. Moreover, we prove some similar properties in the classical theory of - ideals and - lters, such as, the class of -ideals and - lters are closed under intersection. We also de ne fuzzy -ideals of fuzzy lattices, some properties analogous to the classical theory are also proved and characterize a fuzzy -ideal on operation of product between bounded fuzzy lattices L and M and prove some results.

Looking for a Matrix model for ABJM theory

Encouraged by the recent construction of fuzzy sphere solutions in the Aharony, Bergman, Jafferis, and Maldacena (ABJM) theory, we re-analyze the latter from the perspective of a Matrix-like model. In particular, we argue that a vortex solution exhibits properties of a supergraviton, while a kink represents a 2-brane. Other solutions are also consistent with the Matrix-type interpretation. We study vortex scattering and compare with graviton scattering in the massive ABJM background, however our results are inconclusive. We speculate on how to extend our results to construct a Matrix theory of ABJM.

Mapping soil pollution by spatial analysis and fuzzy classification

Spatial analysis and fuzzy classification techniques were used to estimate the spatial distributions of heavy metals in soil. The work was applied to soils in a coastal region that is characterized by intense urban occupation and large numbers of different industries. Concentrations of heavy metals were determined using geostatistical techniques and classes of risk were defined using fuzzy classification. The resulting prediction mappings identify the locations of high concentrations of Pb, Zn, Ni, and Cu in topsoils of the study area. The maps show that areas of high pollution of Ni and Cu are located at the northeast, where there is a predominance of industrial and agricultural activities; Pb and Zn also occur in high concentrations in the northeast, but the maps also show significant concentrations of Pb and Zn in other areas, mainly in the central and southeastern parts, where there are urban leisure activities and trade centers. Maps were also prepared showing levels of pollution risk. These maps show that (1) Cu presents a large pollution risk in the north-northwest, midwest, and southeast sectors, (2) Pb represents a moderate risk in most areas, (3) Zn generally exhibits low risk, and (4) Ni represents either low risk or no risk in the studied area. This study shows that combining geostatistics with fuzzy theory can provide results that offer insight into risk assessment for environmental pollution.

Theory with a unique thermal effective potential

We show that for the pion-nucleon theory the thermal bubble graph is analytic at the origin of the momentum-frequency space, although the internal propagators in the loop have the same mass. This means that, for this theory, the thermal effective potential is uniquely defined. We then examine how a slight modification of the interaction term results in a theory for which the thermal bubble graph displays the usual nonanalyticity at the origin and the thermal effective potential is not uniquely defined.

The Meaningful Fractal Fuzzy Dimension Applied to the Design of Self Organizing Maps

This paper presents the principal results of a detailed study about the use of the Meaningful Fractal Fuzzy Dimension measure in the problem in determining adequately the topological dimension of output space of a Self-Organizing Map. This fractal measure is conceived by combining the Fractals Theory and Fuzzy Approximate Reasoning. In this work this measure was applied on the dataset in order to obtain a priori knowledge, which is used to support the decision making about the SOM output space design. Several maps were designed with this approach and their evaluations are discussed here.

Fuzzy distributed artificial intelligence systems

In this paper, we introduce a DAI approach called hereinafter Fuzzy Distributed Artificial Intelligence (FDAI). Through the use of fuzzy logic, we have been able to develop mechanisms that we feel may effectively improve current DAI systems, giving much more flexibility and providing the subsidies which a formal theory can bring. The appropriateness of the FDAI approach is explored in an important application, a fuzzy distributed traffic-light control system, where we have been able to aggregate and study several issues concerned with fuzzy and distributed artificial intelligence. We also present a number of current research directions necessary to develop the FDAI approach more fully.

Tuning of fuzzy inference systems through unconstrained optimization techniques

This paper presents a new methodology for the adjustment of fuzzy inference systems. A novel approach, which uses unconstrained optimization techniques, is developed in order to adjust the free parameters of the fuzzy inference system, such as its intrinsic parameters of the membership function and the weights of the inference rules. This methodology is interesting, not only for the results presented and obtained through computer simulations, but also for its generality concerning to the kind of fuzzy inference system used. Therefore, this methodology is expandable either to the Mandani architecture or also to that suggested by Takagi-Sugeno. The validation of the presented methodology is accomplished through an estimation of time series. More specifically, the Mackey-Glass chaotic time series estimation is used for the validation of the proposed methodology.

Bifundamental fuzzy 2-Sphere and fuzzy killing spinors

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.

Fuzzy community structure detection by particle competition and cooperation

Identification and classification of overlapping nodes in networks are important topics in data mining. In this paper, a network-based (graph-based) semi-supervised learning method is proposed. It is based on competition and cooperation among walking particles in a network to uncover overlapping nodes by generating continuous-valued outputs (soft labels), corresponding to the levels of membership from the nodes to each of the communities. Moreover, the proposed method can be applied to detect overlapping data items in a data set of general form, such as a vector-based data set, once it is transformed to a network. Usually, label propagation involves risks of error amplification. In order to avoid this problem, the proposed method offers a mechanism to identify outliers among the labeled data items, and consequently prevents error propagation from such outliers. Computer simulations carried out for synthetic and real-world data sets provide a numeric quantification of the performance of the method. © 2012 Springer-Verlag.

Formulação do controle preventivo em sistemas de distribuição de energia elétrica baseada na lógica fuzzy e redes neurais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Desenvolvimento de um modelo fuzzy para otimização da energia gerada por um sistema híbrido (solar-fotovoltaico e eólico)

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Uma aplicação da lógica Fuzzy

Pós-graduação em Matemática Universitária - IGCE

Análise da estabilidade transitória via rede neural Art-Artmap fuzzy Euclidiana modificada com treinamento continuado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Previsão de carga multinodal usando a rede neural ART-ARTMAP fuzzy

Pós-graduação em Engenharia Elétrica - FEIS