Concept lattices associated with L-Fuzzy W-contexts

\begin{abstract} \noindent We generalize in this paper the $L$-Fuzzy concept theory we developed in a previous paper ([1]), using the composition of $L$-Fuzzy relations. This theory models knowledge acquisition and classification and takes as departure point Wille's idea ([5]). We begin the work defining $L$-Fuzzy W-contexts as the tuples (L,W,X,Y, $\underset{\textstyle \backsim}{R}$) where W, X and Y are the sets of labels, objects and attributes respectively, and $\underset{\textstyle \backsim}{R}\in L^{X\times Y}$ is an $L$-Fuzzy relation. From these contexts, we will give the operators needed to define the \linebreak $L$-Fuzzy W-concepts. These concepts will be pairs of relations ($\underset{\textstyle \backsim}{P}, \underset{\textstyle \backsim}{Q}$) where $\underset{\textstyle \backsim}{P}\in L^{W\times X}$, $\underset{\textstyle \backsim}Q\in L^{W\times Y}$ satisfying $\underset{\textstyle \backsim}{P_{1}}= \underset{\textstyle \backsim}Q$ and $\underset{\textstyle \backsim}Q_{2}= \underset{\textstyle \backsim}P$ with the operator 1 and 2 definitions given. After proving the lattice structure of the $L$-Fuzzy W-concepts set, we analyse a practical example where we interpret the new concept definition \bigskip \noindent {\bf Key words:} $L$-Fuzzy concepts, $L$-Fuzzy W-concepts, $L$-Fuzzy W-contexts, Conceptual knowledge. \end{abstract

The use of two relations in L-fuzzy contexts

In the analysis of relations among the elements of two sets it is usual to obtain different values depending on the point of view from which these relations are measured. The main goal of the paper is the modelization of these situations by means of a generalization of the L-fuzzy concept analysis called L-fuzzy bicontext. We study the L-fuzzy concepts of these L-fuzzy bicontexts obtaining some interesting results. Specifically, we will be able to classify the biconcepts of the L-fuzzy bicontext. Finally, a practical case is developed using this new tool.This work has been partially supported by the Research Group “Intelligent Systems and Energy (SI+E)” of the Basque Government, under Grant IT677-13, by the Research Groups “Artificial Intelligence and Approximate Reasoning” and “Adquisición de conocimiento y minería de datos, funciones especiales y métodos numéricos avanzados” of the Public University of Navarra and by project TIN2013-40765-P

Generation of fuzzy mathematical morphologies

Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications), the paper includes a study on their practical effects on digital image processing. We also present some graphic examples of erosion and dilation with three different structuring elements $B(i, j)=1$, $B(i, j)=0.7$, $B(i, j)=0.4$, $i, j \in \{ 1,2, 3\}$ and various fuzzy implications

Fuzzy morphological operators in image processing

First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz's one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout's manner) that satisfies the axioms of Divyendu and Dogherty. Second, we propose a method to define fuzzy morphological operators (erosions and dilations). A family of fuzzy implication operators and the inclusion grade are the basis for this method

Computational approach to design face-milled spiral bevel gear drives with favorable conditions of meshing and contact

The micro-geometry of the tooth surfaces of spiral bevel and hypoid pinions has to be fine adjusted to obtain enhanced meshing and contact characteristics during the meshing process with their corresponding mating gears. In this paper, a new methodology is proposed to design face-milled spiral bevel gear drives to, firstly, derive favorable orientation and dimensions of the contact pattern between the mating surfaces of the gears and, secondly, obtain a predesigned parabolic function of negative transmission errors with limited magnitude of maximum transmission errors. The proposed approach is based on the definition of the desired topography for the active surfaces of the pinion followed by a numerical derivation of their finishing machine-tool settings through a bound-constrained optimization algorithm. Increasing mechanical strength and reducing the levels of noise and vibration of face-milled spiral bevel gear drives constitute the main objectives of the proposed design process. A numerical example is provided to illustrate the applicability of the developed theory.The work of the second author has been funded by the FPI scholarship Ref. BES-2011-045995 granted by the Spanish Ministry of Economy and Competitiveness (MINECO)

A composite indicator index as a proxy for measuring the quality of water supply as perceived by users for urban water services

The objective of this study is to develop a composite indicator (CI) to measure the quality of water supply based on the variables that are considered to affect users’ perceptions of water supply quality. The proposed CI includes six relevant aspects that determine users’ perceptions of water supply quality (network quality, water quality, water price, complaints, inconvenience caused by upgrading the network, and continuity of service) in a simple, economical, and objective way, using multi-criteria decision analysis (MCDA) with weights based on data envelopment analysis (DEA). The CI was applied to 32 municipalities in the metropolitan area of Valencia (Spain). The results show the high quality of the water supply service in this area. The use of this CI to measure the quality of the water supply service may prove useful for public institutions and managers of urban water supply, giving them an instrument to improve the management, efficiency, and quality of the water services they provide

La reconversión azucarera en la provincia de Guantánamo, Cuba. Una mirada desde lo local

Un análisis antes y después del proceso reconversión azucarera en la provincia de Guantánamo, Cuba, posibilitó identificar las principales experiencias de su aplicación; además, se destacan los beneficios que una perspectiva local hubiera podido aportar. Se abordó el impacto socioeconómico de dicho proceso en la agroindustria azucarera de la provincia. Se concluyó que el proceso de reconversión azucarera y el desarrollo económico local están sujetos al perfeccionamiento de los modelos de desarrollo tradicionales y a su adaptación a particularidades locales. Así, la evaluación del impacto de la reconversión en las comunidades debe considerar los principios de sostenibilidad (dimensiones económica, ambiental y social)

Knowledge discovery in databases using fuzzy mathematical morphology techniques

En este artículo se analiza el efecto, la utilidad y la interpretación de los filtros asociados a la Morfología Matemática Borrosa en procesos de Descubrimiento de Conocimiento en Bases de Datos. En particular se estudian los operadores morfológicos erosión, dilatación, apertura, cierre, Top-Hat y Hit-or-Miss. Usando información de las bases de datos y relaciones binarias ordinarias como elementos estructurales, se implementan algunos de estos filtros. Con esta implementación se justifica que, con estos filtros morfológicos, pueden analizarse datos estructurados como tabla de registros, obteniéndose información útil no evidente. Finalmente se analizan diversas características de los operadores definidos, ilustrando los resultados con un ejemplo.In this paper the effect and usefulness of some filters associated to Fuzzy Mathematical Morphology operators, erosion, dilation, opening, closing, Top-Hat and Hit-or-Miss are analyzed. We propose the interpretation of those operators in processes of Database Knowledge Discovery. Using database information and binary crisp relations as structuring elements, some of these filters are implemented. Also, and using the morphological filters, it is verified that it is possible to analyze information constructed in table of records, interpreted as fuzzy subsets, obtaining not evident useful information. Finally, some properties of the defined operators are analyzed, illustrating the results with an example

La reconversión azucarera en la provincia de Guantánamo, Cuba. Una mirada desde lo local

Un análisis antes y después del proceso reconversión azucarera en la provincia de Guantánamo, Cuba, posibilitó identificar las principales experiencias de su aplicación; además, se destacan los beneficios que una perspectiva local hubiera podido aportar. Se abordó el impacto socioeconómico de dicho proceso en la agroindustria azucarera de la provincia. Se concluyó que el proceso de reconversión azucarera y el desarrollo económico local están sujetos al perfeccionamiento de los modelos de desarrollo tradicionales y a su adaptación a particularidades locales. Así, la evaluación del impacto de la reconversión en las comunidades debe considerar los principios de sostenibilidad (dimensiones económica, ambiental y social)