A first approach to an axiomatic model of multi-measures

We establish an axiomatic model of multi-measures, capturing some classes of measures studied in the fuzzy sets literature, where they are applied to only one or two arguments.

Some geometrical methods for constructing contradiction measures on Atanassov's intuitionistic fuzzy sets

Trillas et al. (1999, Soft computing, 3 (4), 197–199) and Trillas and Cubillo (1999, On non-contradictory input/output couples in Zadeh's CRI proceeding, 28–32) introduced the study of contradiction in the framework of fuzzy logic because of the significance of avoiding contradictory outputs in inference processes. Later, the study of contradiction in the framework of Atanassov's intuitionistic fuzzy sets (A-IFSs) was initiated by Cubillo and Castiñeira (2004, Contradiction in intuitionistic fuzzy sets proceeding, 2180–2186). The axiomatic definition of contradiction measure was stated in Castiñeira and Cubillo (2009, International journal of intelligent systems, 24, 863–888). Likewise, the concept of continuity of these measures was formalized through several axioms. To be precise, they defined continuity when the sets ‘are increasing’, denominated continuity from below, and continuity when the sets ‘are decreasing’, or continuity from above. The aim of this paper is to provide some geometrical construction methods for obtaining contradiction measures in the framework of A-IFSs and to study what continuity properties these measures satisfy. Furthermore, we show the geometrical interpretations motivating the measures.

Contribución al estudio de la incompatibilidad y otras medidas relacionadas en la lógica borrosa

Resumen La investigación descrita en esta memoria se enmarca en el campo de la lógica borro¬sa. Más concretamente, en el estudio de la incompatibilidad, de la compatibilidad y de la suplementaridad en los conjuntos borrosos y en los de Atanassov. En este orden de ideas, en el primer capítulo, se construyen, tanto de forma directa como indirecta, funciones apropiadas para medir la incompatibilidad entre dos conjuntos borro-sos. Se formulan algunos axiomas para modelizar la continuidad de dichas funciones, y se determina si las medidas propuestas, y otras nuevas que se introducen, verifican algún tipo de continuidad. Finalmente, se establece la noción de conjuntos borrosos compatibles, se introducen axiomas para medir esta propiedad y se construyen algunas medidas de compa¬tibilidad. El segundo capítulo se dedica al estudio de la incompatibilidad y de la compatibilidad en el campo de los conjuntos de Atanassov. Así, en primer lugar, se presenta una definición axiomática de medida de incompatibilidad en este contexto. Después, se construyen medidas de incompatibilidad por medio de los mismos métodos usados en el caso borroso. Además, se formulan axiomas de continuidad y se determina el tipo de continuidad de las medidas propuestas. Finalmente, se sigue un camino similar al caso borroso para el estudio de la compatibilidad. En el tercer capítulo, después de abordar la antonimia de conjuntos borrosos y de conjuntos de Atanassov, se formalizan las nociones de conjuntos suplementarios en estos dos entornos y se presenta, en ambos casos, un método para obtener medidas de suplementaridad a partir de medidas de incompatibilidad vía antónimos. The research described in this report pertains to the field of fuzzy logic and specifically studies incompatibility, compatibility and supplementarity in fuzzy sets and Atanassov's fuzzy sets. As such is the case, Chapter 1 describes both the direct and indirect construction of appropriate functions for measuring incompatibility between two fuzzy sets. We formulate some axioms for modelling the continuity of functions and determine whether the proposed and other measures introduced satisfy any type of continuity. Chapter 2 focuses on the study of incompatibility and compatibility in the field of Ata¬nassov's fuzzy sets. First, we present an axiomatic definition of incompatibility measure in this field. Then, we use the same methods to construct incompatibility measures as in the fuzzy case. Additionally, we formulate continuity axioms and determine the type of conti¬nuity of the proposed measures. Finally, we take a similar approach as in the fuzzy case to the study of compatibility. After examining the antonymy of fuzzy sets and Atanassov's sets, Chapter 3 formalizes the notions of supplementary sets in these two domains, and, in both cases, presents a method for obtaining supplementarity measures from incompatibility measures via antonyms.

OPPL-Galaxy, a Galaxy tool for enhancing ontology exploitation as part of bioinformatics workflows

Biomedical ontologies are key elements for building up the Life Sciences Semantic Web. Reusing and building biomedical ontologies requires flexible and versatile tools to manipulate them efficiently, in particular for enriching their axiomatic content. The Ontology Pre Processor Language (OPPL) is an OWL-based language for automating the changes to be performed in an ontology. OPPL augments the ontologists’ toolbox by providing a more efficient, and less error-prone, mechanism for enriching a biomedical ontology than that obtained by a manual treatment. Results We present OPPL-Galaxy, a wrapper for using OPPL within Galaxy. The functionality delivered by OPPL (i.e. automated ontology manipulation) can be combined with the tools and workflows devised within the Galaxy framework, resulting in an enhancement of OPPL. Use cases are provided in order to demonstrate OPPL-Galaxy’s capability for enriching, modifying and querying biomedical ontologies. Conclusions Coupling OPPL-Galaxy with other bioinformatics tools of the Galaxy framework results in a system that is more than the sum of its parts. OPPL-Galaxy opens a new dimension of analyses and exploitation of biomedical ontologies, including automated reasoning, paving the way towards advanced biological data analyses.

Obtaining contradiction measure on intuitionistic fuzzy sets from fuzzy connectives

In a previous paper, we proposed an axiomatic model for measuring self-contradiction in the framework of Atanassov fuzzy sets. This way, contradiction measures that are semicontinuous and completely semicontinuous, from both below and above, were defined. Although some examples were given, the problem of finding families of functions satisfying the different axioms remained open. The purpose of this paper is to construct some families of contradiction measures firstly using continuous t-norms and t-conorms, and secondly by means of strong negations. In both cases, we study the properties that they satisfy. These families are then classified according the different kinds of measures presented in the above paper.

Integration of design tools and knowledge capture into a CAD system: a case study

onceptual design phase is partially supported by product lifecycle management/computer-aided design (PLM/CAD) systems causing discontinuity of the design information flow: customer needs — functional requirements — key characteristics — design parameters (DPs) — geometric DPs. Aiming to address this issue, it is proposed a knowledge-based approach is proposed to integrate quality function deployment, failure mode and effects analysis, and axiomatic design into a commercial PLM/CAD system. A case study, main subject of this article, was carried out to validate the proposed process, to evaluate, by a pilot development, how the commercial PLM/CAD modules and application programming interface could support the information flow, and based on the pilot scheme results to propose a full development framework.

El límite y su reversibilidad

La propuesta busca desarrollar herramientas nuevas para entendimiento de los límites y bordes arquitectónicos. Entendiendo las características tanto físicas como psicológicas de los límites, busco que la arquitectura que se propone genere una ruptura de las simplistas contraposiciones binarias que se encuentran en la base de la comprensión arquitectónica tradicional; los conceptos de interior / exterior, dentro / fuera, sujeto / objeto, ciudad / campo, naturaleza/ artificio; son desde mi punto de vista atavismos que deben ser superados para poder producir una arquitectura acorde a los nuevos tiempos, que se adapte a las condicionantes de su entorno. Al entender que los límites encarnan la existencia de situaciones duales e hibridas, que suceden a los dos lados del límite busco aprovechar las situaciones de tensión, negación, negociación, confrontación, contraposición, etc., la propuesta busca poner en valor las características de convivencia, dialogo y relación de la ciudad tradicional. Es decir las características políticas de la polis y la civitas. Entendiendo que el hombre es un animal político por excelencia, la propuesta busca potenciar el carácter político y de socialización de la arquitectura. Por medio del entendimiento de las relaciones y espacializaciones que generan los choques cuerpos en el espacio; y la necesidad de que los límites de la arquitectura y la ciudad sean transgredidos física y programáticamente para que adquieran un carácter más dinámico y poroso que ayuden a esta relación. La propuesta introduce ejemplos de líneas de fuga y rupturas, que se puedan materializar mediante pequeñas intervenciones. Intervenciones arquitectónicas, que a pesar de sus limitados recursos formales, puedan generar resultados exponencialmente superiores que transformen las condiciones iniciales del sitio. The proposal seeks to develop new tools for the understanding of the Architectural limits and borders. By understanding of limit`s physical and psychological qualities, I seek that architecture could generate a breakdown of the simplistic binary oppositions that are at the base of the traditional Architectural understanding; concepts such as interior / exterior, inside / outside, object/subject, city/countryside, nature/artifice; They are from my point of view atavism that must be overcome in order to produce an architecture according to the times, that suit the conditions of their milieu. By understanding that limits embodies the existence of dual and hybrid situations that occur on both sides of the limit, I manage to take stressful situations of , denial, bargaining, confrontation, contrast, etc., the proposal seeks to assess the characteristics of living , dialogue and respect of the traditional city. I.e. the political characteristics of the polis and civitas. By realizing that the man is a political animal par excellence, the proposal seeks to strengthen political and socialization architectural character. Through the understanding of spatial relationships that shocking bodies generates in space; and the need for architecture and city limits get physically and programmatically transgressed to acquire a more dynamic and porous nature that helps in this relationship. The proposal introduces examples of flight lines and breaks, which can be realized through small interventions. Architectural interventions, despite his limited formal resources can generate exponentially greater results that transform the initial conditions of the site.

Modelado y Comparación de Colecciones en la Web Semántica

En esta tesis se estudia la representación, modelado y comparación de colecciones mediante el uso de ontologías en el ámbito de la Web Semántica. Las colecciones, entendidas como agrupaciones de objetos o elementos con entidad propia, son construcciones que aparecen frecuentemente en prácticamente todos los dominios del mundo real, y por tanto, es imprescindible disponer de conceptualizaciones de estas estructuras abstractas y de representaciones de estas conceptualizaciones en los sistemas informáticos, que definan adecuadamente su semántica. Mientras que en muchos ámbitos de la Informática y la Inteligencia Artificial, como por ejemplo la programación, las bases de datos o la recuperación de información, las colecciones han sido ampliamente estudiadas y se han desarrollado representaciones que responden a multitud de conceptualizaciones, en el ámbito de la Web Semántica, sin embargo, su estudio ha sido bastante limitado. De hecho hasta la fecha existen pocas propuestas de representación de colecciones mediante ontologías, y las que hay sólo cubren algunos tipos de colecciones y presentan importantes limitaciones. Esto impide la representación adecuada de colecciones y dificulta otras tareas comunes como la comparación de colecciones, algo crítico en operaciones habituales como las búsquedas semánticas o el enlazado de datos en la Web Semántica. Para solventar este problema esta tesis hace una propuesta de modelización de colecciones basada en una nueva clasificación de colecciones de acuerdo a sus características estructurales (homogeneidad, unicidad, orden y cardinalidad). Esta clasificación permite definir una taxonomía con hasta 16 tipos de colecciones distintas. Entre otras ventajas, esta nueva clasificación permite aprovechar la semántica de las propiedades estructurales de cada tipo de colección para realizar comparaciones utilizando las funciones de similitud y disimilitud más apropiadas. De este modo, la tesis desarrolla además un nuevo catálogo de funciones de similitud para las distintas colecciones, donde se han recogido las funciones de (di)similitud más conocidas y también algunas nuevas. Esta propuesta se ha implementado mediante dos ontologías paralelas, la ontología E-Collections, que representa los distintos tipos de colecciones de la taxonomía y su axiomática, y la ontología SIMEON (Similarity Measures Ontology) que representa los tipos de funciones de (di)similitud para cada tipo de colección. Gracias a estas ontologías, para comparar dos colecciones, una vez representadas como instancias de la clase más apropiada de la ontología E-Collections, automáticamente se sabe qué funciones de (di)similitud de la ontología SIMEON pueden utilizarse para su comparación. Abstract This thesis studies the representation, modeling and comparison of collections in the Semantic Web using ontologies. Collections, understood as groups of objects or elements with their own identities, are constructions that appear frequently in almost all areas of the real world. Therefore, it is essential to have conceptualizations of these abstract structures and representations of these conceptualizations in computer systems, that define their semantic properly. While in many areas of Computer Science and Artificial Intelligence, such as Programming, Databases or Information Retrieval, the collections have been extensively studied and there are representations that match many conceptualizations, in the field Semantic Web, however, their study has been quite limited. In fact, there are few representations of collections using ontologies so far, and they only cover some types of collections and have important limitations. This hinders a proper representation of collections and other common tasks like comparing collections, something critical in usual operations such as semantic search or linking data on the Semantic Web. To solve this problem this thesis makes a proposal for modelling collections based on a new classification of collections according to their structural characteristics (homogeneity, uniqueness, order and cardinality). This classification allows to define a taxonomy with up to 16 different types of collections. Among other advantages, this new classification can leverage the semantics of the structural properties of each type of collection to make comparisons using the most appropriate (dis)similarity functions. Thus, the thesis also develops a new catalog of similarity functions for the different types of collections. This catalog contains the most common (dis)similarity functions as well as new ones. This proposal is implemented through two parallel ontologies, the E-Collections ontology that represents the different types of collections in the taxonomy and their axiomatic, and the SIMEON ontology (Similarity Measures Ontology) that represents the types of (dis)similarity functions for each type of collection. Thanks to these ontologies, to compare two collections, once represented as instances of the appropriate class of E-Collections ontology, we can know automatically which (dis)similarity functions of the SIMEON ontology are suitable for the comparison. Finally, the feasibility and usefulness of this modeling and comparison of collections proposal is proved in the field of oenology, applying both E-Collections and SIMEON ontologies to the representation and comparison of wines with the E-Baco ontology.

Graphoids and separoids in model theory

We treat graphoid and separoid structures within the mathematical framework of model theory, specially suited for representing and analysing axiomatic systems with multiple semantics. We represent the graphoid axiom set in model theory, and translate algebraic separoid structures to another axiom set over the same symbols as graphoids. This brings both structures to a common, sound theoretical ground where they can be fairly compared. Our contribution further serves as a bridge between the most recent developments in formal logic research, and the well-known graphoid applications in probabilistic graphical modelling.