http://hdl.handle.net/2117/1174 Wed, 19 Jun 2013 06:55:42 GMT 2013-06-19T06:55:42Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2117/19494 Title: Elogio de una nueva sección a propósito de la optimización del tubo Authors: Albareda Valls, Albert; Maristany Carreras, Jordi; Alentorn Puigcerver, Jaume Tue, 04 Jun 2013 10:43:21 GMT http://hdl.handle.net/2117/19494 2013-06-04T10:43:21Z Albareda Valls, Albert; Maristany Carreras, Jordi; Alentorn Puigcerver, Jaume no http://hdl.handle.net/2117/19443 Title: Gaudi and reinforced concrete in construction Authors: Grima Lopez, Rosa; Aguado de Cea, Antonio; Gómez Serrano, José Abstract: The first two decades of the 20th century witnessed the introduction and expansion of reinforced concrete as a building material in Spain. Few years passed between the introduction of the first patents in the most industrialized areas of the Iberian Peninsula and the subsequent generalization of the technique through scientific knowledge obtained in universities. This period coincides almost completely with the professional career of Antoni Gaudí, one of the most famous Catalan architects. This study reports that Gaudí had contact with this new material and discusses the transition he made from the traditional construction methods to the use of reinforced concrete in his later works. Placing the starting point in the relationship between Antonio Gaudí and the industrialists who built the first cement factories in Catalonia (especially Eusebi Güell), the research on the patents to which he had access are presented and the characteristics of his works with reinforced structures and materials are described. Wed, 29 May 2013 08:40:07 GMT http://hdl.handle.net/2117/19443 2013-05-29T08:40:07Z Grima Lopez, Rosa; Aguado de Cea, Antonio; Gómez Serrano, José no Antoni Gaudi, reinforced concrete, patent, Sagrada Familia, Park Guell The first two decades of the 20th century witnessed the introduction and expansion of reinforced concrete as a building material in Spain. Few years passed between the introduction of the first patents in the most industrialized areas of the Iberian Peninsula and the subsequent generalization of the technique through scientific knowledge obtained in universities. This period coincides almost completely with the professional career of Antoni Gaudí, one of the most famous Catalan architects. This study reports that Gaudí had contact with this new material and discusses the transition he made from the traditional construction methods to the use of reinforced concrete in his later works. Placing the starting point in the relationship between Antonio Gaudí and the industrialists who built the first cement factories in Catalonia (especially Eusebi Güell), the research on the patents to which he had access are presented and the characteristics of his works with reinforced structures and materials are described. http://hdl.handle.net/2117/19441 Title: Evolution of the formwork used in the temple of the Sagrada Familia Authors: Gómez Serrano, José; Espel, R; Grima, R; Burry, Mc; Aguado de Cea, Antonio Abstract: The Sagrada Família is Gaudi's unfinished work, to which he exclusively dedicated his last years of life. Even though he only got to build a small part of the total, he defined the rest through models and photographs. Gaudi's design for the inside of the Temple was based on a new geometric architecture that made extensive use of ruled surfaces (paraboloids, hyperboloids, ellipsoids), opening a new field which later architects have followed. The following article aims at showing the construction complexity of these structures, especially in relation to the set-up of their formwork. The vaults, which cover the naves at 30, 45, and 60 m heights, will be discussed. This discussion will show how the construction method, and in consequence the formwork, is adapted to the construction needs according to the geometric shape, size, position, material, and repetitions of each vault. Wed, 29 May 2013 08:29:09 GMT http://hdl.handle.net/2117/19441 2013-05-29T08:29:09Z Gómez Serrano, José; Espel, R; Grima, R; Burry, Mc; Aguado de Cea, Antonio no Gaudí, Sagrada Familia, geometric architecture, formwork, molds The Sagrada Família is Gaudi's unfinished work, to which he exclusively dedicated his last years of life. Even though he only got to build a small part of the total, he defined the rest through models and photographs. Gaudi's design for the inside of the Temple was based on a new geometric architecture that made extensive use of ruled surfaces (paraboloids, hyperboloids, ellipsoids), opening a new field which later architects have followed. The following article aims at showing the construction complexity of these structures, especially in relation to the set-up of their formwork. The vaults, which cover the naves at 30, 45, and 60 m heights, will be discussed. This discussion will show how the construction method, and in consequence the formwork, is adapted to the construction needs according to the geometric shape, size, position, material, and repetitions of each vault. http://hdl.handle.net/2117/19246 Title: Modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator Authors: Soto, De A R; Recasens Ferrés, Jorge Abstract: This work shows a method to obtain a hierarchy of partitions on the universe [0,1] in such a way that each of them is compatible with a refinement of Lukasiewicz indistinguishability operator. The classes of the partition at a given level present a relation of antonymy between them. Moreover, the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers. Due to this fact, they seem appropriate for modeling linguistic labels of a linguistic variable. The associated indistinguishability operators show the increasing granularity when the number of classes rises up. Wed, 15 May 2013 11:39:15 GMT http://hdl.handle.net/2117/19246 2013-05-15T11:39:15Z Soto, De A R; Recasens Ferrés, Jorge no This work shows a method to obtain a hierarchy of partitions on the universe [0,1] in such a way that each of them is compatible with a refinement of Lukasiewicz indistinguishability operator. The classes of the partition at a given level present a relation of antonymy between them. Moreover, the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers. Due to this fact, they seem appropriate for modeling linguistic labels of a linguistic variable. The associated indistinguishability operators show the increasing granularity when the number of classes rises up. http://hdl.handle.net/2117/19242 Title: A reformulation of entropy in the presence of indistinguishability operators Authors: Recasens Ferrés, Jorge; Hernández, E Abstract: This paper deals with the measurement of entropy when an indistinguishability relation on the set of events has been defined. Our approach states that entropy could be measured in terms of the observed distinguishability of the set of events. In this sense, the “observer paradigm” is introduced, and definitions for joint and conditional entropy under this paradigm are given. We also present some interesting properties and relationships with Shannon's entropy measure. Wed, 15 May 2013 10:58:59 GMT http://hdl.handle.net/2117/19242 2013-05-15T10:58:59Z Recasens Ferrés, Jorge; Hernández, E no This paper deals with the measurement of entropy when an indistinguishability relation on the set of events has been defined. Our approach states that entropy could be measured in terms of the observed distinguishability of the set of events. In this sense, the “observer paradigm” is introduced, and definitions for joint and conditional entropy under this paradigm are given. We also present some interesting properties and relationships with Shannon's entropy measure. http://hdl.handle.net/2117/19241 Title: On a geometric combinatorial problem Authors: Recasens Ferrés, Jorge Abstract: The study of the betweenness relations defined by metrics leads to a geometric problem that yields an upper bound to Turán's number T(n,5,3). Wed, 15 May 2013 10:49:35 GMT http://hdl.handle.net/2117/19241 2013-05-15T10:49:35Z Recasens Ferrés, Jorge no The study of the betweenness relations defined by metrics leads to a geometric problem that yields an upper bound to Turán's number T(n,5,3). http://hdl.handle.net/2117/19240 Title: Finite-valued indistinguishability operators Authors: Mayor, Gaspar; Recasens Ferrés, Jorge Abstract: Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this assignment cannot be done in such a precise way and the use of indistinguishability operators valued on a finite set of linguistic labels such as small, very much, etc. would be advisable. Recent advances in the study of finite-valued t-norms allow us to combine this kind of linguistic labels and makes the development of a theory of finite-valued indistinguishability operators and their application to real problems possible. Wed, 15 May 2013 10:41:27 GMT http://hdl.handle.net/2117/19240 2013-05-15T10:41:27Z Mayor, Gaspar; Recasens Ferrés, Jorge no Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this assignment cannot be done in such a precise way and the use of indistinguishability operators valued on a finite set of linguistic labels such as small, very much, etc. would be advisable. Recent advances in the study of finite-valued t-norms allow us to combine this kind of linguistic labels and makes the development of a theory of finite-valued indistinguishability operators and their application to real problems possible. http://hdl.handle.net/2117/19237 Title: Fixed points and generators of fuzzy relations Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: The fixed points of a T-indistinguishability operator are characterized as its generators in the sense of the Representation Theorem of Valverde. The geometric description of the set of fixed points of a reflexive and symmetric fuzzy relation based on this characterization gives a way to explicitly calculate it. Wed, 15 May 2013 10:27:44 GMT http://hdl.handle.net/2117/19237 2013-05-15T10:27:44Z Jacas Moral, Juan; Recasens Ferrés, Jorge no The fixed points of a T-indistinguishability operator are characterized as its generators in the sense of the Representation Theorem of Valverde. The geometric description of the set of fixed points of a reflexive and symmetric fuzzy relation based on this characterization gives a way to explicitly calculate it. http://hdl.handle.net/2117/19235 Title: E-T-lipschitzian and E-T-kernel aggregation operators Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: Lipschitzian and kernel aggregation operators with respect to natural T-indistinguishability operators ET and their powers are studied. A t-norm T is proved to be ET-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T. Wed, 15 May 2013 10:10:56 GMT http://hdl.handle.net/2117/19235 2013-05-15T10:10:56Z Jacas Moral, Juan; Recasens Ferrés, Jorge no Lipschitzian and kernel aggregation operators with respect to natural T-indistinguishability operators ET and their powers are studied. A t-norm T is proved to be ET-lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to T. http://hdl.handle.net/2117/19234 Title: Aggregation of T-transitive Relations Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: This article studies the aggregation of transitive fuzzy relations. We first find operators that preserve transitivity and then extend the results to aggregating operators. As special cases, means and some kind of suitable ordered weighted averaging (OWAs) are used to aggregate transitive fuzzy relations with respect to an Archimedean t-norm. Three families of transitive relations that allow us to modify the entries of a given relation R continuously towards the smallest and the greatest ones in our universe are given. Aggregation of nonfinite families of transitive relations also is studied and applied to calculate the degree of inclusion or similarity of fuzzy quantities (fuzzy subsets of an interval of the real line). © 2003 Wiley Periodicals, Inc. Wed, 15 May 2013 10:05:21 GMT http://hdl.handle.net/2117/19234 2013-05-15T10:05:21Z Jacas Moral, Juan; Recasens Ferrés, Jorge no This article studies the aggregation of transitive fuzzy relations. We first find operators that preserve transitivity and then extend the results to aggregating operators. As special cases, means and some kind of suitable ordered weighted averaging (OWAs) are used to aggregate transitive fuzzy relations with respect to an Archimedean t-norm. Three families of transitive relations that allow us to modify the entries of a given relation R continuously towards the smallest and the greatest ones in our universe are given. Aggregation of nonfinite families of transitive relations also is studied and applied to calculate the degree of inclusion or similarity of fuzzy quantities (fuzzy subsets of an interval of the real line). © 2003 Wiley Periodicals, Inc. http://hdl.handle.net/2117/19228 Title: The group of isometries of an indistinguishability operator Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: This paper studies some geometric aspects of indistinguishability operators (also called similarities and fuzzy equivalences). Concretely, it will be focused on the (geometric) group associated to a T-indistinguishability operator E on X (i.e., the group of all bijective maps View the MathML source such that E(x,y)=E(h(x),h(y))∀x,y∈X). The cases for E being one dimensional and invariant under translations on the real line will be completely studied. This last property will be generalized to any group and there will be stated a bijection between indistinguishability operators invariant under translations on a group and its normal fuzzy subgroups. Wed, 15 May 2013 08:28:50 GMT http://hdl.handle.net/2117/19228 2013-05-15T08:28:50Z Jacas Moral, Juan; Recasens Ferrés, Jorge no This paper studies some geometric aspects of indistinguishability operators (also called similarities and fuzzy equivalences). Concretely, it will be focused on the (geometric) group associated to a T-indistinguishability operator E on X (i.e., the group of all bijective maps View the MathML source such that E(x,y)=E(h(x),h(y))∀x,y∈X). The cases for E being one dimensional and invariant under translations on the real line will be completely studied. This last property will be generalized to any group and there will be stated a bijection between indistinguishability operators invariant under translations on a group and its normal fuzzy subgroups. http://hdl.handle.net/2117/19227 Title: One dimensional indistinguishability operators Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: The main result of the paper is an algorithm that allows us to decide when a given fuzzy relation is a one-dimensional T-indistinguishability operator for some archimedean t-norm T (in the sense of the Representation Theorem of Valverde (Fuzzy Sets and Systems 17 (1985) 313–328)). The algorithm also finds all t-norms with this property. Wed, 15 May 2013 08:20:17 GMT http://hdl.handle.net/2117/19227 2013-05-15T08:20:17Z Jacas Moral, Juan; Recasens Ferrés, Jorge no The main result of the paper is an algorithm that allows us to decide when a given fuzzy relation is a one-dimensional T-indistinguishability operator for some archimedean t-norm T (in the sense of the Representation Theorem of Valverde (Fuzzy Sets and Systems 17 (1985) 313–328)). The algorithm also finds all t-norms with this property. http://hdl.handle.net/2117/19226 Title: Fuzzy t-transitive relations: eigenvectors and generators Authors: Jacas Moral, Juan; Recasens Ferrés, Jorge Abstract: After some preliminaries, the set of generators of a generalized equality relation (T-indistinguishability operator) is studied. This set is identified with the set of the eigenvectors of the relation. The relation between the fuzzy and “metric” topologies derived from these equalities is stablished. The concept of basis is introduced and the construction of a procedure in order to calculate explicitly a basis of a T-indistinguishability operator, for T archimedean, is proposed. Wed, 15 May 2013 08:08:39 GMT http://hdl.handle.net/2117/19226 2013-05-15T08:08:39Z Jacas Moral, Juan; Recasens Ferrés, Jorge no After some preliminaries, the set of generators of a generalized equality relation (T-indistinguishability operator) is studied. This set is identified with the set of the eigenvectors of the relation. The relation between the fuzzy and “metric” topologies derived from these equalities is stablished. The concept of basis is introduced and the construction of a procedure in order to calculate explicitly a basis of a T-indistinguishability operator, for T archimedean, is proposed. http://hdl.handle.net/2117/19223 Title: How to make T-transitive a proximity relation Authors: Garmendia, L; Recasens Ferrés, Jorge Abstract: Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R macr of R with a (maximal) T-transitive relation B contained in R . The second one computes the closest homotecy of R macr or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Lukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a min-transitive relation (a similarity) is given in the last section of the paper. Wed, 15 May 2013 07:39:50 GMT http://hdl.handle.net/2117/19223 2013-05-15T07:39:50Z Garmendia, L; Recasens Ferrés, Jorge no Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R macr of R with a (maximal) T-transitive relation B contained in R . The second one computes the closest homotecy of R macr or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Lukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a min-transitive relation (a similarity) is given in the last section of the paper. http://hdl.handle.net/2117/19204 Title: A model for CAGD using fuzzy logic Authors: Jacas Moral, Juan; Monreal Pujadas, Amadeo; Recasens Ferrés, Jorge Abstract: This paper presents a first approach to a system based on fuzzy logic for the design of curves and surfaces in the context of computer aided geometric design. Bézier curves and surfaces can be seen as particular cases of this system. Tue, 14 May 2013 11:56:35 GMT http://hdl.handle.net/2117/19204 2013-05-14T11:56:35Z Jacas Moral, Juan; Monreal Pujadas, Amadeo; Recasens Ferrés, Jorge no This paper presents a first approach to a system based on fuzzy logic for the design of curves and surfaces in the context of computer aided geometric design. Bézier curves and surfaces can be seen as particular cases of this system.