http://hdl.handle.net/2099/2069 EUSTYL'98 Tue, 18 Jun 2013 05:07:05 GMT 2013-06-18T05:07:05Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2099/3680 Title: Editorial [8th. Spanish Congress on Fuzzy Logic and Technology: selection of extended new versions of papers] Authors: Burillo López, Pedro; Sobrino Cerdeiriña, Alejandro Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3680 1999-01-01T00:00:00Z Burillo López, Pedro; Sobrino Cerdeiriña, Alejandro no http://hdl.handle.net/2099/3563 Title: A mixed-signal architecture for high complexity CMOS fuzzy controllers Authors: Navas González, Rafael; Vidal Verdú, Fernando; Rodríguez-Vázquez, Ángel Abstract: Analog circuits provide better area/power efficiency than their digital counterparts for low-medium precision requirements [1]. This limit in precision, as well as the lack of design tools when compared to the digital approach, imposes a limit of complexity, hence fuzzy analog controllers are usually oriented to fast low-power systems with low-medium complexity. This paper presents a strategy to preserve most of the advantages of an analog implementation, while allowing a notorious increment of the system complexity. Such strategy consists in implementing a reduced number of rules, those that really determine the output in a lattice controller, which we call analog core, then this core is dynamically programmed to perform the computation related to a specific rule set. The data to program the analog core are stored in a memory, and constitutes the whole knowledge base in a kind of virtual rule set. An example 64-rule, 2-input, 4-bit singleton controller has been designed in a CMOS 0.7$\mu$mm technology to demonstrate the viability of the architecture. The measured input-output delay is around 500ns for a power consumption of 16mW and a chip area (without pads) of 2.65mm$^2$. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3563 1999-01-01T00:00:00Z Navas González, Rafael; Vidal Verdú, Fernando; Rodríguez-Vázquez, Ángel no Analog circuits, CMOS fuzzy controllers Analog circuits provide better area/power efficiency than their digital counterparts for low-medium precision requirements [1]. This limit in precision, as well as the lack of design tools when compared to the digital approach, imposes a limit of complexity, hence fuzzy analog controllers are usually oriented to fast low-power systems with low-medium complexity. This paper presents a strategy to preserve most of the advantages of an analog implementation, while allowing a notorious increment of the system complexity. Such strategy consists in implementing a reduced number of rules, those that really determine the output in a lattice controller, which we call analog core, then this core is dynamically programmed to perform the computation related to a specific rule set. The data to program the analog core are stored in a memory, and constitutes the whole knowledge base in a kind of virtual rule set. An example 64-rule, 2-input, 4-bit singleton controller has been designed in a CMOS 0.7$\mu$mm technology to demonstrate the viability of the architecture. The measured input-output delay is around 500ns for a power consumption of 16mW and a chip area (without pads) of 2.65mm$^2$. http://hdl.handle.net/2099/3562 Title: Fast prototyping of computing-oriented fuzzy logic systems Authors: Martínez Torre, José Ignacio; Deschamps, Jean Pierre; Fernández Centeno, Milagros Abstract: In this paper we propose to explore different dedicated hardware solutions in terms of area-speed trade-offs for computing-oriented fuzzy logic systems in the algorithmic abstraction level that fulfil the application requirements applying high level synthesis techniques. The main benefits of this proposal are the capability of selecting the best implementation for any application not being tied down to a predefined architecture, the use of the required number of hardware units and the reduction of the design cycle time. The results obtained in the control of a maximum power point of a photovoltaic plant are presented as an example. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3562 1999-01-01T00:00:00Z Martínez Torre, José Ignacio; Deschamps, Jean Pierre; Fernández Centeno, Milagros no Fast prototyping, Dedicated hardware, High level synthesis, Hardware reuse, Schedulling, Design cycle In this paper we propose to explore different dedicated hardware solutions in terms of area-speed trade-offs for computing-oriented fuzzy logic systems in the algorithmic abstraction level that fulfil the application requirements applying high level synthesis techniques. The main benefits of this proposal are the capability of selecting the best implementation for any application not being tied down to a predefined architecture, the use of the required number of hardware units and the reduction of the design cycle time. The results obtained in the control of a maximum power point of a photovoltaic plant are presented as an example. http://hdl.handle.net/2099/3561 Title: Formal Validation of Fuzzy Control Techniques. Perspectives Authors: Sala Piqueras, Antonio; Albertos Pérez, Pedro Abstract: In this paper, a survey of the state of the art and perspectives of two main lines of research in fuzzy control systems is presented: on one hand, the \emph{interpolative-functional line} representing fuzzy systems as parameterized universal function approximators, thus applying nonlinear control and neural network paradigms; on the other hand, a \emph{logic-formal} approach where fuzzy systems are analysed in terms of logic interpretations, exploring validation, consistency and completeness, uncertainty management and knowledge supervision. The former approach is not widely used in the control field, and asserting its possibilities is one of the main motivations of this paper. References in both lines and some abridged results in the second case are cited, in particular some of the author's contributions, to which the interested reader is referred. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3561 1999-01-01T00:00:00Z Sala Piqueras, Antonio; Albertos Pérez, Pedro no Fuzzy control, Expert control, Fuzzy logic, Validation In this paper, a survey of the state of the art and perspectives of two main lines of research in fuzzy control systems is presented: on one hand, the \emph{interpolative-functional line} representing fuzzy systems as parameterized universal function approximators, thus applying nonlinear control and neural network paradigms; on the other hand, a \emph{logic-formal} approach where fuzzy systems are analysed in terms of logic interpretations, exploring validation, consistency and completeness, uncertainty management and knowledge supervision. The former approach is not widely used in the control field, and asserting its possibilities is one of the main motivations of this paper. References in both lines and some abridged results in the second case are cited, in particular some of the author's contributions, to which the interested reader is referred. http://hdl.handle.net/2099/3560 Title: On the global stability of Takagi-Sugeno general model Authors: Matía, Fernando; Al-Hadithi, Basil M.; Jiménez, Agustín Abstract: Global stability of Takagi-Sugeno (T-S) fuzzy model is presented. First, stability conditions for T-S fuzzy model presented by Tanaka and Sugeno are reviewed. Second, new theorems for the stability of the general form of T-S model is derived in the sense of Lyapunov. The T-S model we studied includes a linear equation with a constant parameter in the consequent part of each rule while other authors have analyzed the model with no constant term, which does not represent a real system. This in turn will impose restrictions on the stability conditions derived in this field. An example is presented to illustrate the new suggested condition. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3560 1999-01-01T00:00:00Z Matía, Fernando; Al-Hadithi, Basil M.; Jiménez, Agustín no Fuzzy control, Dynamical analysis, Stability, T-S fuzzy model Global stability of Takagi-Sugeno (T-S) fuzzy model is presented. First, stability conditions for T-S fuzzy model presented by Tanaka and Sugeno are reviewed. Second, new theorems for the stability of the general form of T-S model is derived in the sense of Lyapunov. The T-S model we studied includes a linear equation with a constant parameter in the consequent part of each rule while other authors have analyzed the model with no constant term, which does not represent a real system. This in turn will impose restrictions on the stability conditions derived in this field. An example is presented to illustrate the new suggested condition. http://hdl.handle.net/2099/3559 Title: Inference of fuzzy regular grammars from examples Authors: Fortes Ruiz, Inmaculada; Morales Bueno, Rafael; Pérez de la Cruz Molina, José Luís; Triguero Ruiz, Francisco; Comino, M. A. Abstract: Let us consider the following situation: An oracle provides us with a finite set of examples considered as words belonging to a regular language. This oracle is not available again. In this paper we study a new and general inference algorithm of fuzzy regular grammars based on this set of words. This algorithm is created by adapting a process discovery method. The main issues in the adaptation are the development of a fuzzy version, the assignation of membership degrees to each production in the grammar, and the treatment of consecutive repeated symbols. In addition to this inference algorithm we present a practical use for automatically generating artistic designs. Specifically, we have collected a set of paintings by Piet Mondrian (1872-1944) and obtained new Mondrian-style paintings. To achieve this, we designed a code to transform the paintings into strings and also to carry out the reverse conversion. We view these strings, which represent the paintings, as words belonging to a regular language and from this finite set of examples infer a fuzzy regular grammar. The entire process has been implemented and some new paintings from the inference algorithm have been obtained. An art expert has judged that these computer-generated paintings are fully in the spirit of those painted by Mondrian. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3559 1999-01-01T00:00:00Z Fortes Ruiz, Inmaculada; Morales Bueno, Rafael; Pérez de la Cruz Molina, José Luís; Triguero Ruiz, Francisco; Comino, M. A. no Fuzzy regular grammars, Process discovery, Fuzzy relations, Computational learning Let us consider the following situation: An oracle provides us with a finite set of examples considered as words belonging to a regular language. This oracle is not available again. In this paper we study a new and general inference algorithm of fuzzy regular grammars based on this set of words. This algorithm is created by adapting a process discovery method. The main issues in the adaptation are the development of a fuzzy version, the assignation of membership degrees to each production in the grammar, and the treatment of consecutive repeated symbols. In addition to this inference algorithm we present a practical use for automatically generating artistic designs. Specifically, we have collected a set of paintings by Piet Mondrian (1872-1944) and obtained new Mondrian-style paintings. To achieve this, we designed a code to transform the paintings into strings and also to carry out the reverse conversion. We view these strings, which represent the paintings, as words belonging to a regular language and from this finite set of examples infer a fuzzy regular grammar. The entire process has been implemented and some new paintings from the inference algorithm have been obtained. An art expert has judged that these computer-generated paintings are fully in the spirit of those painted by Mondrian. http://hdl.handle.net/2099/3558 Title: Method of least squares applied to the generalized modus ponens with interval-valued fuzzy sets Authors: Agustench Cotilla, Eduard; Bustince Sola, Humberto Nicanor; Mohedano Salillas, Mª Victoria Abstract: Firstly we present a geometric interpretation of interval-valued fuzzy sets. Secondly, we apply the method of least squares to the fuzzy inference rules when working with these sets. We begin approximating the lower and upper extremes of the membership intervals to axb type functions by means of the method of least squares. Then we analyze a technique for evaluating the conclusion of the generalized modus ponens and we verify the fulfillment of Fukami and alumni axioms [9]. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3558 1999-01-01T00:00:00Z Agustench Cotilla, Eduard; Bustince Sola, Humberto Nicanor; Mohedano Salillas, Mª Victoria no Approximate reasoning, Fuzzy inference rules, Generalized modus ponens, Interval-valued fuzzy set, Method of least squares Firstly we present a geometric interpretation of interval-valued fuzzy sets. Secondly, we apply the method of least squares to the fuzzy inference rules when working with these sets. We begin approximating the lower and upper extremes of the membership intervals to axb type functions by means of the method of least squares. Then we analyze a technique for evaluating the conclusion of the generalized modus ponens and we verify the fulfillment of Fukami and alumni axioms [9]. http://hdl.handle.net/2099/3557 Title: On the learning of weights in some aggregation operators: the weighted mean and OWA operators Authors: Torra Ferré, Vicenç Abstract: We study the determination of weights for two types of aggregation operators: the weighted mean and the OWA operator. We assume that there is at our disposal a set of examples for which the outcome of the aggregation operator is known. In the case of the OWA operator, we compare the results obtained by our method with another one in the literature. We show that the optimal weighting vector is reached with less cost. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3557 1999-01-01T00:00:00Z Torra Ferré, Vicenç no Learning weigths, Modelling, Aggregation operators, Weighted mean, OWA operators, WOWA operators We study the determination of weights for two types of aggregation operators: the weighted mean and the OWA operator. We assume that there is at our disposal a set of examples for which the outcome of the aggregation operator is known. In the case of the OWA operator, we compare the results obtained by our method with another one in the literature. We show that the optimal weighting vector is reached with less cost. http://hdl.handle.net/2099/3556 Title: Idempotent operators on a finite chain Authors: Mas Grimalt, Margarita; Torrens Sastre, Joan; Calvo Sánchez, Tomasa; Carbonell Huguet, Marc Abstract: This work is devoted to find and study some possible idempotent operators on a finite chain $L$. Specially, all idempotent operators on $L$ which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3556 1999-01-01T00:00:00Z Mas Grimalt, Margarita; Torrens Sastre, Joan; Calvo Sánchez, Tomasa; Carbonell Huguet, Marc no T-norms, T-conorms, Idempotent operators, Labels, Expert systems, Uncertainty This work is devoted to find and study some possible idempotent operators on a finite chain $L$. Specially, all idempotent operators on $L$ which are associative, commutative and non-decreasing in each place are characterized. By adding one smoothness condition, all these operators reduce to special combinations of Minimum and Maximum. http://hdl.handle.net/2099/3555 Title: Putting together Łukasiewicz and product logics Authors: Esteva Massaguer, Francesc; Godo Lacasa, Lluís Abstract: In this paper we investigate a propositional fuzzy logical system $\L\Pi$ which contains the well-known \L ukasiewicz, Product and G\"{o}del fuzzy logics as sublogics. We define the corresponding algebraic structures, called $\L\Pi$-algebras and prove the following completeness result: a formula $\varphi$ is provable in the $\L\Pi$ logic iff it is a tautology for all linear $\L\Pi$-algebras. Moreover, linear $\L\Pi$-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3555 1999-01-01T00:00:00Z Esteva Massaguer, Francesc; Godo Lacasa, Lluís no Ł∏ algebras In this paper we investigate a propositional fuzzy logical system $\L\Pi$ which contains the well-known \L ukasiewicz, Product and G\"{o}del fuzzy logics as sublogics. We define the corresponding algebraic structures, called $\L\Pi$-algebras and prove the following completeness result: a formula $\varphi$ is provable in the $\L\Pi$ logic iff it is a tautology for all linear $\L\Pi$-algebras. Moreover, linear $\L\Pi$-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law. http://hdl.handle.net/2099/3554 Title: A reflection on what is a membership function Authors: Trillas i Gay, Enric; Alsina Català, Claudi Abstract: This paper is just a first approach to the idea that the membership function $\mu _{P}$ of a fuzzy set labelled $P$ is, basically, a measure on the set of linguistic expressions ``$x$ is $P"$ for each $x$ in the corresponding universe of discourse $X.$ Estimating that the meaning of $P$ (relatively to $X)$ is nothing else than the use of $P$ on $X,$ these ``measures'' seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the predicate $P,$ that is a basic relationship like ``$x$ is less $P$ than $y".$ The paper only deals with predicates whose use is made by means of numerical characteristics, but those cases on which the characteristics (if they exist) are not of a numerical nature are not considered. By generalizing DeLuca-Termini's sharpened order some typical membership functions are studied as measures Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3554 1999-01-01T00:00:00Z Trillas i Gay, Enric; Alsina Català, Claudi no Use of a predicate, General concept of a measure, General measures on an interval of IR, General measures and membership functions This paper is just a first approach to the idea that the membership function $\mu _{P}$ of a fuzzy set labelled $P$ is, basically, a measure on the set of linguistic expressions ``$x$ is $P"$ for each $x$ in the corresponding universe of discourse $X.$ Estimating that the meaning of $P$ (relatively to $X)$ is nothing else than the use of $P$ on $X,$ these ``measures'' seem to be reached by generalizing to a preordered set the concept of Fuzzy Measure, introduced by M. Sugeno, when the preorder translates the primary use of the predicate $P,$ that is a basic relationship like ``$x$ is less $P$ than $y".$ The paper only deals with predicates whose use is made by means of numerical characteristics, but those cases on which the characteristics (if they exist) are not of a numerical nature are not considered. By generalizing DeLuca-Termini's sharpened order some typical membership functions are studied as measures http://hdl.handle.net/2099/3553 Title: Truth and utility in fuzzy logic Authors: Sobrino Cerdeiriña, Alejandro Abstract: The notion of degree of truth used in fuzzy logic can be interpreted in terms of partial truth or in terms of utility. By investigating how these interpretations fit in with Tarski's definition of truth, this paper explores some of their implications and their consequences for the foundations and credibility of fuzzy logic. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3553 1999-01-01T00:00:00Z Sobrino Cerdeiriña, Alejandro no Vagueness, Truth, Utility, Fuzzy logic The notion of degree of truth used in fuzzy logic can be interpreted in terms of partial truth or in terms of utility. By investigating how these interpretations fit in with Tarski's definition of truth, this paper explores some of their implications and their consequences for the foundations and credibility of fuzzy logic. http://hdl.handle.net/2099/3552 Title: Some practical problems in fuzzy sets-based decision support systems Authors: Sancho Royo, Antonio; Verdegay, José Luis; Vergara-Moreno, Edmundo Abstract: In this paper some problems arising in the interface between two different areas, Decision Support Systems and Fuzzy Sets and Systems, are considered. The Model-Base Management System of a Decision Support System which involves some fuzziness is considered, and in that context the question, first, of the practical determination of membership functions, second of the management of the fuzziness in some optimisation models, and finally of using fuzzy rules for terminating conventional algorithms are presented, discussed and analyzed. Finally, for the concrete case of the Travelling Salesman Problem, and as an illustration of determination, management and using of fuzzy rules, a new algorithm easy of implementing in the Model-Base Management System of any oriented Decision Support System is shown. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3552 1999-01-01T00:00:00Z Sancho Royo, Antonio; Verdegay, José Luis; Vergara-Moreno, Edmundo no Decision support system, Fuzzy rules, Membership function, Travelling salesman problem, Algorithm In this paper some problems arising in the interface between two different areas, Decision Support Systems and Fuzzy Sets and Systems, are considered. The Model-Base Management System of a Decision Support System which involves some fuzziness is considered, and in that context the question, first, of the practical determination of membership functions, second of the management of the fuzziness in some optimisation models, and finally of using fuzzy rules for terminating conventional algorithms are presented, discussed and analyzed. Finally, for the concrete case of the Travelling Salesman Problem, and as an illustration of determination, management and using of fuzzy rules, a new algorithm easy of implementing in the Model-Base Management System of any oriented Decision Support System is shown. http://hdl.handle.net/2099/3551 Title: Towards a fuzzy computability? Authors: Moraga, Claudio Abstract: The subject of the present paper is the study of fuzzy computability based on fuzzy Turing machines. Two different models of fuzzy Turing machines will be discussed. It is shown that most work on fuzzy mathematics may be conducted within the frame of classical computability and the rest falls within the area of computability of the reals. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3551 1999-01-01T00:00:00Z Moraga, Claudio no Fuzzy Turing machines The subject of the present paper is the study of fuzzy computability based on fuzzy Turing machines. Two different models of fuzzy Turing machines will be discussed. It is shown that most work on fuzzy mathematics may be conducted within the frame of classical computability and the rest falls within the area of computability of the reals. http://hdl.handle.net/2099/3550 Title: The limits of fuzzy logic Authors: Castro Peña, Juan Luis Abstract: In this paper we try to answer to the following questions: What can be made by applying fuzzy logic? and What can not be made by applying fuzzy logic? The question will be analyzed from both theoretical and applied point of view. A (partial) answer will be given for three topics: a) as calculus procedure b) as reasoning mechanism and c) as engineering tool. Fri, 01 Jan 1999 00:00:00 GMT http://hdl.handle.net/2099/3550 1999-01-01T00:00:00Z Castro Peña, Juan Luis no Fuzzy logic, Fuzzy rule based systems In this paper we try to answer to the following questions: What can be made by applying fuzzy logic? and What can not be made by applying fuzzy logic? The question will be analyzed from both theoretical and applied point of view. A (partial) answer will be given for three topics: a) as calculus procedure b) as reasoning mechanism and c) as engineering tool.