http://hdl.handle.net/2099/1488 Tue, 18 Jun 2013 21:08:59 GMT 2013-06-18T21:08:59Z webmaster.bupc@upc.edu Universitat Politècnica de Catalunya. Servei de Biblioteques i Documentació no http://hdl.handle.net/2099/1738 Title: Fuzzy morphological operators in image processing Authors: Burillo López, Pedro; Frago Paños, Noé; Fuentes-González, Ramón Abstract: 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. Wed, 01 Jan 2003 00:00:00 GMT http://hdl.handle.net/2099/1738 2003-01-01T00:00:00Z Burillo López, Pedro; Frago Paños, Noé; Fuentes-González, Ramón no Implication operators, Inclusion grade, Erosion and dilation 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. http://hdl.handle.net/2099/13216 Title: Infinitary simultaneous recursion theorem Authors: Vaggione, D. Abstract: We prove an in nitary version of the Double Recursion Theorem of Smullyan. We give some applications which show how this form of the Recursion Theo- rem can be naturally applied to obtain interesting in nite sequences of pro- grams Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13216 2008-01-01T00:00:00Z Vaggione, D. no We prove an in nitary version of the Double Recursion Theorem of Smullyan. We give some applications which show how this form of the Recursion Theo- rem can be naturally applied to obtain interesting in nite sequences of pro- grams http://hdl.handle.net/2099/13215 Title: Interval-valued fuzzy ideals generated by an interval-valued fuzzy subset in ordered semigroups Authors: Shabir, M.; Israr, Ali Khan Abstract: In this paper, we de ne the concept of interval-valued fuzzy left (right, two sided, interior, bi-) ideal in ordered semigroups. We show that the interval- valued fuzzy subset J is an interval-valued fuzzy left (right, two sided, interior, bi-) ideal generated by an interval-valued fuzzy subset A i J and J + are fuzzy left (right, two sided, interior, bi-) ideals generated by A and A + respectively Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13215 2008-01-01T00:00:00Z Shabir, M.; Israr, Ali Khan no Interval-valued fuzzy subsemigroup, Interval-valued fuzzy left (right, two-sided) ideal, Interval-valued fuzzy interior ideal, Interval-valued fuzzy bi-ideal In this paper, we de ne the concept of interval-valued fuzzy left (right, two sided, interior, bi-) ideal in ordered semigroups. We show that the interval- valued fuzzy subset J is an interval-valued fuzzy left (right, two sided, interior, bi-) ideal generated by an interval-valued fuzzy subset A i J and J + are fuzzy left (right, two sided, interior, bi-) ideals generated by A and A + respectively http://hdl.handle.net/2099/13214 Title: Orderings of fuzzy sets based on fuzzy orderings. Part II: generalizations Authors: Bodenhofer, Ulrich Abstract: In Part I of this series of papers, a general approach for ordering fuzzy sets with respect to fuzzy orderings was presented. Part I also highlighted three limitations of this approach. The present paper addresses these lim- itations and proposes solutions for overcoming them. We rst consider a fuzzi cation of the ordering relation, then ways to compare fuzzy sets with di erent heights, and nally we introduce how to re ne the ordering relation by lexicographic hybridization with a di erent ordering method Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13214 2008-01-01T00:00:00Z Bodenhofer, Ulrich no In Part I of this series of papers, a general approach for ordering fuzzy sets with respect to fuzzy orderings was presented. Part I also highlighted three limitations of this approach. The present paper addresses these lim- itations and proposes solutions for overcoming them. We rst consider a fuzzi cation of the ordering relation, then ways to compare fuzzy sets with di erent heights, and nally we introduce how to re ne the ordering relation by lexicographic hybridization with a di erent ordering method http://hdl.handle.net/2099/13213 Title: A logic approach for exceptions and anomalies in association rules Authors: Delgado, M.; Sánchez, Daniel; Ruiz, M.D. Abstract: Association rules have been used for obtaining information hidden in a database. Recent researches have pointed out that simple associations are insu cient for representing the diverse kinds of knowledge collected in a database. The use of exceptions and anomalies deal with a di erent type of knowledge sometimes more useful than simple associations. Moreover ex- ceptions and anomalies provide a more comprehensive understanding of the information provided by a database. This work intends to go deeper in the logic model studied in [5]. In the model, association rules can be viewed as general relations between two or more attributes quanti ed by means of a convenient quanti er. Using this formulation we establish the true semantics of the distinct kinds of knowledge we can nd in the database hidden in the four folds of the contingency table. The model is also useful for providing some measures for assessing the validity of those kinds of rules Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13213 2008-01-01T00:00:00Z Delgado, M.; Sánchez, Daniel; Ruiz, M.D. no Association rules have been used for obtaining information hidden in a database. Recent researches have pointed out that simple associations are insu cient for representing the diverse kinds of knowledge collected in a database. The use of exceptions and anomalies deal with a di erent type of knowledge sometimes more useful than simple associations. Moreover ex- ceptions and anomalies provide a more comprehensive understanding of the information provided by a database. This work intends to go deeper in the logic model studied in [5]. In the model, association rules can be viewed as general relations between two or more attributes quanti ed by means of a convenient quanti er. Using this formulation we establish the true semantics of the distinct kinds of knowledge we can nd in the database hidden in the four folds of the contingency table. The model is also useful for providing some measures for assessing the validity of those kinds of rules http://hdl.handle.net/2099/13212 Title: A connection between computer science and fuzzy theory: midpoints and running time of computing Authors: Casanovas, Jaume; Valero, O. Abstract: Following the mathematical formalism introduced by M. Schellekens [Elec- tronic Notes in Theoret. Comput. Sci. 1 (1995), 211-232] in order to give a common foundation for Denotational Semantics and Complexity Analysis, we obtain an application of the theory of midpoints for asymmetric distances de ned between fuzzy sets to the complexity analysis of algorithms and pro- grams. In particular we show that the average running time for the algorithm known as Largetwo is exactly a midpoint between the best and the worst case running time of computing Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13212 2008-01-01T00:00:00Z Casanovas, Jaume; Valero, O. no fuzzy set, asymmetric distance, midpoint, complexity analysis, running time of computing Following the mathematical formalism introduced by M. Schellekens [Elec- tronic Notes in Theoret. Comput. Sci. 1 (1995), 211-232] in order to give a common foundation for Denotational Semantics and Complexity Analysis, we obtain an application of the theory of midpoints for asymmetric distances de ned between fuzzy sets to the complexity analysis of algorithms and pro- grams. In particular we show that the average running time for the algorithm known as Largetwo is exactly a midpoint between the best and the worst case running time of computing http://hdl.handle.net/2099/13205 Title: Orderings of fuzzy sets based on fuzzy orderings. Part I: the basic approach Authors: Bodenhofer, Ulrich Abstract: The aim of this paper is to present a general framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known|no matter whether linear or partial Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13205 2008-01-01T00:00:00Z Bodenhofer, Ulrich no The aim of this paper is to present a general framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known|no matter whether linear or partial http://hdl.handle.net/2099/13204 Title: On the threshold of bounded pseudo-distances Authors: Trillas, Enric; Soto, Adolfo R. de Abstract: This paper deals with the relationship between bounded pseudo-distances and its associated W'-indistinguishabilities, from which the idea of threshold of transitivity comes. By the way, bounded pseudo-distances are characterized Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13204 2008-01-01T00:00:00Z Trillas, Enric; Soto, Adolfo R. de no T-indistinguishabilities, bounded-distances, threshold This paper deals with the relationship between bounded pseudo-distances and its associated W'-indistinguishabilities, from which the idea of threshold of transitivity comes. By the way, bounded pseudo-distances are characterized http://hdl.handle.net/2099/13203 Title: Exploring a syntactic notion of modal many-valued logics Authors: Bou, F.; Esteva, F.; Godo, L. Abstract: We propose a general semantic notion of modal many-valued logic. Then, we explore the di culties to characterize this notion in a syntactic way and analyze the existing literature with respect to this framework Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13203 2008-01-01T00:00:00Z Bou, F.; Esteva, F.; Godo, L. no modal fuzzy logic, modal many-valued logic We propose a general semantic notion of modal many-valued logic. Then, we explore the di culties to characterize this notion in a syntactic way and analyze the existing literature with respect to this framework http://hdl.handle.net/2099/13198 Title: Representing upper probability Measures over rational Lukasiewicz logic Authors: Marchioni, Enrico Abstract: Upper probability measures are measures of uncertainty that generalize probability measures in order to deal with non-measurable events. Following an approach that goes back to previous works by H ajek, Esteva, and Godo, we show how to expand Rational Lukasiewicz Logic by modal operators in order to reason about upper probabilities of classical Boolean events ' so that ( ' ) can be read as \the upper probability of ' ". We build the logic U (R L) for representing upper probabilities and show it to be complete w.r.t. a class of Kripke structures equipped with an upper probability measure. Finally, we prove that the set of U (R L)-satis able formulas is NP-complete. Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13198 2008-01-01T00:00:00Z Marchioni, Enrico no Upper probability measures are measures of uncertainty that generalize probability measures in order to deal with non-measurable events. Following an approach that goes back to previous works by H ajek, Esteva, and Godo, we show how to expand Rational Lukasiewicz Logic by modal operators in order to reason about upper probabilities of classical Boolean events ' so that ( ' ) can be read as \the upper probability of ' ". We build the logic U (R L) for representing upper probabilities and show it to be complete w.r.t. a class of Kripke structures equipped with an upper probability measure. Finally, we prove that the set of U (R L)-satis able formulas is NP-complete. http://hdl.handle.net/2099/13197 Title: Aggregation operators and lipschitzian conditions Authors: Recasens Ferrés, Jorge Abstract: Lipschitzian aggregation operators with respect to the natural T - indistin- guishability operator Et and their powers, and with respect to the residuation ! T with respect to a t-norm T and its powers are studied. A t-norm T is proved to be E T -Lipschitzian and -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 Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13197 2008-01-01T00:00:00Z Recasens Ferrés, Jorge no Aggregation operator, Residuation, T -indistinguishability operator, Lipschitzian condition Lipschitzian aggregation operators with respect to the natural T - indistin- guishability operator Et and their powers, and with respect to the residuation ! T with respect to a t-norm T and its powers are studied. A t-norm T is proved to be E T -Lipschitzian and -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/2099/13196 Title: Robust rank correlation coefficients on the basis of fuzzy Authors: Bodenhofer, U.; Klawonn, F. Abstract: The goal of this paper is to demonstrate that established rank correlation measures are not ideally suited for measuring rank correlation for numerical data that are perturbed by noise. We propose to use robust rank correlation measures based on fuzzy orderings. We demonstrate that the new measures overcome the robustness problems of existing rank correlation coe cients. As a rst step, this is accomplished by illustrative examples. The paper closes with an outlook on future research and applications Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13196 2008-01-01T00:00:00Z Bodenhofer, U.; Klawonn, F. no The goal of this paper is to demonstrate that established rank correlation measures are not ideally suited for measuring rank correlation for numerical data that are perturbed by noise. We propose to use robust rank correlation measures based on fuzzy orderings. We demonstrate that the new measures overcome the robustness problems of existing rank correlation coe cients. As a rst step, this is accomplished by illustrative examples. The paper closes with an outlook on future research and applications http://hdl.handle.net/2099/13175 Title: Optimization of fuzzy rule sets using a bacterial evolutionary algorithm Authors: Drobics, Mario; Botzheim, J. Abstract: In this paper we present a novel approach where we rst create a large set of (possibly) redundant rules using inductive rule learning and where we use a bacterial evolutionary algorithm to identify the best subset of rules in a subsequent step. This enables us to nd an optimal rule set with respect to a freely de nable global goal function, which gives us the possibility to integrate interpretability related quality criteria explicitly in the goal function and to consider the interplay of the overlapping fuzzy rules Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13175 2008-01-01T00:00:00Z Drobics, Mario; Botzheim, J. no In this paper we present a novel approach where we rst create a large set of (possibly) redundant rules using inductive rule learning and where we use a bacterial evolutionary algorithm to identify the best subset of rules in a subsequent step. This enables us to nd an optimal rule set with respect to a freely de nable global goal function, which gives us the possibility to integrate interpretability related quality criteria explicitly in the goal function and to consider the interplay of the overlapping fuzzy rules http://hdl.handle.net/2099/13166 Title: Fuzzy sequential pattern mining in incomplete databases Authors: Fiot, Céline; Laurent, Anne; Teisseire, Maguelonne Abstract: Recent widening of data mining application areas have lead to new issues. For instance, frequent sequence discovery techniques that were developed for customer behaviour analysis are now applied to analyse industrial or biological databases. Thus frequent sequence mining algorithm must be adapted to handle particular characteristics of these data. Among these specificities one should consider numerical attributes and incomplete data. In this paper, we propose a method for discovering crisp or fuzzy sequential patterns from an incomplete database. This approach uses partial information contained in incomplete records, only temporary discarding the missing part of the record. Experiments run on various synthetic datasets show the validity of our proposal as well in terms of quality as in terms of the robustness to the rate of missing values. Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13166 2008-01-01T00:00:00Z Fiot, Céline; Laurent, Anne; Teisseire, Maguelonne no Sequential patterns, Fuzzy sequential patterns, Missing values Recent widening of data mining application areas have lead to new issues. For instance, frequent sequence discovery techniques that were developed for customer behaviour analysis are now applied to analyse industrial or biological databases. Thus frequent sequence mining algorithm must be adapted to handle particular characteristics of these data. Among these specificities one should consider numerical attributes and incomplete data. In this paper, we propose a method for discovering crisp or fuzzy sequential patterns from an incomplete database. This approach uses partial information contained in incomplete records, only temporary discarding the missing part of the record. Experiments run on various synthetic datasets show the validity of our proposal as well in terms of quality as in terms of the robustness to the rate of missing values. http://hdl.handle.net/2099/13165 Title: Automatic video annotation with forests of fuzzy decision trees Authors: Detyniecki, Marcin; Marsala, Christophe Abstract: Nowadays, the annotation of videos with high-level semantic concepts or features is a great challenge. In this paper, this problem is tackled by learning, by means of Fuzzy Decision Trees (FDT), automatic rules based on a limited set of examples. Rules intended, in an exploitation step, to reduce the need of human usage in the process of indexation. However, when addressing large, unbalanced, multiclass example sets, a single classi er - such as the FDT - is insu cient. Therefore we introduce the use of forests of fuzzy decision trees (FFDT) and we highlight: (a) its e ectiveness on a high level feature detection task, compared to other competitive systems and (b) the e ect on performance from the number of classi ers point of view. Moreover, since the resulting indexes are, by their nature, to be used in a retrieval application, we discuss the results under the lights of a ranking (vs. a classi cation) context. Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2099/13165 2008-01-01T00:00:00Z Detyniecki, Marcin; Marsala, Christophe no Video annotation, High level Features, Forest of Fuzzy Decisions Trees Nowadays, the annotation of videos with high-level semantic concepts or features is a great challenge. In this paper, this problem is tackled by learning, by means of Fuzzy Decision Trees (FDT), automatic rules based on a limited set of examples. Rules intended, in an exploitation step, to reduce the need of human usage in the process of indexation. However, when addressing large, unbalanced, multiclass example sets, a single classi er - such as the FDT - is insu cient. Therefore we introduce the use of forests of fuzzy decision trees (FFDT) and we highlight: (a) its e ectiveness on a high level feature detection task, compared to other competitive systems and (b) the e ect on performance from the number of classi ers point of view. Moreover, since the resulting indexes are, by their nature, to be used in a retrieval application, we discuss the results under the lights of a ranking (vs. a classi cation) context.