DSpace Community:
http://hdl.handle.net/2099/1488
Wed, 27 Aug 2014 11:32:28 GMT2014-08-27T11:32:28Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoFuzzy morphological operators in image processing
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 GMThttp://hdl.handle.net/2099/17382003-01-01T00:00:00ZBurillo López, Pedro; Frago Paños, Noé; Fuentes-González, RamónnoImplication operators, Inclusion grade, Erosion and dilationFirst 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.Infinitary simultaneous recursion theorem
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-
gramsTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132162008-01-01T00:00:00ZVaggione, D.noWe 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-
gramsInterval-valued fuzzy ideals generated by an interval-valued fuzzy subset in ordered semigroups
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
+
respectivelyTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132152008-01-01T00:00:00ZShabir, M.; Israr, Ali KhannoInterval-valued fuzzy subsemigroup, Interval-valued fuzzy left (right, two-sided) ideal, Interval-valued fuzzy interior ideal, Interval-valued fuzzy bi-idealIn 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
+
respectivelyOrderings of fuzzy sets based on fuzzy orderings. Part II: generalizations
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 methodTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132142008-01-01T00:00:00ZBodenhofer, UlrichnoIn 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 methodA logic approach for exceptions and anomalies in association rules
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 rulesTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132132008-01-01T00:00:00ZDelgado, M.; Sánchez, Daniel; Ruiz, M.D.noAssociation 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 rulesA connection between computer science and fuzzy theory: midpoints and running time of computing
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 computingTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132122008-01-01T00:00:00ZCasanovas, Jaume; Valero, O.nofuzzy set, asymmetric distance, midpoint, complexity analysis, running time of computingFollowing 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 computingOrderings of fuzzy sets based on fuzzy orderings. Part I: the basic approach
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 partialTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132052008-01-01T00:00:00ZBodenhofer, UlrichnoThe 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 partialOn the threshold of bounded pseudo-distances
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 characterizedTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132042008-01-01T00:00:00ZTrillas, Enric; Soto, Adolfo R. denoT-indistinguishabilities, bounded-distances, thresholdThis 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 characterizedExploring a syntactic notion of modal many-valued logics
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 frameworkTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/132032008-01-01T00:00:00ZBou, F.; Esteva, F.; Godo, L.nomodal fuzzy logic, modal many-valued logicWe 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 frameworkRepresenting upper probability Measures over rational Lukasiewicz logic
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 GMThttp://hdl.handle.net/2099/131982008-01-01T00:00:00ZMarchioni, EnriconoUpper 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.Aggregation operators and lipschitzian conditions
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 TTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/131972008-01-01T00:00:00ZRecasens Ferrés, JorgenoAggregation operator, Residuation, T -indistinguishability operator, Lipschitzian conditionLipschitzian 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 TRobust rank correlation coefficients on the basis of fuzzy
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 applicationsTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/131962008-01-01T00:00:00ZBodenhofer, U.; Klawonn, F.noThe 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 applicationsOptimization of fuzzy rule sets using a bacterial evolutionary algorithm
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 rulesTue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2099/131752008-01-01T00:00:00ZDrobics, Mario; Botzheim, J.noIn 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 rulesFuzzy sequential pattern mining in incomplete databases
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 GMThttp://hdl.handle.net/2099/131662008-01-01T00:00:00ZFiot, Céline; Laurent, Anne; Teisseire, MaguelonnenoSequential patterns, Fuzzy sequential patterns, Missing valuesRecent 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.Automatic video annotation with forests of fuzzy decision trees
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 GMThttp://hdl.handle.net/2099/131652008-01-01T00:00:00ZDetyniecki, Marcin; Marsala, ChristophenoVideo annotation, High level Features, Forest of Fuzzy Decisions TreesNowadays, 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.