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This book constitutes the refereed proceedings of the 9th International Workshop on Fuzzy Logic and Applications, WILF 2011 held in Trani, Italy in August 2011. The 34 revised full papers presented were carefully reviewed and selected from 50 submissions. The papers are organized in topical sections on advances in theory of fuzzy sets, advances in fuzzy systems, advances in classification and clustering; and applications.



Advances in Theory of Fuzzy Sets

Solutions of Equation I(x,y) = I(x,I(x,y)) for Implications Derived from Uninorms

Uninorms are one of the most studied classes of aggregation functions and with more applications in the field of the aggregation of information. Their conjunctive or disjunctive behaviour is essential for their use as logical connectives and for obtaining fuzzy implications derived from uninorms. In this communication, we want to analyse which fuzzy implications derived from uninorms satisfy the iterative equation






) = 










)). This equation comes from






 → (




), a tautology in classical logic, and it is related with the law of importation respect to the minimum





Sebastia Massanet, Joan Torrens

On the Behavior of WOWA Operators

In this paper we analyze the behavior of WOWA operators, a class of functions that simultaneously generalize weighted means and OWA operators. Moreover, we introduce functions that also generalize both operators and characterize those satisfying a condition imposed to maintain the relationship among the weights.

Bonifacio Llamazares

Measuring the Amount of Knowledge for Atanassov’s Intuitionistic Fuzzy Sets

We address the problem of how to measure amount of knowledge conveyed by an Atanassov’s intuitionistic fuzzy set (A-IFS for short). The problem is useful from the point of view of a specific purpose, notably related to decision making. An amount of knowledge is strongly linked to its related amount of information. We pay particular attention to the relationship between the positive and negative information and a lack of information expressed by the hesitation margin.

Eulalia Szmidt, Janusz Kacprzyk, Paweł Bujnowski

Distributivity of Implication Operations over t-Representable T-Norms Generated from Nilpotent T-Norms

Recently, in [3], we have discussed the distributive equation of implications

$\mathcal{I}(x,\mathcal{T}_1(y,z)) = \mathcal{T}_2(\mathcal{I}(x,y),\mathcal{I}(x,z))$

over t-representable t-norms generated from strict t-norms in interval-valued fuzzy sets theory. In this work we continue these investigations, but for t-representable t-norms generated from nilpotent t-norms. As a byproduct result we show all solutions of some functional equation related to this case.

Michał Baczyński

Cuts of IF-sets Respecting Fuzzy Connectives

Intuitionistic fuzzy sets (IF-sets) are a suitable tool to describe cases where it is useful to account not only the grade of membership to a collection, but also the grade of its non-membership. We consider the


-cuts of an IF-set


as crisp sets consisting of those elements


for which the truth value (in fuzzy logic) of the statement ”


belongs to


and it is not true that


does not belong to


” is at least


. We describe properties of such cuts depending on the chosen type of conjunction and negation.

Davide Martinetti, Vladimír Janiš, Susana Montes

Generation of Interval-Valued Fuzzy Implications from K α Operators

This paper introduces the interval-valued fuzzy implications generated from fuzzy implications and from



operators showing that such construction generalizes the canonical representation of fuzzy implications. In addition, we also analyzed their conjugate construction preserving their main properties.

Renata Hax Sander Reiser, Benjamín René Callejas Bedregal

An Approach to General Quantification Using Representation by Levels

In this paper we propose an extension of generalized quantification to the fuzzy case using a recently proposed level representation of fuzziness. The level representation allows the extension of crisp quantification to the fuzzy case in a simple way, keeping all its properties. The expressive power of this extension to the theory of generalized quantifiers goes far beyond the usual fuzzy quantification framework based on absolute and relative fuzzy quantifiers. The proposal offer many potentially interesting possibilities for developing applications inspired in the Computing with Words and Perceptions paradigm, remarkably linguistic summarization of data.

Daniel Sánchez, Miguel Delgado, María-Amparo Vila

Towards Learning Fuzzy DL Inclusion Axioms

Fuzzy Description Logics (DLs) are logics that allow to deal with vague structured knowledge. Although a relatively important amount of work has been carried out in the last years concerning the use of fuzzy DLs as ontology languages, the problem of automatically managing fuzzy ontologies has received no attention so far. We report here our preliminary investigation on this issue by describing a method for inducing inclusion axioms in a fuzzy DL-Lite like DL.

Francesca A. Lisi, Umberto Straccia

A Rough Set Approach to Spatio-temporal Outlier Detection

Detecting outliers which are grossly different from or inconsistent with the remaining spatio-temporal dataset is a major challenge in real-world knowledge discovery and data mining applications. In this paper, we deal with the outlier detection problem in spatio-temporal data and we describe a rough set approach that finds the top outliers in an unlabeled spatio-temporal dataset. The proposed method, called Rough Outlier Set Extraction (ROSE), relies on a rough set theoretic representation of the outlier set using the rough set approximations, i.e. lower and upper approximations. It is also introduced a new set, called Kernel set, a representative subset of the original dataset, significative to outlier detection. Experimental results on real world datasets demonstrate its superiority over results obtained by various clustering algorithms. It is also shown that the kernel set is able to detect the same outliers set but with such less computational time.

Alessia Albanese, Sankar K. Pal, Alfredo Petrosino

Advances in Fuzzy Systems

From Fuzzy Models to Granular Fuzzy Models

Fuzzy models occupy one of the dominant positions on the research agenda of fuzzy sets exhibiting a wealth of conceptual developments and algorithmic pursuits as well as a plethora of applications. Granular fuzzy modeling dwelling on the principles of fuzzy modeling opens new horizons of investigations and augments the existing design methodology exploited in fuzzy modeling. In a nutshell, granular fuzzy models are constructs built upon fuzzy models or a family of fuzzy models. We elaborate on a number of compelling reasons behind the emergence of granular fuzzy modelling, and granular modeling, in general. Information granularity present in such models plays an important role. Given a fuzzy model M, the associated granular model incorporates granular information to quantify a performance of the original model, facilitate collaborative pursuits of knowledge management and knowledge transfer. We discuss several main categories of granular fuzzy models where such categories depend upon the formalism of information granularity giving rise to interval-valued fuzzy models, fuzzy fuzzy model (fuzzy


models, for short), and rough -fuzzy models. The design of granular fuzzy models builds upon two fundamental concepts of Granular Computing: the principle of justifiable granularity and an optimal allocation (distribution) of information granularity. The first one supports a construction of information granules of a granular fuzzy model. The second one emphasizes the role of information granularity being treated as an important design asset. The underlying performance indexes guiding the design of granular fuzzy models are discussed and a multiobjective nature of the construction of these models is stressed.

Witold Pedrycz

Multi-objective Evolutionary Fuzzy Systems

Several methods have been proposed to automatically generate fuzzy rule-based systems (FRBSs) from data. At the beginning, the unique objective of these methods was to maximize the accuracy with the result of often neglecting the most distinctive feature of the FRBSs, namely their interpretability. Thus, in the last years, the automatic generation of FRBSs from data has been handled as a multi-objective optimization problem, with accuracy and interpretability as objectives. Multi-objective evolutionary algorithms (MOEAs) have been so often used in this context that the FRBSs generated by exploiting MOEAs have been denoted as multi-objective evolutionary fuzzy systems. In this paper, we introduce a taxonomy of the different approaches which have been proposed in this framework. For each node of the taxonomy, we describe the relevant works pointing out the most interesting features. Finally, we highlight current trends and future directions.

Pietro Ducange, Francesco Marcelloni

Interpretability, Interpolation and Rule Weights in Linguistic Fuzzy Modeling

Linguistic fuzzy modeling that is usually implemented using Mamdani type of fuzzy systems suffers from the lack of accuracy and high computational costs. The paper shows that product-sum inference is an immediate remedy to both problems and that in this case it is sufficient to consider symmetrical output membership functions. For the identification of the latter, a numerically efficient method is suggested and arising interpretational aspects are discussed. Additionally, it is shown that various rule weighting schemes brought into the game to improve accuracy in linguistic modeling only increase computational overhead and can be reduced to the proposed model configuration with no loss of information.

Andri Riid, Ennu Rüstern

A Double Axis Classification of Interpretability Measures for Linguistic Fuzzy Rule-Based Systems

In this paper, we present a simple classification of the papers devoted to interpretability of Linguistic Fuzzy Rule-Based Systems attending to the type of interpretability measures and the part of the system for which they are applied, i.e., a double axis classification. A taxonomy considering this double axis is used to easily categorize the proposals in the existing literature. In this way, this work also represents a simple summary of the current state-of-the-art to assess the interpretability of Linguistic Fuzzy Rule-Based Systems.

M. J. Gacto, R. Alcalá, F. Herrera

Tagging Ontologies with Fuzzy WordNet Domains

The use of WordNet Domains is confined in the present days to Text Mining field. Moreover, the tagging of WordNet synsets with WordNet Domain labels is a crisp one. This paper introduces an approach for automatically tagging both ontologies and their concepts with WordNet domains in a fuzzy fashion, for topic classification purposes. Our fuzzy WordNet Domains model is presented as well as our domain disambiguation procedure. Experiments show promising results and are introduced in this paper as well as a final discussion on envisioned scenarios for our approach.

Angela Locoro

On the Notions of Residuated-Based Coherence and Bilattice-Based Consistence

Different notions of coherence and consistence have been proposed in the literature on fuzzy systems. In this work we focus on the relationship between some of the approaches developed, on the one hand, based on residuated lattices and, on the other hand, based on the theory of bilattices.

Carlos V. Damásio, Nicolás Madrid, M. Ojeda-Aciego

Investigation of Evolving Fuzzy Systems Methods FLEXFIS and eTS on Predicting Residential Prices

In this paper, we investigate on-line fuzzy modeling for predicting the prices of residential premises using the concept of evolving fuzzy models. These combine the aspects of incrementally updating the parameters and expanding the inner structure on demand with the concepts of uncertainty modeling in a possibilistic and linguistic manner (via fuzzy sets and fuzzy rule bases). The FLEXFIS and eTS approaches are evolving fuzzy models used to compare with an expert-based property valuating method as well as with a classic genetic fuzzy system. We use a real-world dataset taken from a cadastral system for that comparison.

Bogdan Trawiński, Krzysztof Trawiński, Edwin Lughofer, Tadeusz Lasota

An Empirical Study on Interpretability Indexes through Multi-objective Evolutionary Algorithms

In the realm of fuzzy systems, interpretability is really appreciated in most applications, but it becomes essential in those cases in which an intensive human-machine interaction is necessary. Accuracy and interpretability are often conflicting goals, thus we used multi-objective fuzzy modeling strategies to look for a good trade-off between them. For assessing interpretability, two different interpretability indexes have been taken into account: Average Fired Rules (AFR), which estimates how simple the comprehension of a specific rule base is, and Logical View Index (LVI), which estimates how much a rule base satisfies logical properties. With the aim of finding possible relationships between AFR and LVI, they have been used in two independent experimental sessions against the classification error. Experimental results have shown that the AFR minimization implies the LVI minimization, while the opposite is not verified.

R. Cannone, J. M. Alonso, L. Magdalena

Team Performance Evaluation Using Fuzzy Logic

In this paper we describe an experiment where team performance is evaluated by intelligent agents with fuzzy logic reasoning. Although not paramount to the study, which seeks to formally define where and how can intelligent agents help assessing team performance, fuzzy logic was implemented using a set of performance evaluation rules. Results show that the intelligent agents are able to perceive and critically evaluate a team’s performance.

Mauro Nunes, Henrique O’Neill

Interpretable Fuzzy Modeling for Decision Support in IgA Nephropathy

The aim of the work is to show the potential usefulness of interpretable fuzzy modeling for decision support in medical applications. For this pursuit, we present an approach for designing interpretable fuzzy systems concerning the prognosis prediction in Immunoglobulin A Nephropathy (IgAN). To deal with such a hard problem, prognosis has been granulated into three classes; then, a number of fuzzy rule based classifiers have been designed so that several interpretability constraints are satisfied. The resulting classifiers have been evaluated in terms of classification accuracy (also compared with a standard neural network), some of interpretability indexes, and in terms of unclassified samples. Experimental results show that such models are capable to provide both a first estimation of prognosis and a readable knowledge base that can be inspected by physicians for further analyses.

Marco Lucarelli, Ciro Castiello

Experimental Comparative Study of Compilation-Based Inference in Bayesian and Possibilitic Networks

Graphical models are important tools for representing and analyzing uncertain information. Diverse inference methods were developed for efficient computations in these models. In particular, compilation-based inference has recently triggered much research, especially in the probabilistic and the possibilistic frameworks. Even though the inference process follows the same principle in the two frameworks, it depends strongly on the specificity of each of them, namely in the interpretation of handled values (probability\possibility) and appropriate operators (*\min and +\max). This paper emphasizes on common points and unveils differences between the compilation-based inference process in the probabilistic and the possibilistic setting from a spatial viewpoint.

Raouia Ayachi, Nahla Ben Amor, Salem Benferhat

Advances in Classification and Clustering

Tuning Graded Possibilistic Clustering by Visual Stability Analysis

When compared to crisp clustering, fuzzy clustering provides more flexible and powerful data representation. However, most fuzzy methods require setting some parameters, as is the case for our Graded Possibilistic


-Means clustering method, which has two parameters in addition to number of centroids. However, for this model selection task there is no well established criterion available. Building on our own previous work on fuzzy clustering similarity indexes, we introduce a technique to evaluate the stability of clusterings by using the fuzzy Jaccard index, and use this procedure to select the most suitable values of parameters. The experiments indicate that the procedure is effective.

Stefano Rovetta, Francesco Masulli, Tameem Adel

Granular Data Regression with Neural Networks

Granular data offer an interesting vehicle of representing the available information in problems where uncertainty, inaccuracy, variability or, in general, subjectivity have to be taken into account. In this paper, we deal with a particular type of information granules, namely interval-valued data. We propose a multilayer perceptron (MLP) to model interval-valued input-output mappings. The proposed MLP comes with interval-valued weights and biases, and is trained using a genetic algorithm designed to fit data with different levels of granularity. The modeling capabilities of the proposed MLP are illustrated by means of its application to both synthetic and real world datasets.

Mario G. C. A. Cimino, Beatrice Lazzerini, Francesco Marcelloni, Witold Pedrycz

A Fuzzy Declarative Approach for Classifying Unlabeled Short Texts Using Thesauri

The classic approach to text categorisation is based on a learning process that requires a large number of labelled training texts to achieve an accurate performance. The most notable problem is that labelled texts are difficult to generate because categorising shorts texts as snippets or messages must be done by human developers, although unlabelled short texts could be easily collected. In this paper, we present an approach to categorising unlabelled short texts which only require, as user input, the category names defined by means of an ontology of terms modelled by a set of

proximity equations

. The proposed classification process is based on the ability of a fuzzy extension of the standard Prolog language named




for flexible matching and knowledge representation. This declarative approach provides a text classifier which is fast and easy to build, as well as a classification process that is easy for the user to understand. The results of the experiment showed that the proposed method achieved a reasonably good performance.

Francisco P. Romero, Pascual Julian-Iranzo, Andres Soto, Mateus Ferreira-Satler, Juan Gallardo-Casero

Subtractive Initialization of Nonnegative Matrix Factorizations for Document Clustering

Nonnegative matrix factorizations (NMF) have recently assumed an important role in several fields, such as pattern recognition, automated image exploitation, data clustering and so on. They represent a peculiar tool adopted to obtain a reduced representation of multivariate data by using additive components only, in order to learn parts-based representations of data. All algorithms for computing the NMF are iterative, therefore particular emphasis must be placed on a proper initialization of NMF because of its local convergence. The problem of selecting appropriate starting initialization matrices becomes more complex when data possess special meaning, and this is the case of document clustering. In this paper, we present a new initialization method which is based on the fuzzy subtractive scheme and used to generate initial matrices for NMF algorithms. A preliminary comparison of the proposed initialization with other commonly adopted initializations is presented by considering the application of NMF algorithms in the context of document clustering.

Gabriella Casalino, Nicoletta Del Buono, Corrado Mencar

Asymmetric Kernel Scaling for Imbalanced Data Classification

Many critical application domains present issues related to imbalanced learning - classification from imbalanced data. Using conventional techniques produces biased results, as the over-represented class dominates the learning process and tend to naturally attract predictions. As a consequence, the false negative rate may result unacceptable and the chosen classifier unusable. We propose a classification procedure based on Support Vector Machine able to effectively cope with data imbalance. Using a first step approximate solution and then a suitable kernel transformation, we enlarge asymmetrically space around the class boundary, compensating data skewness. Results show that while in case of moderate imbalance the performances are comparable to standard SVM, in case of heavily skewed data the proposed approach outperforms its competitors.

Antonio Maratea, Alfredo Petrosino

Advanced Applications

Improving Expert Meta-schedulers for Grid Computing through Weighted Rules Evolution

Grid computing is an emerging framework which has proved its effectiveness to solve large-scale computational problems in science, engineering and technology. It is founded on the sharing of distributed and heterogeneous resources capabilities of diverse domains to achieve a common goal. Given the high dynamism and uncertainty of these systems, a major issue is the workload allocation or scheduling problem which is known to be NP-hard. In this sense, recent works suggest the consideration of expert schedulers based on Fuzzy Rule-Based Systems (FRBSs) able to cope with the imprecise and changing nature of the grid system. However, the dependence of these systems with the quality of their expert knowledge makes it relevant to incorporate efficient learning strategies offering the highest accuracy. In this work, fuzzy rule-based schedulers are proposed to consider two learning stages where good quality IF-THEN rule bases acquired with a successful and well-known strategy rule learning approach, i.e., Pittsburgh, are subject to a second learning stage where the evolution of rule weights is entailed through Particle Swarm Optimization. Simulations results show that evolution of rule weights through this swarm intelligence -based strategy allows the improvement of the expert system schedules in terms of workload completion and increase the accuracy of the classical genetic learning strategy in FRBSs.

R. P. Prado, J. E. Muñoz Expósito, S. García-Galán

Generating Understandable and Accurate Fuzzy Rule-Based Systems in a Java Environment

Looking for a good interpretability-accuracy trade-off is one of the most challenging tasks on fuzzy modelling. Indeed, interpretability is acknowledged as a distinguishing capability of linguistic fuzzy systems since the proposal of Zadeh and Mamdani’s seminal ideas. Anyway, obtaining interpretable fuzzy systems is not straightforward. It becomes a matter of careful design which must cover several abstraction levels. Namely, from the design of each individual linguistic term (and its related fuzzy set) to the analysis of the cooperation among several rules, what depends on the fuzzy inference mechanism. This work gives an overview on existing tools for fuzzy system modelling. Moreover, it introduces GUAJE which is an open-source free-software java environment for building understandable and accurate fuzzy rule-based systems by means of combining several pre-existing tools.

J. M. Alonso, L. Magdalena

Serendipitous Fuzzy Item Recommendation with ProfileMatcher

In this paper an approach to serendipitous item recommendation is outlined. The model used for this task is an extension of ProfileMatcher, which is based on fuzzy metadata describing both user and items to be recommended. To address the task of recommending serendipitous resources, a priori knowledge on the relations occurring among metadata values is injected in the recommendation process. This is achieved using fuzzy graphs to model similarity relations among the elements of the fuzzy sets describing the metadata. An experimentation has been carried out on the MovieLens data set to show the impact of serendipity injection in the item recommendation process.

Danilo Dell’Agnello, Anna Maria Fanelli, Corrado Mencar, Massimo Minervini

Fuzzy Models for Fingerprint Description

Fuzzy models, traditionally used in the control field to model controllers or plants behavior, are used in this work to describe fingerprint images. The textures, in this case the directions of the fingerprint ridges, are described for the whole image by fuzzy if-then rules whose antecedents consider a part of the image and the consequent is the associated dominant texture. This low-level fuzzy model allows extracting higher-level information about the fingerprint, such as the existence of singular points and their fuzzy position within the image. This is exploited in two applications: to provide comprehensive information for users of unattended automatic recognition systems and to extract linguistic patterns to classify fingerprints.

Rosario Arjona, Andrés Gersnoviez, Iluminada Baturone

A Fuzzy Set Approach for Shape-Based Image Annotation

In this paper, we present a shape labeling approach for automatic image annotation. A fuzzy clustering process is applied to shapes represented by Fourier descriptors in order to derive a set of shape prototypes. Then, prototypes are manually annotated by textual labels corresponding to semantic categories. Based on the labeled prototypes, a new shape is automatically labeled by associating a fuzzy set that provides membership degrees of the shape to all semantic classes. Preliminary results show the suitability of the proposed approach to image annotation by encouraging its application in wider application contexts.

Giovanna Castellano, Anna Maria Fanelli, Maria Alessandra Torsello

Stable Automatic Unsupervised Segmentation of Retinal Vessels Using Self-Organizing Maps and a Modified Fuzzy C-Means Clustering

In this paper an automatic unsupervised method for the segmentation of retinal vessels is proposed. Three features are extracted from the tested image. The features are scaled down by a factor of 2 and mapped into a Self-Organizing Map. A modified Fuzzy C-Means clustering algorithm is used to divide the neuron units of the map in 2 classes. The entire image is again input for the Self-Organizing Map and the class of each pixel will be the class of its best matching unit in the Self-Organizing Map. Finally, the vessel network is post-processed using a hill climbing strategy on the connected components of the segmented image.

The experimental evaluation on the DRIVE database shows accurate extraction of vessels network and a good agreement between our segmentation and the ground truth. The mean accuracy, 0.9482 with a standard deviation of 0.0075, is outperforming the manual segmentation rates obtained by other widely used unsupervised methods. A good kappa value of 0.6565 is comparable with state-of-the-art supervised or unsupervised approaches.

Carmen Alina Lupaşcu, Domenico Tegolo

Cytoplasm Image Segmentation by Spatial Fuzzy Clustering

This work presents an approach based on image texture analysis to obtain a description of oocyte cytoplasm which could aid the clinicians in the selection of oocytes to be used in the assisted insemination process. More specifically, we address the problem of providing a description of the oocyte cytoplasm in terms of regular patterns of granularity which are related to oocyte quality. To this aim, we perform a texture analysis on the cytoplasm region and apply a spatial fuzzy clustering to segment the cytoplasm into different granular regions. Preliminary experimental results on a collection of light microscope images of oocytes are reported to show the effectiveness of the proposed approach.

Laura Caponetti, Giovanna Castellano, Vito Corsini, Teresa M. A. Basile

A Memetic Island Model for Discrete Tomography Reconstruction

Soft computing is a term indicating a coalition of methodologies, and its basic dogma is that, in general, better results can be obtained through the use of constituent methodologies in combination, rather than in a stand alone mode. Evolutionary computing belongs to this coalition, and thus memetic algorithms. Here, we present a combination of several instances of a recently proposed memetic algorithm for

discrete tomography reconstruction

, based on the

island model

parallel implementation. The combination is motivated by the fact that, even though the results of the recently proposed approach are finally better and more robust compared to other approaches, we advised that its major drawback was the computational time. The underlying combination strategy consists in separated populations of agents evolving by means of different processes which share some individuals, from time to time. Experiments were performed to test the benefits of this paradigm in terms of computational time and correctness of the solutions.

Marco Cipolla, Giosuè Lo Bosco, Filippo Millonzi, Cesare Valenti

An Intelligent Model for Self-compensation and Self-validation of Sensor Measurements

This article presents a hybrid system for self-compensation and self-validation of intelligent industrial instruments that combines a Neuro-Fuzzy model, based on the ANFIS architecture, capable of compensating errors caused by non-calibrated instruments, and a validation model based on Fuzzy Logic that provides the level of confidence of measurements. The proposed system indicates to the specialist when a new calibration must be performed. The hybrid system is tested with a differential pressure instrument, used in mining for level and pressure controls.

Javier E. Reyes Sanchez, Marley M. B. R. Vellasco, Ricardo Tanscheit


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