# FCTA 2013 Abstracts

Full Papers
Paper Nr: 5
Title:

### Fuzzy Model-based Algorithm for 3-D Bone Tumour Analysis

Authors:

#### Joanna Czajkowska

Abstract: In this paper, a new fuzzy model based algorithm for 3-D bone tumour segmentation in MR series is introduced. The presented segmentation procedure is based on a modified fuzzy connectedness method. The there required fuzzy affinity values are estimated using a fuzzy inference system, whose fuzzy membership functions are structured on the basis of gaussian mixture model of analyzed image regions. The 3-D fuzzy tumour model is generated using different MR modalities acquired during a single examination. The segmentation abilities of prototype system have been tested on a MR database consisting of 27 examinations composed of two different sequences each.

Paper Nr: 14
Title:

### Fuzzy Similarity based Fuzzy TOPSIS with Multi-distances

Authors:

#### Pasi Luukka, Mario Fedrizzi, Leoncie Niyigena and Mikael Collan

Abstract: This article introduces a new extension to fuzzy similarity based fuzzy TOPSIS that uses multi-distance in aggregation. OWA-based multi-distances are used in the aggregation process. For the weight generation in OWA the O'Hagan's method is used to find optimal weights. Several different, predefined orness values were tested. The presented method is applied to a project selection problem.

Paper Nr: 16
Title:

### Improving a Fuzzy Discretization Process by Bagging

Authors:

#### José Manuel Cadenas, María del Carmen Garrido and Raquel Martínez

Abstract: Classification problems in which the number of attributes is larger than the number of examples are increasingly common with rapid technological advances in data collection. Also numerical data are predominant in real world applications and many algorithms in supervised learning are restricted to discrete attributes. Focusing on these issues, we proposed an improvement in a fuzzy discretization method by means of introduction of a bagging process in the different phases of the method. The bagging process tries to solve problems which can appear with small size datasets. Also we show the benefits that bagging introduces in the method by means of several experiments. The experiments are validated by means of statistical test.

Paper Nr: 20
Title:

### A DPLL Procedure for the Propositional Product Logic

Authors:

#### Dušan Guller

Abstract: In the paper, we investigate the deduction problem of a formula from a finite theory in the propositional Product logic from a perspective of automated deduction.Our approach is based on the translation of a formula to an equivalent satisfiable finite order clausal theory, consisting of order clauses. An order clause is a finite set of order literals of the form $\varepsilon_1\diamond \varepsilon_2$ where $\varepsilon_i$ is either a conjunction of propositional atoms or the propositional constant $\gz$ (false) or $\gu$ (true), and $\diamond$ is a connective either $<$ or $=$. $<$ and $=$ are interpreted by the equality and standard strict linear order on $[0,1]$, respectively. A variant of the DPLL procedure, operating over order clausal theories, is proposed. The DPLL procedure is proved to be refutation sound and complete for finite order clausal theories.

Short Papers
Paper Nr: 13
Title:

### Behaviour of Fuzzy Agents within a Collaborative Design Platform

Authors:

#### Alain-Jérôme Fougères and Egon Ostrosi

Abstract: This paper presents first a fuzzy agent-based approach for assisting collaborative design, and then, an analysis of behaviours of fuzzy agents evolving within a collaborative design platform. In a collaborative design platform, more effective design decisions can be made by fuzzy agents when fuzzy design information is considered in a fuzzy interaction based process and fuzzy evolving systems. The modelling of fuzzy agents, their fuzzy interactions, their fuzzy roles, and their fuzzy organization, are presented. During design process, fuzzy agents grouped in communities interact and play fuzzy roles for converging to solutions of design. A case study of product configuration illustrates the analysis of fuzzy agents’ behaviour.

Paper Nr: 15
Title:

### Wood Piece Quality Evaluation using Choquet Integral and Fuzzy Merging

Authors:

#### Jeremy Jover, Vincent Bombardier and Andre Thomas

Abstract: This paper presents a way to evaluate the wood product quality according to his tomographic image. The use of X ray computed tomography and ad-hoc software allows to have a representation of an item (a product) before the first cutting operation. From this representation, singularity features are extracted and their impact on the product visual quality is assesed thanks to the Choquet integrals. Next, the visual quality is evaluated by merging singularity impacts and singularity number criterion using suitable operators. Three operators are compared to the mean operator which is the commonly used one when there are few knowledge on the decision process.

Paper Nr: 17
Title:

### A Fuzzy Approach to Discriminant Analysis based on the Results of an Iterative Fuzzy k-Means Method

Authors:

#### Francesco Campobasso and Annarita Fanizzi

Abstract: The common classification techniques are designed for a rigid (even if probabilistic) allocation of each unit into one of several groups. Nevertheless the dissimilarity among combined units often leads to consider the opportunity of assigning each of them to more than a single group with different degrees of membership. In previous works we proposed a fuzzy approach to discriminant analysis, structured by linearly regressing the degrees of membership of each unit to every groups on the same variables used in a preliminary clustering. In this work we show that non-linear regression models can be used more profitably than linear ones. The applicative case concerns the entrepreneurial propensity of provinces in Central and Southern Italy, even if our methodological proposal was initially conceived to assign new customers to defined groups for Customer Relationship Management (CRM) purposes.

Paper Nr: 18
Title:

### Getting Answers to Fuzzy and Flexible Searches by Easy Modelling of Real-World Knowledge

Authors:

#### Victor Pablos-Ceruelo and Susana Munoz-Hernandez

Abstract: We present a framework for merging the non-fuzzy real-world information stored in databases with the fuzzy knowledge that we (human beings) have. The interest in this aggregation is providing a (fuzzy and non-fuzzy) search engine able to answer flexible and expressive queries without sacrificing a friendly user interface. We achieve this task by using a new syntax (whose semantics are included too) for modelling the domain knowledge and a flexible and enough general structure to represent any user query. We expect this work contributes to the development of more human-oriented fuzzy search engines.

Paper Nr: 26
Title:

### The Effects of Edge Weights on Correlating Dynamical Networks - Comparing Unweighted and Weighted Brain Graphs of nervus opticus Patients

Authors:

#### Christian Moewes and Rudolf Kruse

Abstract: We are interested in the regression analysis of dynamical networks. Our goal is to predict real-valued function values from a given observation which is manifested as series of graphs. Every observation is described by a set of dependent variables that we want to predict using the dynamical graphs. These graphs change their edges over time, while the set of nodes is assumed to be constant. Such settings can be found in many real-world applications, e.g., communication networks, brain connectivity, microblogging. We apply several measures to every graph in the series to globally describe its evolution. The resulting multivariate time series is used to learn vector autoregressive (VAR) models. The parameters of these models can be used to correlate them with the dependent variables. The graph measures typically depend on the type of edges, i.e., weighted or unweighted. So do the VAR models and thus the regression results. In this paper we argue that it is beneficial to keep edge weights in this setting. To support this claim, we analyze electroencephalographic (EEG) networks from patients suffering from visual field defects. The edge weights are in the unit interval and might be thresholded. We show that dynamical network models for weighted edges lead to similar regression performances compared to those of unweighted graphs.

Posters
Paper Nr: 6
Title:

### Air Defense Threat Evaluation using Fuzzy Bayesian Classifier

Authors:

#### Wei Mei

Abstract: The connection between probability and fuzzy sets has been investigated among the community of approximate reasoning for decades. A typical viewpoint is that the grade of membership could be interpreted as a conditional probability. This note extend this viewpoint a step further by introducing the concepts of conditional probability mass function (CPMF) and the likelihood mass function (LMF). We draw the conclusion that conditional probability can be used for describing either randomness or fuzziness depending on how it is interpreted. If expanded to CPMF, then it can be used for modelling randomness; if expanded to LMF, then it can be a useful expression for modelling fuzziness. A fuzzy Bayesian theorem is derived based on the fuzziness interpretation of conditional probability. Its successful application to an example of target recognition demonstrates that the proposed fuzzy Bayesian theorem provides alternative approach for handling uncertainty.

Paper Nr: 7
Title:

### A Fuzzy Metadata to Index and Retrieve Images of Roman Mosaics

Authors:

#### Wafa Maghrebi, Mohamed A. Khabou and Adel M. Alimi

Abstract: We present a fuzzy metadata based system for indexing and retrieving images of historical Roman mosaics. The metadata consist of object fuzzy position, fuzzy inter-object spatial position, fuzzy color quantization and curvature scale space shape descriptors. The system allows two user-friendly querying modes of the indexed mosaics in the database: a textual mode using intelligent knowledge and a drawing mode using a fuzzy similarity measure. The system was tested on a database containing 200 images of historical Roman mosaics from the 1st to 4th century AD displayed in numerous Tunisian museums. Based on 100 queries of variable complexity, the system achieved a recall and precision rates of 86.6% and 87.1%, respectively, with textual queries and 72.8% and 43.9%, respectively, with drawing queries.

Paper Nr: 23
Title:

### Identification of Fuzzy Measures for Machinery Fault Diagnosis

Authors:

#### Masahiro Tsunoyama, Yuki Imai, Hayato Hori, Hirokazu Jinno, Masayuki Ogawa and Tatsuo Sato

Abstract: This paper proposes an identification method of fuzzy measure for fault diagnosis of rotating machineries using vibration spectra method. The membership degrees for spectra in fuzzy set composed of vibration spectra are obtained from the optimized membership functions. The fuzzy measure is identified by the proposed method using the partial correlation coefficients between two spectra and the weight of each spectrum given by skilled engineers. The possibility of faults are determined by the fuzzy integral that is made by using the membership degrees and fuzzy measures for spectra. This paper also evaluates the method using field data.