Mini Workshop: Methods and Models to Decision Support

Fraud Measurement Using Ordered Weighted Aggregation

Viviana Ventre

Mario Fedrizzi

Abstract: The aim of the present paper is to investigate the use of ordered weighted averaging (OWA) operators and their extensions for fraud measurement in financial transactions. Fraud is an unpleasant and expensive reality that all banks, retailers and credit granting companies face. It is important to provide expertise to help a financial institution to resolve and recover assets and develop a solid business experience and base its policy on succesful fraud prevention and recovery. We consider the fraudulent behaviour in some components (criteria) and argue that the aggregation of the corresponding information can be effectively carried on introducing a parameterized family of aggregation operators (OWA, GOWA) that provide a fusion of pieces of information when the selection of the weights supports the modelling of some aggregation imperative depending on the rationality of the experts. Then, starting from the assumption that in many situations the input arguments are linguistic because of lack of information, limited expertise of decision makers and uncertainty of the context we sketch the introduction of the uncertain linguistic ordered weighted averaging (ULOWA) operator , an extension of Yager's OWA operator. Indeed These operators are successfully used in situations where the input arguments are linguistic values. Based on the ULOWA operator, we propose an approach to evaluate the fraud profiles when more experts are involved in the fraud detection process.

Generalized Consistency and Preferences Representation by Pairwise Comparisons

Luciano Basile

L. D'Apuzzo G.

G. Marcarelli

Massimo Squillante

Abstract: Let X = {x1, x2, . . . , xn} be a set of alternatives. A crucial problem in a decision making process is the determination of a scale of relative importance for alternatives either with respect to a criterion C or an expert E. A widely used tool in Multicriteria Decision Making is the pairwise comparison matrix A = (aij), for which entry aij is a positive number expressing how much the alternative xi is preferred to the alternative xj. Under suitable hypothesis of no indifference

and transitivity

over the matrix A = (aij), the alternatives can be ordered as a chain . Then a coherent priority vector is a vector giving a weighted ranking agreeing with the chain that is a vector verifying the condition

and an intensity vector is a coherent priority vector encoding information about the intensities of the preferences, that is:

We have investigated the properties of a pairwise comparison matrix lying between the
property t and the property of consistency " aijajk = aik" and their relationships with the existence of coherent priority vectors or intensity vectors. Furthermore we have looked for operators F that, acting on the row vectors , translate the matrix A in such type of vectors.

A Proposal for a Fully Automatic Image Segmentation Algorithm

Luciano Nieddu

G. Manfredi

Abstract: Image segmentation is an important task of scene analysis bound for the subdivision of a scene into meaningful and homogeneous regions. In the last few years these techniques have experienced great growth, especially in the field of medical imaging where they can be used as a substantial aid in surgery planning and in the search of tumors, edemas, necrosis or for monitoring the development of evolving diseases such as Alzehimer. The aim of this paper is to present a fully automatic k-means segmentation algorithm for MR Images based on the MAP estimate of the region process given the observed image. In particular we model the gray scale values of the volume image with a White Gaussian Process and we superimpose a Gibbs prior on the region process. The estimation of the parameters is carried out during the segmentation process starting from an initial k-means segmentation of the whole image.

Three-Way Ordinal non Symmetrical Correspondence Analysis for the Evaluation of the Patient Satisfaction

Biagio Simonetti

Luigi D'Ambra

Eric J. Beh

Abstract: The evaluation of the performance of various aspects of the health care industry is an important aspect when monitoring the requirements of society's health needs. For hospitals, components, including sanitation, quality of care, professionalism and the caring behaviour of staff ensures that these qualities are maintained. From a statistical point of view, such monitoring often requires carrying out surveys and questionnaires. Such sources of important information usually consist of multiple questions with a variety of possible responses. One popular method of determining important relationships among variables of a categorical nature is to consider Non Symmetrical Correspondence Analysis (NSCA, D'Ambra, Lauro, 1989). Often, for many studies, the structure of categorical variables is of an ordinal nature, and the classical approach to NSCA does not guarantee that the structure of these variables is maintained. This paper looks at the application of the method of three way ordinal non symmetrical correspondence analysis (Beh, Simonetti, D'Ambra, 2005) to the evaluation of patient satisfaction on data collected in hospitals in Naples (Italy).

Parallel Factor Analysis for Compositional Data

Michele Gallo

Abstract: The compositional data have particular proprieties that pose special problems for imputation and they can rarely be analyzed with the usual multivariate statistical methods: a very strong assumption of strict positivity and the curvature that generally the compositional data present. The principal approach to analysis of compositional data is the log-ratio transformation of the original data. In this paper we examine the problems that potentially occur when one performs a Parallel Factor Analysis on the compositional data and suggest a constrained Parafac algorithm.