On fuzzy-qualitative descriptions and entropy

This paper models the assessments of a group of experts when evaluating different magnitudes, features or objects by using linguistic descriptions. A new general representation of linguistic descriptions is provided by unifying ordinal and fuzzy perspectives. Fuzzy qualitative labels are proposed as a generalization of the concept of qualitative labels over a well-ordered set. A lattice structure is established in the set of fuzzy-qualitative labels to enable the introduction of fuzzy-qualitative descriptions as L-fuzzy sets. A theorem is given that characterizes finite fuzzy partitions using fuzzy-qualitative labels, the cores and supports of which are qualitative labels. This theorem leads to a mathematical justification for commonly-used fuzzy partitions of real intervals via trapezoidal fuzzy sets. The information of a fuzzy-qualitative label is defined using a measure of specificity, in order to introduce the entropy of fuzzy-qualitative descriptions. (C) 2016 Elsevier Inc. All rights reserved.Peer ReviewedPostprint (author's final draft

Synergy Modelling and Financial Valuation : the contribution of Fuzzy Integrals.

Les méthodes d’évaluation financière utilisent des opérateurs d’agrégation reposant sur les propriétés d’additivité (sommations, intégrales de Lebesgue). De ce fait, elles occultent les phénomènes de renforcement et de synergie (ou de redondance) qui peuvent exister entre les éléments d’un ensemble organisé. C’est particulièrement le cas en ce qui concerne le problème d’évaluation financière du patrimoine d’une entreprise : en effet, en pratique, il est souvent mis en évidence une importante différence de valorisation entre l’approche « valeur de la somme des éléments » (privilégiant le point de vue financier) et l’approche « somme de la valeur des différents éléments » (privilégiant le point de vue comptable). Les possibilités offertes par des opérateurs d’agrégation comme les intégrales floues (Sugeno, Grabisch, Choquet) permettent, au plan théorique, de modéliser l’effet de synergie. La présente étude se propose de valider empiriquement les modalités d’implémentation opérationnelle de ce modèle à partir d’un échantillon d’entreprises cotées ayant fait l’objet d’une évaluation lors d’une OPA.Financial valuation methods use additive aggregation operators. But a patrimony should be regarded as an organized set, and additivity makes it impossible for these aggregation operators to formalize such phenomena as synergy or mutual inhibition between the patrimony’s components. This paper considers the application of fuzzy measure and fuzzy integrals (Sugeno, Grabisch, Choquet) to financial valuation. More specifically, we show how integration with respect to a non additive measure can be used to handle positive or negative synergy in value construction.Fuzzy measure; Fuzzy integral; Aggregation operator; Synergy; Financial valuation;

An Overview of Classifier Fusion Methods

A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided

An Overview of Classifier Fusion Methods

A number of classifier fusion methods have been recently developed opening an alternative approach leading to a potential improvement in the classification performance. As there is little theory of information fusion itself, currently we are faced with different methods designed for different problems and producing different results. This paper gives an overview of classifier fusion methods and attempts to identify new trends that may dominate this area of research in future. A taxonomy of fusion methods trying to bring some order into the existing “pudding of diversities” is also provided

An intelligent system for risk classification of stock investment projects

The proposed paper demonstrates that a hybrid fuzzy neural network can serve as a risk classifier of stock investment projects. The training algorithm for the regular part of the network is based on bidirectional incremental evolution proving more efficient than direct evolution. The approach is compared with other crisp and soft investment appraisal and trading techniques, while building a multimodel domain representation for an intelligent decision support system. Thus the advantages of each model are utilised while looking at the investment problem from different perspectives. The empirical results are based on UK companies traded on the London Stock Exchange

Cosmological Deformation of Lorentzian Spin Foam Models

We study the quantum deformation of the Barrett-Crane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector quantum gravity in de-Sitter space. This spin foam model is constructed using harmonic analysis on the quantum Lorentz group. The evaluation of simple spin networks are shown to be non commutative integrals over the quantum hyperboloid defined as a pile of fuzzy spheres. We show that the introduction of the cosmological constant removes all the infrared divergences: for any fixed triangulation, the integration over the area variables is finite for a large class of normalization of the amplitude of the edges and of the faces.Comment: 37 pages, 7 figures include

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

Coreference detection in XML metadata

Preserving data quality is an important issue in data collection management. One of the crucial issues hereby is the detection of duplicate objects (called coreferent objects) which describe the same entity, but in different ways. In this paper we present a method for detecting coreferent objects in metadata, in particular in XML schemas. Our approach consists in comparing the paths from a root element to a given element in the schema. Each path precisely defines the context and location of a specific element in the schema. Path matching is based on the comparison of the different steps of which paths are composed. The uncertainty about the matching of steps is expressed with possibilistic truth values and aggregated using the Sugeno integral. The discovered coreference of paths can help for determining the coreference of different XML schemas