Some Aggregation Operators of General Misinformation

2007

Abstract One of the major problems that artificial intelligence needs to tackle is the combination of different and potentially conflicting sources of information. Examples are multi-sensor fusion, database integration and expert systems development. In this paper we are interested in the aggregation of propositional logic-based information, a problem recently addressed in the literature on information fusion.

Uncertainty and Intelligent information Systems, 2008

We start from a general concept of conditional event in which the "third" value is not the same for all conditional events, but depends on E|H. Following the same line adopted in previous papers to point out conditional uncertainty measures ([8], [9], [3], [4]), we obtain in a natural way the axioms defining a generalized (, ⊕)-decomposable conditional information measure, which, for any fixed conditioning event H is adecomposable information measure in the sense of Kampé de Feriet and Forte ([15],[17]).

Advances in Science, Technology and Engineering Systems Journal

The aim of this paper is to continue our study of information in the setting of Pseudo-Analysis. We shall present, by axiomatic way, the definition of measures of general conditional information and we shall study particular measure by using a system of functional equations in which it is present a pseudo-operation. We know that J.Aczel is the founder of the Theory of Functional Equations and he solved the so called "Cauchy Equation". The method used in this paper consists in reducing the principal equation, to some basic known equations solved by Aczel and his school. With Benvenuti we studied a generalization of the Cauchy Equation and following these our results, we are able to give the general solution of the system and the expression for this measure of general conditional information.

Information Sciences, 2011

In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions and on special classes of aggregation functions, covering the well-known conjunctive, disjunctive, and mixed aggregation functions. Some fields of applications are included.

Decision Support Systems, 2013

In the belief function framework, a unique function is induced from the use of a combination rule so allowing to synthesize all the knowledge of the initial belief functions. When information sources are reliable and independent, the conjunctive rule of combination, proposed by Smets, may be used. This rule is equivalent to the Dempster rule without the normalization process. The conjunctive combination provides interesting properties, as the commutativity and the associativity. However, it is characterized by having the empty set, called also the conflict, as an absorbing element. So, when we apply a significant number of conjunctive combinations, the mass assigned to the conflict tends to 1 which makes impossible returning the distinction between the problem arisen during the fusion and the effect due to the absorption power of the empty set. The objective of this paper is then to define a formalism preserving the initial role of the conflict as an alarm signal announcing that there is a kind of disagreement between sources. More exactly, that allows to preserve some conflict, after the fusion by keeping only the part of conflict reflecting the opposition between the belief functions. This approach is based on dissimilarity measures and on a normalization process between belief functions. Our proposed formalism is tested and compared with the conjunctive rule of combination on synthetic belief functions.

Kybernetika Praha, 2004

Information Sciences, 1981

The weighted additivity corresponding to additivity plays a very important role in study of useful information. By using the sum property, the equation satisfied by weighted additivity has been convcrtcd to a functional equation, which is further generaliz in two ways. The real and continuous solutions of the generalized functional equations have been obtained. In terms of these real and continuous solutions, two new generalized measures of useful information have been characterized, and their particular cases have been studied. Some bounds and comparison results have also been obtained.

2012

The problem of conflict measurement between information sources knows a regain of interest. In most works related to this issue, Dempter's rule plays a central role. In this paper, we propose to revisit conflict from a different perspective. We do not make a priori assumption about dependencies and start from the definition of conflicting sets, studying its possible extensions to the framework of belief functions.

We consider the problem of merging several belief bases in the presence of integrity con- straints. We propose a logical characterization of operators having a majority behaviour or a consensual one. Then we give a representation theorem in terms of pre-orders on interpre- tations. We show the close connection between belief revision and merging operators and we show that our proposal extends the pure merging case (i.e. without integrity constraints) we study in a previous work. Finally we show that Liberatore and Schaerf commutative revision operators can be seen as a special case of merging.

Fuzzy Sets and Systems, 2004

In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed.

1997

Abstract The aim of this paper is to model the processes of the aggregation of weighted information in a linguistic framework. Three aggregation operators of weighted linguistic information are presented: linguistic weighted disjunction operator, linguistic weighted conjunction operator, and linguistic weighted averaging operator. A study of their axiomatics is presented to demonstrate their rational aggregation

2002

The paper considers the problem of merging several belief bases in the presence of integrity constraints and proposes a logical characterization of operators having a majority behaviour or a consensual one. Then a representation theorem in terms of pre-orders on interpretations is given. The close connection between belief revision and merging operators is shown and it is shown that the proposal extends the pure merging case (i.e. without integrity constraints) studied in a previous work. Finally it is shown that Liberatore and Schaerf commutative revision operators can be seen as a special case of merging.

1 2 This formulation ensures that linear constraint conditions such as w(θ) = a , w(φ | ψ) = b , and w(ψ | θ) ≤ c , where a, b, c ∈ [0, 1] and θ , φ , and ψ are Boolean combinations of the α j 's, are all permissible in K provided that the resulting constraint set K is consistent. Here a conditional constraint such as w(ψ | θ) ≤ c is interpreted as w(ψ ∧ θ) ≤ c w(θ) which is always a well-defined linear constraint, albeit vacuous when w(θ) = 0 .. See e.g.

2012

We explore how belief aggregation in the fuzzy framework can be molded into an optimization problem which helps avoid paradoxical outcomes without the fear of indecision. We further illustrate that depending on the choice of t-norm and fuzzy implication, we can find aggregation functions that produce collectively rational outcome without compromising on systematicity.

International Journal of Intelligent Systems and Applications, 2015

A problem that humans must face very often is that of having to add, melt or synthesize information, that is, combine together a series of data from various sources to reach a certain conclusion or make a certain decision. This involves the use of one or more aggregation operators capable to provide a collective preference relation. These operators must be chosen according to specific criteria taking into account the characteristic properties of each operator. Some conditions to be taken into account to identify them are the following: axiomatic strength, empirical setting, adaptability, numerical efficiency, compensation and compensation range, added behavior and scale level required of the membership functions. It is possible to establish a general list of possible mathematical properties whose verification might be desirable in certain cases: