bice cavallo | Università degli Studi di Napoli "Federico II" (original) (raw)

Papers by bice cavallo

Fuzzy Optimization and Decision Making, 2009

Some properties of convergence for archimedean t-conorms and t-norms are investigated and a defin... more Some properties of convergence for archimedean t-conorms and t-norms are investigated and a definition of independence for events, evaluated by a decomposable measure, is introduced. This definition generalizes the concept of independence provided by Kruse and Qiang for λ-additive fuzzy measures. Finally, we derive the two Borel–Cantelli lemmas in the context of the general framework considered.

We present a general approach to pairwise comparison matrices and introduce a consistency index t... more We present a general approach to pairwise comparison matrices and introduce a consistency index that is easy to compute in the additive and multiplicative case; in the other cases it can be computed easily starting from a suitable additive or multiplicative matrix.

In multicriteria decision making, the pairwise comparisons are an useful starting point for deter... more In multicriteria decision making, the pairwise comparisons are an useful starting point for determining a ranking on a set X = {x 1,x 2,..., x n } of alternatives or criteria; the pairwise comparison between x i and x j is quantified in a number a ij expressing how much x i is preferred to x j and the quantitative preference relation is represented by means of the matrix A = (a ij ). In literature the number a ij can assume different meanings (for instance a ratio or a difference) and so several kind of pairwise comparison matrices are proposed. A condition of consistency for the matrix A = (a ij ) is also considered; this condition, if satisfied, allows to determine a weighted ranking that perfectly represents the expressed preferences. The shape of the consistency condition depends on the meaning of the number a ij . In order to unify the different approaches and remove some drawbacks, related for example to the fuzzy additive consistency, in a previous paper we have considered pairwise comparison matrices over an abelian linearly ordered group; in this context we have provided, for a pairwise comparison matrix, a general definition of consistency and a measure of closeness to consistency. With reference to the new general unifying context, in this paper we provide some issue on a consistent matrix and a new measure of consistency that is easier to compute; moreover we provide an algorithm to check the consistency of a pairwise comparison matrix and an algorithm to build consistent matrices.

A crucial step in a decision making process is the determination of a weighted ranking on a set X... more A crucial step in a decision making process is the determination of a weighted ranking on a set X = {x1, x2, ..., xn} of alternatives with respect to criteria or experts. A way to determine the weighted ranking is to start from a relation A : (xi, xj) ∈ X × X → aij = A(xi, xj) ∈ G ⊆ R represented by the matrix

International Journal of Intelligent Systems, 2009

In a multicriteria decision making context, a pairwise comparison matrix A = (aij) is a helpful t... more In a multicriteria decision making context, a pairwise comparison matrix A = (aij) is a helpful tool to determine the weighted ranking on a set X of alternatives or criteria. The entry aij of the matrix can assume different meanings: aij can be a preference ratio (multiplicative case) or a preference difference (additive case) or aij belongs to [0, 1] and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix A has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix. © 2009 Wiley Periodicals, Inc.

International Journal of Intelligent Systems, 2010

We consider the framework of pairwise comparison matrices over abelian linearly ordered groups. W... more We consider the framework of pairwise comparison matrices over abelian linearly ordered groups. We introduce the notion of ⊙-proportionality that allows us to provide new characterizations of the consistency, efficient algorithms for checking the consistency and for building a consistent matrix. Moreover, we provide a new consistency index. © 2010 Wiley Periodicals, Inc.

Soft Computing

In this paper, at first, we provide some results on the group of vectors with components in a div... more In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered group, the related subgroup of odot\odotodot -normal vectors, the relation of odot\odotodot -proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a weighting ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages; it satisfies, for instance, the independence of scale-inversion condition.

In the paper, algorithms are provided to check the consistency of pairwise comparison matrices an... more In the paper, algorithms are provided to check the consistency of pairwise comparison matrices and to build consistent matrices over abelian linearly ordered groups. A measure of consistency is also given; this measure improves a consistent index provided in a previous paper.

In this paper we consider the on-line max query auditing problem: given a private association bet... more In this paper we consider the on-line max query auditing problem: given a private association between fields in a data set, a sequence of max queries that have already been posed about the data, their corresponding answers and a new query, deny the answer if a private information is inferred or give the true answer otherwise. We give a probabilistic definition of privacy and demonstrate that max queries can be audited in a simulatable paradigm by means of a Bayesian network. Moreover, we show how our auditing approach is able to manage user prior-knowledge.

In this paper we consider the on-line max and min query auditing problem: given a private associa... more In this paper we consider the on-line max and min query auditing problem: given a private association between fields in a data set, a sequence of max and min queries that have already been posed about the data, their corresponding answers and a new query, deny the answer if a private information is inferred or give the true answer otherwise. We give a probabilistic definition of privacy and demonstrate that max and min queries, without "no duplicates"assumption, can be audited by means of a Bayesian network. Moreover, we show how our auditing approach is able to manage user prior-knowledge.

Data & Knowledge Engineering, 2009

The paper proposes a novel approach for on-line max and min query auditing, in which a Bayesian n... more The paper proposes a novel approach for on-line max and min query auditing, in which a Bayesian network addresses disclosures based on probabilistic inferences that can be drawn from released data. In the literature, on-line max and min auditing has been addressed with some restrictive assumptions, primarily that sensitive values must be all distinct and the sensitive field has a uniform distribution. We remove these limitations and propose a model able to: provide a graphical representation of user knowledge; deal with the implicit delivery of information that derives from denying the answer to a query; and capture user background knowledge. Finally, we discuss the results of experiments aimed at assessing the scalability of the approach, in terms of response time and size of the conditional probability table, and the usefulness of the auditor system, in terms of probability to deny.

We propose a Bayesian approach to reasoning under uncertainty in on-line auditing of Statistical ... more We propose a Bayesian approach to reasoning under uncertainty in on-line auditing of Statistical Databases. A Bayesian network addresses disclosures based on probabilistic inferences that can be drawn from released data. In particular, we deal with on-line max and min auditing. Moreover, we show how our model is able to deal with the implicit delivery of information that derives from denying the answer to a query and to manage user prior-knowledge.

In this paper we consider the problem of auditing databases which support statistical sum-queries... more In this paper we consider the problem of auditing databases which support statistical sum-queries to protect the security of sensitive information. We study the special case in which the domain of the sensitive information is a discrete set; in particular, we focus on a boolean domain. Principles and techniques developed for the security of statistical databases in the case of continuous attributes do not apply here. We provide a probabilistic framework for the on-line sum-auditing and we show that sum-queries can be audited by means of a Bayesian network. Finally, we provide a preliminary analysis of the usefulness of the probabilistic approach.

Run-time binding is an important and useful feature of Service Oriented Architectures (SOA), whic... more Run-time binding is an important and useful feature of Service Oriented Architectures (SOA), which aims at selecting, among functionally equivalent services, the ones that optimize some QoS objective of the overall application. To this aim, it is particularly relevant to forecast the QoS a service will likely exhibit in future invocations.

In this paper we propose a method for on-line max auditing of dynamic statistical databases. The ... more In this paper we propose a method for on-line max auditing of dynamic statistical databases. The method extends the Bayesian approach presented in [2], [3] and [4] for static databases. A Bayesian network addresses disclosures based on probabilistic inferences that can be drawn from released data; we have developed algorithms to update the network whenever the database changes. In particular, we consider the case in which records are added or deleted, or some sensitive values change their value. The paper introduces the algorithms and discusses results of a preliminary set of of experimental trials.

Fuzzy Optimization and Decision Making, 2009

Some properties of convergence for archimedean t-conorms and t-norms are investigated and a defin... more Some properties of convergence for archimedean t-conorms and t-norms are investigated and a definition of independence for events, evaluated by a decomposable measure, is introduced. This definition generalizes the concept of independence provided by Kruse and Qiang for λ-additive fuzzy measures. Finally, we derive the two Borel–Cantelli lemmas in the context of the general framework considered.

We present a general approach to pairwise comparison matrices and introduce a consistency index t... more We present a general approach to pairwise comparison matrices and introduce a consistency index that is easy to compute in the additive and multiplicative case; in the other cases it can be computed easily starting from a suitable additive or multiplicative matrix.

In multicriteria decision making, the pairwise comparisons are an useful starting point for deter... more In multicriteria decision making, the pairwise comparisons are an useful starting point for determining a ranking on a set X = {x 1,x 2,..., x n } of alternatives or criteria; the pairwise comparison between x i and x j is quantified in a number a ij expressing how much x i is preferred to x j and the quantitative preference relation is represented by means of the matrix A = (a ij ). In literature the number a ij can assume different meanings (for instance a ratio or a difference) and so several kind of pairwise comparison matrices are proposed. A condition of consistency for the matrix A = (a ij ) is also considered; this condition, if satisfied, allows to determine a weighted ranking that perfectly represents the expressed preferences. The shape of the consistency condition depends on the meaning of the number a ij . In order to unify the different approaches and remove some drawbacks, related for example to the fuzzy additive consistency, in a previous paper we have considered pairwise comparison matrices over an abelian linearly ordered group; in this context we have provided, for a pairwise comparison matrix, a general definition of consistency and a measure of closeness to consistency. With reference to the new general unifying context, in this paper we provide some issue on a consistent matrix and a new measure of consistency that is easier to compute; moreover we provide an algorithm to check the consistency of a pairwise comparison matrix and an algorithm to build consistent matrices.

A crucial step in a decision making process is the determination of a weighted ranking on a set X... more A crucial step in a decision making process is the determination of a weighted ranking on a set X = {x1, x2, ..., xn} of alternatives with respect to criteria or experts. A way to determine the weighted ranking is to start from a relation A : (xi, xj) ∈ X × X → aij = A(xi, xj) ∈ G ⊆ R represented by the matrix

International Journal of Intelligent Systems, 2009

In a multicriteria decision making context, a pairwise comparison matrix A = (aij) is a helpful t... more In a multicriteria decision making context, a pairwise comparison matrix A = (aij) is a helpful tool to determine the weighted ranking on a set X of alternatives or criteria. The entry aij of the matrix can assume different meanings: aij can be a preference ratio (multiplicative case) or a preference difference (additive case) or aij belongs to [0, 1] and measures the distance from the indifference that is expressed by 0.5 (fuzzy case). For the multiplicative case, a consistency index for the matrix A has been provided by T.L. Saaty in terms of maximum eigenvalue. We consider pairwise comparison matrices over an abelian linearly ordered group and, in this way, we provide a general framework including the mentioned cases. By introducing a more general notion of metric, we provide a consistency index that has a natural meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix. © 2009 Wiley Periodicals, Inc.

International Journal of Intelligent Systems, 2010

We consider the framework of pairwise comparison matrices over abelian linearly ordered groups. W... more We consider the framework of pairwise comparison matrices over abelian linearly ordered groups. We introduce the notion of ⊙-proportionality that allows us to provide new characterizations of the consistency, efficient algorithms for checking the consistency and for building a consistent matrix. Moreover, we provide a new consistency index. © 2010 Wiley Periodicals, Inc.

Soft Computing

In this paper, at first, we provide some results on the group of vectors with components in a div... more In this paper, at first, we provide some results on the group of vectors with components in a divisible Abelian linearly ordered group, the related subgroup of odot\odotodot -normal vectors, the relation of odot\odotodot -proportionality and the corresponding quotient group. Then, we apply the achieved results to the groups of reciprocal and consistent matrices over divisible Abelian linearly ordered groups; this allows us to deal with the problem of deriving a weighting ranking for the alternatives from a pairwise comparison matrix. The proposed weighting vector has several advantages; it satisfies, for instance, the independence of scale-inversion condition.

In the paper, algorithms are provided to check the consistency of pairwise comparison matrices an... more In the paper, algorithms are provided to check the consistency of pairwise comparison matrices and to build consistent matrices over abelian linearly ordered groups. A measure of consistency is also given; this measure improves a consistent index provided in a previous paper.

In this paper we consider the on-line max query auditing problem: given a private association bet... more In this paper we consider the on-line max query auditing problem: given a private association between fields in a data set, a sequence of max queries that have already been posed about the data, their corresponding answers and a new query, deny the answer if a private information is inferred or give the true answer otherwise. We give a probabilistic definition of privacy and demonstrate that max queries can be audited in a simulatable paradigm by means of a Bayesian network. Moreover, we show how our auditing approach is able to manage user prior-knowledge.

In this paper we consider the on-line max and min query auditing problem: given a private associa... more In this paper we consider the on-line max and min query auditing problem: given a private association between fields in a data set, a sequence of max and min queries that have already been posed about the data, their corresponding answers and a new query, deny the answer if a private information is inferred or give the true answer otherwise. We give a probabilistic definition of privacy and demonstrate that max and min queries, without "no duplicates"assumption, can be audited by means of a Bayesian network. Moreover, we show how our auditing approach is able to manage user prior-knowledge.

Data & Knowledge Engineering, 2009

The paper proposes a novel approach for on-line max and min query auditing, in which a Bayesian n... more The paper proposes a novel approach for on-line max and min query auditing, in which a Bayesian network addresses disclosures based on probabilistic inferences that can be drawn from released data. In the literature, on-line max and min auditing has been addressed with some restrictive assumptions, primarily that sensitive values must be all distinct and the sensitive field has a uniform distribution. We remove these limitations and propose a model able to: provide a graphical representation of user knowledge; deal with the implicit delivery of information that derives from denying the answer to a query; and capture user background knowledge. Finally, we discuss the results of experiments aimed at assessing the scalability of the approach, in terms of response time and size of the conditional probability table, and the usefulness of the auditor system, in terms of probability to deny.

We propose a Bayesian approach to reasoning under uncertainty in on-line auditing of Statistical ... more We propose a Bayesian approach to reasoning under uncertainty in on-line auditing of Statistical Databases. A Bayesian network addresses disclosures based on probabilistic inferences that can be drawn from released data. In particular, we deal with on-line max and min auditing. Moreover, we show how our model is able to deal with the implicit delivery of information that derives from denying the answer to a query and to manage user prior-knowledge.

In this paper we consider the problem of auditing databases which support statistical sum-queries... more In this paper we consider the problem of auditing databases which support statistical sum-queries to protect the security of sensitive information. We study the special case in which the domain of the sensitive information is a discrete set; in particular, we focus on a boolean domain. Principles and techniques developed for the security of statistical databases in the case of continuous attributes do not apply here. We provide a probabilistic framework for the on-line sum-auditing and we show that sum-queries can be audited by means of a Bayesian network. Finally, we provide a preliminary analysis of the usefulness of the probabilistic approach.

Run-time binding is an important and useful feature of Service Oriented Architectures (SOA), whic... more Run-time binding is an important and useful feature of Service Oriented Architectures (SOA), which aims at selecting, among functionally equivalent services, the ones that optimize some QoS objective of the overall application. To this aim, it is particularly relevant to forecast the QoS a service will likely exhibit in future invocations.

In this paper we propose a method for on-line max auditing of dynamic statistical databases. The ... more In this paper we propose a method for on-line max auditing of dynamic statistical databases. The method extends the Bayesian approach presented in [2], [3] and [4] for static databases. A Bayesian network addresses disclosures based on probabilistic inferences that can be drawn from released data; we have developed algorithms to update the network whenever the database changes. In particular, we consider the case in which records are added or deleted, or some sensitive values change their value. The paper introduces the algorithms and discusses results of a preliminary set of of experimental trials.