A general unified framework for pairwise comparison matrices in multicriterial methods

In a Multicriteria Decision Making context, a pairwise comparison matrix $A=(a_{ij})$ is a helpful tool to determine the weighted ranking on a set $X$ of alternatives or criteria. The entry $a_{ij}$ of the matrix can assume different meanings: $a_{ij}$ can be a preference ratio (multiplicative case) or a preference difference (additive case) or $a_{ij}$ 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

A bayesian approach for on-line max and min auditing

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

A survey on pairwise comparison matrices over abelian linearly ordered groups

In this paper, we provide a survey of our results about the pairwise comparison matrices defined over abelian linearly ordered groups

Comparing inconsistency of pairwise comparison matrices depending on entries

Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods. Since several types of pairwise comparison matrices (e.g., multiplicative, additive, fuzzy) are proposed in literature, in this paper, we investigate, for which type of matrix, decision-makers are more coherent when they express their subjective preferences. By performing an experiment, we found that the additive approach provides the worst level of coherence

A comparative study on distance-based inconsistency indices defined over Abelian linearly ordered groups

Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods. Pairwise comparisons can be performed within several theoretical frameworks such as multiplicative, additive and fuzzy preference systems, which are particular instances of a more general framework based on Abelian linearly ordered groups. Although, in this general algebraic framework, three distance-based inconsistency indices have been proposed, no comparative study has been conducted on them; thus, this paper aims at filling this gap. In particular, we look for relationships and functional relations between these inconsistency indices and whenever a functional relation does not exist, we analyze their correlation and determine the regression curve of an index on another one

Computing random consistency indices and assessing priority vectors reliability

The paper deals with two crucial steps in multi-criteria decision analysis, that are consistency of the judgments and priority vectors for alternatives/criteria. From a side, several consistency indices are proposed for measuring the consistency of a Pairwise Comparison Matrix. From another one, conditions weaker than consistency, such as transitivity and weak consistency, are proposed for representing further levels of coherence of a Decision Maker when he/she expresses his/her preferences by means of reciprocal Pairwise Comparison Matrix. Firstly, in this paper, a simulation is performed in order to establish a relation between random consistency index and coherence level. Then, since weak consistency ensures reliability to priority vectors proposed in literature, a second simulation is performed in order to measure, in case of no weak consistency, the reliability of these priority vectors

Metodi, modelli e tecnologie per la Data Privacy

In un mondo sempre più digitale, dove i nostri dati risiedono in centinaia di database, come proteggere la privacy? Dalla ricerca scientifica, un progetto basato su reti bayesiane ed analytic hierarchy process, per sviluppare un modello atto a garantire la data privacy, è il vincitore del premio TR35 - giovani innovatori organizzato dal Forum Ricerca Innovazione Imprenditorialità e da Technology Review del MIT

Safeguarding the fundamental right of privacy

Technological progress and globalisation have profoundly changed the way our data is collected, accessed and used. We are in an era in which a huge rate of information of physical, biological, environmental, social and economic systems is produced. Recording, accessing and disseminating this information affect in a crucial way the progress of knowledge and the productivity of economy. Public opinion has shown a growing awareness of privacy issues over the last few years. High-profile losses of personal information and growing concerns about the nature and extent of personal information collected by organizations has led to a growing debate about the impact of ICT pervasiveness on privacy. The paper provides a brief overview of methods, tools and technologies for protecting the privacy, it encompasses disclosure control tools in statistical databases and privacy requirements prioritization, and encourages further research in this research field