On Fuzzy Confirmation Measures of Fuzzy Association Rules

Many researchers from different sciences focused their attention on quantifying the degree to which an antecedent in a rule supports a conclusion. This long-standing problem results to be particularly interesting in the case of fuzzy association rules between a fuzzy antecedent and a fuzzy consequence: in fact, rules become much more flexible in describing information hidden in the data and new interestingness measures can be defined in order to assess their relevance. This implies, in particular, a new definition of support and of confidence of the association rule. In this framework, we focus on fuzzy confirmation measures defined in terms of confidence. In this way, it is possible to propose new fuzzy confirmation measures in a setting that allows their comparison with reference to some potential properties

Monotonicity and Symmetry of IFPD Bayesian Confirmation Measures

IFPD confirmation measures are used in ranking inductive rules in Data Mining. Many measures of this kind have been defined in literature. We show how some of them are related to each other via weighted means. The special structure of IFPD measures allows to define also new monotonicity and symmetry properties which appear quite natural in such context. We also suggest a way to measure the degree of symmetry of IFPD confirmation measures

Symmetry properties and asymmetry evaluation of Bayesian Confirmation Measures

Bayesian Confirmation Measures (BCMs) are used to assess the degree to which an evidence (or premise) E supports or contradicts an hypothesis (or conclusion) H, making use of prior probability Pr(H), posterior probability Pr(H|E) and of probability of evidence Pr(E). In the literature many BCMs have been defined with the consequent need for their comparison. For this purpose, various criteria have been proposed and some of these refer to symmetry properties. We relate the set of possible symmetries of BCMs, via an isomorphism, to the dihedral group of symmetries of the square. In this way it is possible to identify 10 subsets of symmetries that can coexist, for each subset we suggest a representative BCM, defining at this aim two new BCMs. The structure of the subgroups of the dihedral group allows also to provide an algorithm that simplifies the verification of the symmetry properties. Addressing the debate on which symmetry properties should be considered as desirable and which should not, we define asymmetry measures for BCMs. In fact, different BCMs that do not satisfy a specific symmetry property may exhibit different levels of asymmetry, this way resulting more (less) desirable. The evidence for the practical use of the approach is given through the numerical evaluation of the asymmetry degrees of some BCMs, showing this way how it is possible to discover some of their characteristics, similarities and differences

Coexistence of Symmetry Properties for Bayesian Confirmation Measures

Many Bayesian Confirmation Measures have been proposed so far. They are used to assess the degree to which an evidence (or premise) E supports or contradicts an hypothesis (or conclusion) H, making use of prior probability P(H), posterior probability P(H|E) and of probability of evidence P(E). Many kinds of comparisons of those measures have already been made. Here we focus on symmetry properties of confirmation measures, which are partly inspired by classical geometric symmetries. We define symmetries relating them to the dihedral group of symmetries of the square, determining the symmetries that can coexist and reconsidering desirable/undesirable symmetry properties for a Bayesian Confirmation Measure

Conveying tourist ratings into an overall destination evaluation

The decision-making process concerning tourism destination choices is nowadays strictly related to the information gathered online and social media are the new form of tourist information offices. Viral diffusion of information through social communities influences and promotes the image and reputation of a tourist destination. New media are therefore crucial in discovering and enhancing notoriety of natural and cultural heritage of small or less known areas. We present, by means of a multicriteria methodology, a way to summarize customer (tourist) evaluations of a destination and to compare them with the DMO (Destination Management Organization) evaluation in terms of, e.g., cultural heritage, attractions and natural resources. The results are expressed as inductive rules representing how multiple ratings and reviews posted by tourists could be conveyed into single scores useful for travel destination selection and benchmarking.The decision-making process concerning tourism destination choices is nowadays strictly related to the information gathered online and social media are the new form of tourist information offices. Viral diffusion of information through social communities influences and promotes the image and reputation of a tourist destination. New media are therefore crucial in discovering and enhancing notoriety of natural and cultural heritage of small or less known areas. We present, by means of a multicriteria methodology, a way to summarize customer (tourist) evaluations of a destination and to compare them with the DMO (Destination Management Organization) evaluation in terms of, e.g., cultural heritage, attractions and natural resources. The results are expressed as inductive rules representing how multiple ratings and reviews posted by tourists could be conveyed into single scores useful for travel destination selection and benchmarking. (C) 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

Asymmetry degree as a tool for comparing interestingness measures in Decision Making: the case of Bayesian Confirmation Measures

Bayesian Confirmation Measures are used to assess the de- gree to which an evidence E supports or contradicts a conclusion H, making use of prior probability P(H), posterior probability P(H|E) and of probability of evidence P(E). Many confirmation measures have been defined till now, their use being motivated in different ways depending on the framework. Comparisons of those measures have already been made but there is an increasing interest for a deeper investigation of relationships, differences and properties. Here we focus on symmetry properties of confirmation measures which are partly inspired by classical geometric symmetries. Measures which do not satisfy a specific symmetry condition may present a different level of asymmetry: we define an asymmetry measure, some examples of its evaluation providing a practical way to appraise the asymmetry degree for Bayesian Confirmation Measures that allows to uncover some of their features, similarities and differences