Probability theory and statistical inference: econometric modelling with observational data
Probability theory and statistical inference: econometric modelling with observational data
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Modeling Decisions: Information Fusion and Aggregation Operators (Cognitive Technologies)
Modeling Decisions: Information Fusion and Aggregation Operators (Cognitive Technologies)
On a family of multivariate copulas for aggregation processes
Information Sciences: an International Journal
Preface: Editorial to the special issue devoted to "Copulas, measures and integrals"
Information Sciences: an International Journal
On copulas and their diagonals
Information Sciences: an International Journal
Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications
Algorithms for Fuzzy Clustering: Methods in c-Means Clustering with Applications
Fuzzy partitions: A way to integrate expert knowledge into distance calculations
Information Sciences: an International Journal
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Mahalanobis distance can be used in problems where variables are not independent. The presence of the covariance matrix in this expression permits us to represent the dependence between the variables. Fuzzy measures and Choquet integrals have a similar purpose. In this paper we compare these two expressions. To do so in the proper setting, we introduce a Choquet integral based distance. Then, we consider probability-density functions based on these two distances. In particular, we review the Gaussian distribution, which is based on the Mahalanobis distance and introduce another distribution based on the Choquet distance. Then, we introduce an operator that generalizes the Choquet integral and the Mahalanobis distance. It is the Choquet-Mahalanobis integral. Some propositions are also proven establishing equivalences and links between the Choquet-Mahalanobis integral, the Choquet integral, and the Mahalanobis distance.