Article ID Journal Published Year Pages File Type
392876 Information Sciences 2014 15 Pages PDF
Abstract

In this paper, some useful properties associated with the probabilistic Hausdorff distance are further derived. Especially, we provide a direct proof for an existing important result. Afterwards, the t-norm-based probabilistic decomposable measure is presented, in which the value of measure is characterized by a probability distribution function. Meantime, several examples are constructed to illustrate different notions, and then further properties are examined. Moreover, for a given Menger PM-space, a probabilistic decomposable measure can be induced by means of the resulting probabilistic Hausdorff distance. We prove that this type of measure is (σ)-⊤-probabilistic subdecomposable measure for the strongest t-norm. Furthermore, we also prove that the class of all measurable sets forms an algebra. Finally, an outer probabilistic measure is induced by a class of probabilistic decomposable measures and the t-norm. Based on this kind of measure, a Menger probabilistic pseudometric space can be obtained for a non-strict continuous Archimedean t-norm.

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Physical Sciences and Engineering Computer Science Artificial Intelligence
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