کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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392876 | 665194 | 2014 | 15 صفحه PDF | دانلود رایگان |

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.
Journal: Information Sciences - Volume 263, 1 April 2014, Pages 126–140