Lebesgue and Saks decompositions of ⊥ -decomposable measures
Fuzzy Sets and Systems
Fuzzy Sets and Systems - Special memorial volume on mathematical aspects of fuzzy set theory
Integrals of set-valued functions for ⊥ -decomposable measures
Fuzzy Sets and Systems
Decomposable measures and nonlinear equations
Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Fuzzy Measure Theory
Independence and convergence in non-additive settings
Fuzzy Optimization and Decision Making
Special fuzzy measures on infinite countable sets and related aggregation functions
Fuzzy Sets and Systems
Fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices
Information Sciences: an International Journal
Aggregation-based extensions of fuzzy measures
Fuzzy Sets and Systems
On distance distribution functions-valued submeasures related to aggregation functions
Fuzzy Sets and Systems
Extension of a class of decomposable measures using fuzzy pseudometrics
Fuzzy Sets and Systems
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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 (@s)-@?-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.