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On probabilistic ψ-contractions in Menger probabilistic metric spaces
Fuzzy Sets and Systems, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zheng, Dingwei, Wang, Pei
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Weaker Forms of Commuting Mappings in Metric and Menger Probabilistic Metric Space
Journal of Institute of Science and TechnologyThis paper aims to discuss the update of the comparative study of non-commuting mappings in metric space and probabilistic metric space. This interrelationship study in weaker commuting maps helps researchers understand, analyze, and reach their research
D. Shah +2 more
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2001
In 1942 K. Menger introduced the notion of a statistical metric space as a natural generalization of the notion of a metric space (M, d) in which the distance d(p, q) (p, q ∈ M) between p and q is replaced by a distribution function F p, q ∈ Δ+. F p,q (x) can be interpreted as the probability that the distance between p and q is less than x.
Olga Hadžić, Endre Pap
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In 1942 K. Menger introduced the notion of a statistical metric space as a natural generalization of the notion of a metric space (M, d) in which the distance d(p, q) (p, q ∈ M) between p and q is replaced by a distribution function F p, q ∈ Δ+. F p,q (x) can be interpreted as the probability that the distance between p and q is less than x.
Olga Hadžić, Endre Pap
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Complete probabilistic metric spaces
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1971Menger [4] initiated the study of probabilistic metric spaces in 1942. A probabilistic metric space (briefly a PM space) is a space in which the "distance" between any two points is a probability distribution function. These spaces are assumed to satisfy axioms which are quite similar to the axioms satisfied in an ordinary metric space.
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Completeness results in probabilistic metric spaces
Chaos, Solitons & Fractals, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alimohammady, Mohsen +2 more
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Metric Distortion Under Probabilistic Voting
ACM Conference on Economics and ComputationMetric distortion in social choice is a framework for evaluating how well voting rules minimize social cost when both voters and candidates exist in a shared metric space, with a voter's cost defined by their distance to a candidate.
Mohak Goyal, Sahasrajit Sarmasakar
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Probabilistic GOSPA: A Metric for Performance Evaluation of Multiobject Filters With Uncertainties
IEEE Transactions on Aerospace and Electronic SystemsThis correspondence presents a probabilistic generalization of the generalized optimal subpattern assignment (GOSPA) metric, termed P-GOSPA. The GOSPA metric has been widely used to evaluate the distance between finite sets, particularly in multiobject ...
Yuxuan Xia +5 more
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2003
This is a presentation without proofs of the key facts about the topology of Probabilistic Metric spaces, Probabilistic Normed spaces and Probabilistic Inner Product spaces.
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This is a presentation without proofs of the key facts about the topology of Probabilistic Metric spaces, Probabilistic Normed spaces and Probabilistic Inner Product spaces.
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Pretopologies, preuniformities and probabilistic metric spaces
Acta Mathematica Hungarica, 2006A pretopology on a given set can be generated from a filter of reflexive relations on that set (we call such a structure a preuniformity). We show that the familly of filters inducing a given pretopology on X form a com- plete lattice in the lattice of filters on X. The smallest and largest elements of that lattice are explicitly given.
Chicourrat, Monique, Charles, Horvath
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Generalized Probabilistic Metric Spaces and Fixed Point Theorems
Mathematische Nachrichten, 1986AbstractSeveral results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces.
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