Probabilistic Metric Spaces

By B. Schweizer, A. Sklar. 2011

1,851 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0217418f01521fca6eb6f9b6e95e2da29ff98e8e

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Citations in the corpus

On Lacunary Statistically Convergent Triple Sequences in Probabilistic Normed Space (2015, background): “3.[3,4] A triple (X ,N,>) is called a probabilistic normed space or shortly PN-space if X is a real vector space, N is a mapping fromX into D (for x ∈ X , the distribution functionN(x) is denoted byNx and Nx (t) is the value ofNx at t ∈ R) and > is a t-norm satisfying the following conditions: (PN-1”
Monoidal topology : a categorical approach to order, metric, and topology (2014, background): “The probabilistic metric spaces presented in 2.1 where introduced in [Menger, 1942]; for more information see [Schweizer and Sklar, 1983].”
Intuitionistic Fuzzy Information Aggregation Using Einstein Operations (2012, background): “All types of the particular operations were included in the general concepts of t-norms and t-conorms [24], [32], [35], [41], [51], which satisfy the requirements of the conjunction and disjunction operators, respectively.”
Copula-Based Approach to Accommodate Residential Self-Selection Effects in Travel Behavior Modeling (2009, methodology): “The effectiveness of a copula approach has been recognized in the statistics field for several decades now (see Schweizer and Sklar, 1983, Ch. 6), but it is only recently that copula-based methods have been explicitly recognized and employed in the finance, actuarial science, hydrological modeling,…”
Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces (2010, unknown): “1 [6].”
Distorted Copulas: Constructions and Tail Dependence (2010, methodology): “Communications in Statistics—Theory and Methods, 39: 2288–2301, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 0361-0926 print/1532-415X online DOI: 10.1080/03610920903039506 Distorted Copulas: Constructions and Tail Dependence FABRIZIO DURANTE1, RACHELE FOSCHI2, AND PETER SARKOCI1 1Department o”
Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions (2009, background): “t is not true. Somewhat surprisingly, the conditions under which a generator ψdeﬁnes a d-dimensional copula by means of (1.1) have not yet been fully clariﬁed except in two cases. Schweizer and Sklar [37] show that a generator ψinduces a bivariate copula if and only if it is convex, whereas Kimberli”
Common fixed points for R-weakly commuting in fuzzy metric spaces (2012, unknown): “Definition 2.1 (Schweizer and Sklar [24]) A continuous t-norm is a binary operation ∗ : [0, 1] × [0, 1] → [0, 1] satisfying the following conditions: (i) ∗ is commutative and associative; (ii) a ∗ 1 = a for all a ∈ [0, 1]; (iii) a ∗ b ≤ c ∗ d whenever a ≤ c and b ≤ d (a, b, c, d ∈ [0, 1]); (iv) ∗ : ”