In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

in this paper, we introduce the  probabilistic normed groups. among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. we also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

The purpose of this paper is to discuss some categorical properties of probabilistic convergence spaces. Its main theses are: (1) the construct P-PrTop of probabilistic pretopological spaces is the extensional topological hull of the construct FTPcs of FT -diagonal probabilistic convergence spaces for every triangular norm T ; (2) the construct P-PsTop of probabilistic pseudotopological spaces ...

Besov spaces classify signals and images through the Besov norm, which is based on a deterministic smoothness measurement. Recently, we revealed the relationship between the Besov norm and the likelihood of an independent generalized Gaussian wavelet probabilistic model. In this paper, we extend this result by providing an information-theoretic interpretation of the Besov norm as the Shannon co...

Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of P...

Prosodic boundary detection is important to disam-biguate parsing, especially in spontaneous speech, where elliptic sentences occur frequently. Word graphs are an eecient interface between word recognition and parser. Prosodic classiication of word chains has been published earlier. The adjustments necessary for applying these classiication techniques to word graphs are discussed in this paper....

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with 13 some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and more general semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such submeasures are also studied. 15 © 2012 Else...

We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the �p-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the �p-norm of differences of parameters as the minimization of that upper bound....