Given a topological dynamical system $(X,T)$, we study properties of the mean orbital pseudo-metric $\bar E$ defined by \[ \bar E(x,y)= \limsup_{n\to\infty } \min_{\sigma\in S_n}\frac{1}{n}\sum_{k=0}^{n-1}d(T^k(x),T^{\sigma(k)}(y)), \] where $x,y\in X$ and $S_n$ is permutation group $\{0,1,\ldots,n-1\}$. Let $\hat\omega_T(x)$ denote set measures quasi-generated point $x\in X$. We show that map ...

fuzzy measures are suitable in analyzing human subjective evaluation processes. several different strategies have been proposed for distance of fuzzy numbers. the distances introduced for fuzzy numbers can be categorized in two groups:1. the crisp distances which explain crisp values for the distance between two fuzzy numbers.2. the fuzzy distance which introduce a fuzzy distance for normal fuz...

We consider probability measure estimation in a nonparametric model using a leastsquares approach under the Prohorov metric framework. We summarize the computational methods and their convergence results that were developed by our group over the past two decades. New results are presented on the bias and the variance due to the approximation and the pointwise asymptotic normality of the approxi...

We compare the expressiveness of variants of Metric Temporal Logic (MTL) obtained by adding the past operators ‘S’ and ‘SI ’. We consider these variants under the “pointwise” and “continuous” interpretations over both finite and infinite models. Among other results, we show that for each of these variants the continuous version is strictly more expressive than the pointwise version. We also pro...