In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic variant of the Hennessy-Milner logic. Our approach is based on the novel notions of mimicking formulae and distance between formulae. The former are a weak versi...

di(x,A) = inf{di(x,A) : a ∈ A}, i ∈ I Hi(A,B) = max{sup di(a,B), sup di(A, b)} = sup{|di(x,A) − di(x,B)|} where a ∈ A, b ∈ B and x ∈ X It is well known that on 2 , Hi is a pseudometric, called the induced Hausdorff pseudometric induced by di, i ∈ I. Let (X,U) be a unifrom space with an augumented associated family p∗. p∗ also induces a uniformity U∗ on 2 defined by the base β∗ = {V ∗(i, ε) : i ...

The pseudometric generating property of non-additive set functions also plays an important role as the autocontinuity in fuzzy measure theory 2, 9]. A further research on this property has been presented in 4]. The aim of this paper is to prove the Egoroo's theorem and Lusin's theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric ...

<p>In this article, we introduce the concept of a soft quasi-pseudometric space. We show that every induces compatible on collection all points absolute set whenever parameter is finite. then Isbell convexity and self non-expansive map quasi-metric space has nonempty convex fixed point set.</p>

Given a Hausdorff uniform space $$X$$ with the countable gage of pseudometrics uniformity , we introduce concept approximate variation function $$f$$ mapping subset $$T$$ reals into : this is infimum family Jordan-type variations all functions $$g:T\to X$$ which differ from in each pseudometric, generated by pseudometric gage, not greater than $$\varepsilon>0$$ . We prove following compactness ...

In this paper we introduce a notion of dimension and codimension for every element of a distributive bounded lattice L. These notions prove to have a good behavior when L is a co-Heyting algebra. In this case the codimension gives rise to a pseudometric on L which satisfies the ultrametric triangle inequality. We prove that the Hausdorff completion of L with respect to this pseudometric is prec...