This paper extends the theory of turbulence of Hjorth to certain classes of equivalence relations that cannot be induced by Polish actions. It applies this theory to analyze the quasi-isometry relation and finite Gromov-Hausdorff distance relation in the space of isometry classes of pointed proper metric spaces, called the Gromov space.

An approach to point-free geometry based on the notion of a quasi-metric is proposed in which the primitives are the regions and a non symmetric distance between regions. The intended models are the bounded regular closed subsets of a metric space together with the Hausdorff excess measure.

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

in this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. we have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. we have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

Multi-objective (vector) combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability) are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05...

In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing par...

We consider the sets of quasi-regular points in the countable symbolic space. We measure the sizes of the sets by Billingsley-Hausdorff dimension defined by Gibbs measures. It is shown that the dimensions of those sets, always bounded from below by the convergence exponent of the Gibbs measure, are given by a variational principle, which generalizes Li and Ma’s result and Bowen’s result.

The terminology and notation used here have been introduced in the following articles: [9], [4], [13], [12], [10], [8], [2], [3], [1], [14], [7], [11], [5], and [6]. Let M be a metric structure, and let x, y be elements of the carrier of M . The predicate x ≈ y is defined by: (Def.1) ρ(x, y) = 0. Let M be a metric structure, and let x be an element of the carrier of M . The functor x yielding a...

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

using the notion of anti fuzzy points and its besideness to and nonquasi-coincidence with a fuzzy set, new concepts in anti fuzzy subalgebras in bck/bci-algebras are introduced and their properties and relationships are investigated.