In this paper, we introduce a stationary M∞-fuzzy metric on the set C B(X), where M∞-fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number and C B(X) is the class of fuzzy sets with nonempty bounded closed α-cut sets. Under the φ-contraction conditions, we give some common fixed point theorems for self-mappings in the space C B(X).

When using a third language to construct a bilingual dictionary, it is necessary to discriminate equivalencies from inappropriate words derived as a result of ambiguity in the third language. We propose a method to treat this by utilizing the structures of dictionaries to measure the nearness of the meanings of words. The resulting dictionary is a word-to-word bilingual dictionary of nouns and ...

While navigating their environments it is essential for autonomous mobile robots to actively avoid collisions with obstacles. Flying insects perform this behavioural task with ease relying mainly on information the visual system provides. Here we implement a bioinspired collision avoidance algorithm based on the extraction of nearness information from visual motion on the hexapod walking robot ...

This article considers the problem of how to formulate a framework for the study of the nearness of collections of subsets of a set (also more tersely termed families of a set). The solution to the problem stems from recent work on approach spaces, near sets, and a specialised form of gap functional. The collection of all subsets of a set equipped with a distance function is an approach space.

The focus of this article is on the detection and classification of patterns based on groupoids. The approach hinges on descriptive proximity of points in a set based on the neighborliness property. This approach lends support to image analysis and understanding and in studying nearness of image segments. A practical application of the approach is in terms of the analysis of natural images for ...

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...