We generalize the concept of a fuzzy metric by introducing its approximating counterpart in order to make it more appropriate for the study of some problems related to combinatorics on words. We establish close relations between fuzzy approximating m...
The notion of indistinguishability operator was introduced by Trillas, E. in 1982, with the aim of fuzzifying the crisp notion of equivalence relation. Such operators allow for measuring the similarity between objects when there is a limitation on th...
In 1994, Matthews introduced the notion of partial metric and established a duality relationship between partial metrics and quasi-metrics defined on a set
Noticing that ordinary metrics do not present an adequate tool for the study of analytic problems of word combinatorics, as well as in the research of some problems related to theoretical computer science, we propose to use fuzzy metrics in this type...
The problem of obtaining new examples of fuzzy metrics is of interest, as this type of fuzzy measurement has been proven to be useful in engineering applications. In this context, different works have addressed the problem of deriving fuzzy metrics f...
With increasing researched focus on industrial anomaly detection, numerous methods have emerged in this domain. Notably, memory bank-based approaches coupled with k distance metrics have demonstrated remarkable performance in anomaly detection (AD) a...
In this paper, we study the concept of fuzzy metrics from the perspective of fuzzy relations. Specifically, we analyze the commonly used definitions of fuzzy metrics. We begin by noting that crisp metrics can be uniquely characterized by linear order...
In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case.
From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the
The notions of modular b-metric and modular b-metric space were introduced by Ege and Alaca as natural generalizations of the well-known and featured concepts of modular metric and modular metric space presented and discussed by Chistyakov. In partic...
We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseud...
In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of t...
The main feature of elliptical space—the topological identification of its antipodal points—could be fundamental for understanding the nature of the cosmological redshift. The physical interpretation of the mathematical (topological) stru...
In this paper, we introduce and examine the notion of a protected quasi-metric. In particular, we give some of its properties and present several examples of distinguished topological spaces that admit a compatible protected quasi-metric, such as the...
We obtain functional inequalities for functions which are metric-preserving with respect to one of the following intrinsic metrics in a canonical plane domain: hyperbolic metric or some restrictions of the triangular ratio metric, respectively, of a...
This paper explores the emerging and evolving landscape for metrics in smart cities in relation to big data challenges. Based on a review of the research literature, the problem of “synthetic quantitative indicators” along with concerns f...
The applicability of the distance aggregation problem has attracted the interest of many authors. Motivated by this fact, in this paper, we face the modular quasi-(pseudo-)metric aggregation problem, which consists of analyzing the properties that a...
We perform a theoretical and empirical analysis of a set of Cascading Style Sheets (CSS) document complexity metrics. The metrics are validated using a practical framework that demonstrates their viability. The theoretical analysis is performed using...
Metrics are important and well-known tools to measure users’ behavior in games, and gameplay in general. Particularities of location-aware games—a class of games where the player’s location plays a central role-demand specific support in metrics to a...
In this note, we present an alternative approach to the concept of a fuzzy metric, calling it a revised fuzzy metric. In contrast to the traditional approach to the theory of fuzzy metric spaces which is based on the use of a t-norm, we proceed from...
The success of Transformer architecture has seen increased interest in machine translation (MT). The translation quality of neural network-based MT transcends that of translations derived using statistical methods. This growth in MT research has enta...
Attending both the United Nations Decade of Education for Sustainable Development (2005–2014) and the United Nations 2030 Agenda for Sustainable Development, this review is presented, bearing in mind that green chemistry is essential to contrib...
Innovations are complex phenomena with important impacts on firms, regions, the economy as a whole, society, and the environment. Measuring innovation is a challenging and time-consuming task with many problems ranging from the conceptual framework t...
Offsets are increasingly used to compensate for unavoidable development impacts on species and habitats. Many offset programs pursue no net loss, but research on the success of these programs is lacking, including research on conservation banking’s s...
The cohesion value is one of the important factors used to evaluate software maintainability. However, measuring the cohesion value is a relatively difficult issue when tracing the source code manually. Although there are many static code analysis to...
The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing...
We introduce the continuity equation of transverse Kähler metrics on Sasakian manifolds and establish its interval of maximal existence. When the first basic Chern class is null (resp. negative), we prove that the solution of the (resp. normaliz...
In this paper, we study left-invariant Einstein-like metrics on the compact Lie group G. Assume that there exist two subgroups,
In this paper, we study the complete ⋆-metric semigroups and groups and the Raǐkov completion of invariant ⋆-metric groups. We obtain the following. (1) Let
Estimating and analyzing the popularity of an entity is an important task for professionals in several areas, e.g., music, social media, and cinema. Furthermore, the ample availability of online data should enhance our insights into the collective co...
We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible) processes...
Spectrum-based fault localization (SBFL) is an automated fault localization technique that uses risk evaluation metrics to compute the suspiciousness scores from program spectra. Thus, risk evaluation metrics determine the technique’s performan...
A large family of new
In this paper, we study Kropina metrics with isotropic scalar curvature. First, we obtain the expressions of Ricci curvature tensor and scalar curvature. Then, we characterize the Kropina metrics with isotropic scalar curvature on by tensor analysis.
Through an interesting physical perspective and a certain contraction of the Ricci curvature tensor in Finsler geometry, Akbar-Zadeh introduced the concept of scalar curvature for the Finsler metric. In this paper, we show that the Kropina metric is...
The selection of an accurate performance metric is highly important to evaluate the quality of a forecasting method. This evaluation may help to select between different forecasting tools of forecasting outputs, and then support many decisions within...
In this article, the error metrics used for evaluating the performance of direction of arrival (DoA) estimation are thoroughly investigated to recommend the most suitable one. This investigation highlights the lack of consensus in the literature rega...
Background/Objectives: The relationship between systemic health and ocular diseases is well-documented, with various body metrics potentially playing significant roles in the pathogenesis of cataracts, glaucoma, and age-related macular degeneration (...
In Kähler geometry, Calabi extremal metrics serves as a class of more available special metrics than Kähler metrics with constant scalar curvatures, as a generalization of Kähler Einstein metrics. In recent years, Maxwell–Einstei...
The evaluation of biodiversity is an essential tool for conservation, management of natural resources, and assessment of ecosystem functioning. Choosing an appropriate and understandable diversity metric is critical to ultimately make better decision...
In this paper, we study those fuzzy metrics M on X, in the George and Veeramani’s sense, such that
Selecting the proper performance metric constitutes a key issue for most classification problems in the field of machine learning. Although the specialized literature has addressed several topics regarding these metrics, their symmetries have yet to...
Metrics are key elements that can give us valuable information about the effectiveness of agile software development processes, particularly considering the Scrum environment. This study aims to learn about the metrics adopted to assess agile develop...
With the rapid advancement of large language models (LLMs), recent systems have demonstrated increasing capability in understanding and expressing human emotions. However, no objective and standardized metric currently exists to evaluate how empathet...
Graphic map load is a property of a map quantifying the amount of map content. It indicates the visual complexity of the map and helps cartographers to adapt maps and other geospatial visualizations to accomplish their purpose. Generally, map design...
Minimally invasive skills assessment methods are essential in developing efficient surgical simulators and implementing consistent skills evaluation. Although numerous methods have been investigated in the literature, there is still a need to further...
The concept of green chemistry is widely recognized in chemical laboratories. To properly measure an environmental impact of chemical processes, dedicated assessment tools are required. This paper summarizes the current state of knowledge in the fie...
In this paper, Mueller polarimetry is applied to study the three groups of common barley leaf samples (Hordeum vulgare) in the visible spectrum (λ = 632.8 nm): Chlorina mutant, Chlorina etiolated mutant and Cesaer varieties. These samples diff...
Metrics are a set of numbers that are used to obtain information about the operation of a process or system. In our case, metrics are used to assess the level of information security of information and communication infrastructure facilities. Metrics...
In regions heavily affected by recurrent typhoons, the need for more resilient electricity infrastructure is pressing. This emphasizes the importance of integrating resilience assessment, including incorporating resilience metrics, into the planning...
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