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Measure and Integration Theory
Published in Athanasios Christou Micheas, Theory of Stochastic Objects, 2018
Measure theory provides tools that allow us to efficiently quantify or measure sets of points, where by point here we could mean anything, from real vectors, to matrices and functions, to points that are collections of points themselves. A measure on a set provides a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size, and consequently, we can think of a measure as a generalization of the concepts of length, area and volume.
Lattice Theory
Published in Gerhard X. Ritter, Gonzalo Urcid, Introduction to Lattice Algebra, 2021
Gerhard X. Ritter, Gonzalo Urcid
Measure theory is the basis of modern integration theory and these two theories play a fundamental role in a wide range of mathematical endeavors. Measures for a set X depend on the set algebras of subsets of 2X defined as follows:
Examining human factors and ergonomics aspects in a manufacturing organisation’s metrics system: measuring up to stakeholder needs
Published in Ergonomics, 2023
Michael A. Greig, Judy Village, Filippo A. Salustri, W. Patrick Neumann
In this paper, we examine HF/E as it relates to an organisation’s metrics system. Our perspective on metrics is framed by the work of Melnyk et al. (2005) and performance measurement system design of Neely, Gregory, and Platts (1995). Building off of this work, we consider the ‘metrics system’ to represent any measurement system used to manage metrics across all aspects of an organisation. A metric consists of a specific measure, a standard for comparison, and a context of use (Melnyk et al. 2005). In this report, we use the term ‘metric’ to refer to qualitative or quantitative information that can be related to a referent for comparison. Qualitative metrics are conceptually more abstract compared to the more common quantitative metrics but could be as simple as a green, yellow, or red indicator showing progress to a goal or operational status. Systems of metrics are used by organisations to monitor and manage operations: relating to the adage that ‘you can’t manage what you don’t measure’. This focus on management through measurement has implications for HF/E. We believe that if HF/E information cannot be communicated appropriately, then it is unlikely that it will be considered when high-level organisational and design decisions are made; thus limiting the benefits available from HF/E. In considering the role of HF/E in the organisation’s metrics system—which is used to steer organisational level activities, we draw on an organizational—or macroergonomic (Nagamachi 1996; Hendrick and Kleiner 2001; Waterson et al. 2014)—perspective on metrics and HF/E in this case study.
A Centralization Measure for Social Networks Assessment
Published in Cybernetics and Systems, 2022
Rafał Palak, Krystian Wojtkiewicz
A measure is a method for assigning a value to an object attribute. Creating such a system is a complex endeavor, so we will begin by supplying several definitions. Let us begin by defining the graph as: where is a set of nodes. Each node represents an individual in a social network or collective, is a set of edges. Each edge symbolizes a direct relationship between two individuals in a social network or collective.