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Function in Engineering
Published in Diane P. Michelfelder, Neelke Doorn, The Routledge Handbook of the Philosophy of Engineering, 2020
Boris Eisenbart, Kilian Gericke
Merriam-Webster (2003) defines function as “the special purpose or activity for which a thing exists”. In mathematics, a function is a clear relation between a set of inputs and admissible outputs, and terms such as transformation or operator are sometimes used synonymously (Halmos 1974). In the engineering literature, function can have very different meanings. Several scholars refer to function as the ability of a system to achieve a specific goal, e.g. by showing a certain behaviour (e.g. Roozenburg and Eekels 1995; Buur 1990). Others refer to an intended or required transformation or conversion of operands (e.g. Rodenacker 1970; Pahl et al. 2007; Fowler 1998; Cockburn 2000), which may be associated with the input/output relations discussed earlier. Others, yet again, refer to the purpose or objective of the system, e.g. to fulfil a goal or provide a specific value, as its function (US DoD 2001; Sakao and Shimomura 2007; Bucciarelli 2010; Ullman 2010). This is often discussed as a teleological notion of function (Hubka and Eder 1988). As one can see, all of these definitions of function revolve around similar themes and partially overlap. However, no single definition of function incorporates all these notions or has superseded the other definitions.
Multi-Criteria Decision-Making Techniques
Published in Chandan Deep Singh, Jaimal Singh Khamba, Manufacturing Competency and Strategic Success in the Automobile Industry, 2019
Chandan Deep Singh, Jaimal Singh Khamba
The function itself can be arbitrary curves whose shape can be define as a function that suits from the point of view of simplicity, convenience, speed, and efficiency. A function is a mathematical representation of the relationship between the input and output of a system or a process. It facilitates the optimization of process output by defining the true relationship between input and the output variables. Basically, it has been applied to validate the input factors determined from earlier tools. Therefore, only the identified factors are tested and results obtained justify the earlier obtained results. The fuzzy logic toolbox graphical user interface (GUI) tool to build a FIS is shown in Figure 6.1a.
Virtualization of the Architectural Components of a System-on-Chip
Published in Lev Kirischian, Reconfigurable Computing Systems Engineering, 2017
As of the general representation of a task algorithm, an example of which is shown in Figure 9.1, the algorithm consists of a determined set of functions, each of which has control and data dependencies with other functions. According to the mathematical definition, a function is as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output [1]. Each function includes a determined set of elementary operations. Elementary operation can be considered as calculation of one output (result) out of two inputs (operands) Arithmetic and logic operations are the most common elementary operations composing a function.
Investigating secondary mathematics teachers’ analogies to function
Published in International Journal of Mathematical Education in Science and Technology, 2022
A function is a special kind of mathematical relation (Thorpe, 1999) ‘that uniquely associates members of one set with members of another set’ (Stover & Weisstein, 2017, para. 1). Stover and Weisstein (2017) writes that ‘More formally, a function from A to B is an object f such that every a ε A is uniquely associated with an object f (a) ε B’ (para. 1). The features of uniqueness (also known as single-valuedness) and arbitrariness distinguish function from other mathematical relations (Cooney et al., 2010; Even, 1990). The requirement of uniqueness is in the relationship between the two sets (domain and range) on which the function is defined; each element of the domain maps exactly one element of the range. The uniqueness feature, therefore, does not allow one-to-many relations, it only allows one-to-one and many-to-one relations. The requirement of arbitrariness is that a function need not be defined by any particular sets of objects; nor do the sets even need to be numbers, and even if a function is defined this way, it need not demonstrate regularity, nor does it need a particular graph or expression to define it (Even, 1993). While uniqueness is explicit in definitions of function, arbitrariness may be invisible as a feature in function definitions (Steele et al., 2013). Nevertheless, any mathematically valid conception of function should certainly include both univalence and arbitrariness, and these features of function should be explicitly addressed in the teaching and learning of functions (Cooney et al., 2010). As these features can be one of students’ main difficulties in understanding function, they need to be unpacked while teaching functions (Tabach & Nachlieli, 2015).