| Ellis, B. (1966). Basic Concepts of Measurement. Cambridge University Press. |
....Mappings can be similarity transformations, linear transformations, non linear transformations of various kinds, and fuzzy membership functions of diverse form. 14] A mapping from an attribute in reality space to a corresponding attribute in benefit space is called a principle of correlation. [15] [9] Such a rule should be validated through consistency testing and graphical means [9] Step Two: Establish benefit priority weights among attributes of benefit space This is done using the same type of ratio scaling techniques used in measuring actual and goal states. Step Three: Compute the ....
Brian Ellis, Basic Concepts of Measurement (Cambridge, England: Cambridge University Press, 1966), P. 41
....that units are useful in writing formal specifications and adapt units to formal specification in the Z notation. 1.1 Units and Dimensions The theory of measurement deals with how best to structure measurements systems in support of scientific theories. The interested reader is referred to [Ell66] as a useful introduction to the theory of measurement in general and the use of dimensions of measurements in the physical sciences. Units and (more properly) dimensions of measurement fulfill a function in the physical sciences comparable to the function of strong typing in the computing ....
....and MEAS[R] and the dimensions system discussed above is designed to reflect and complement the algebraic properties of the reals. For example, the usefulness of dimensional analysis relies heavily on the ability to express a smooth, real valued function as a Taylor series of polynomials [Bri31, Ell66]. Other measurement domains are possible, e.g. MEAS[fred ; amber ; greeng] for traffic lights or MEAS[flong ; medium; shortg] for qualitative length measurements, but in such domains it may not be possible to apply the full power of dimensional analysis, either because of the lack of ....
B. Ellis. Basic Concepts in Measurement. Cambridge University Press, 1966.
....good, valid measurement. For instance, for measurement on an ordinal scale, the numbers assigned to the entities should reflect the intuitive ordering of these entities based on the quantities of the attribute we wish to measure. Formally, to define a measure on an ordinal scale, we need to define [5,7,10,14]: An empirical relational system (A,R) consisting of a set A of entities and a set R of relations on A as can be observed in reality. The relations in R order the entities of A according to the inherent quantity of a certain attribute of these entities. A numerical relational system (B,S) ....
....d(P,Q) is not a direct measure. Its value depends on the values of the d i (P,Q) s. The measurement of the global difference between object types involves the measurement of various aspects of this difference. Therefore d(P,Q) is an indirect measure of difference between object types. According to [5] an indirect measure involving two or more direct measures is a derived measure. Hence, we shall also speak of d(P,Q) as a derived measure. A derived measure has a derived scale. The type of a derived scale can be determined the same way as was done for direct measures. Note first that each of the ....
Ellis B., Basic Concepts of Measurement, Cambridge University Press, 1968, 220 pp.
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Ellis, B. (1966). Basic Concepts of Measurement. Cambridge University Press.
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Brian Ellis, Basic Concepts of Measurement (Cambridge, England: Cambridge University Press, 1966).
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ELLIS, B., Basic Concepts of Measurement, Cambridge University Press, London (1966).
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