Lecture
The use of mathematical apparatus is an indispensable condition for the development and improvement of various sciences, belonging both to the natural-science field and to the humanities. Psychology, sociology, and economics need mathematical tools no less than physics or mechanics. Within the humanities, specialized scientific disciplines have emerged, such as mathematical psychology, mathematical linguistics, and mathematical economics , which use mathematical models to collect, process, and present large volumes of heterogeneous information. A researcher in any field needs instruments and a methodology for measuring the properties of the processes, phenomena, and objects under study. For these purposes, the mathematical theory of measurement has been developed. Today the term «measurement theory» is used to denote a whole range of scientific disciplines: classical metrology, representational theory of measurement (RTM), algorithmic measurement theory, etc. One of the most general definitions characterizes measurement theory (MT) as a discipline that systematizes the principles of the measurement process and also provides the mathematical apparatus for implementing this process .
Historically, the first area of application of MT was psychophysics; later, in the second half of the 20th century, the scope of MT's use expanded considerably, first encompassing psychological science as a whole, and then such scientific disciplines as pedagogy, sociology, expert assessment, and others. The methodological foundations of MT have been developed in a number of works by foreign and domestic authors — such as S. S. Stevens, P. Suppes, A. Tversky, J. Pfanzagl, M. N. Selivanov, A. I. Orlov, and others.
To present the principles of MT at an abstract-theoretical level, axioms developed within theoretical metrology — the science of measurement — are used. The literature presents various approaches to forming a system of axioms that make it possible to establish the relationship between the basic terms and concepts of MT. Two versions of the axiom system are given below .
Axioms of measurement theory according to M. N. Selivanov.
Axiom 1. Measurement is possible provided that the qualitative definiteness of the property has been established, making it possible to distinguish it from other properties.
Axiom 2. Measurement is possible provided that a unit for measuring the quantity has been established.
Axiom 3. Measurement is possible provided that the unit of measurement is materialized by a technical means.
Axiom 4. Measurement is possible provided that the size of the measurement unit remains unchanged during the measurement.
Axioms of measurement theory according to V. A. Granovsky.
Axiom 1. Within the accepted model of the object of study, there exist a certain measured quantity and its true value.
Axiom 2. The measured quantity is constant.
Axiom 3. There is a discrepancy between the measured quantity and the studied property of the object.
Axiom 4. There is always a possibility of increasing the accuracy of measurements.
The study of the properties of a real economic phenomenon (process), the construction of its mathematical model, and the measurement of its parameters require the correct use of the basic categories that make it possible to assess the current state of the phenomenon under study.
Note!
To assess the current state and forecast the development of socio-economic systems, the following categories are used: attributes, indicators, criteria.
Mass socio-economic phenomena appear in every study as statistical populations. A statistical population is a relatively homogeneous group of objects or phenomena characterized by the presence of certain common attributes and subjected to study through the collection of quantitative and qualitative data, and their processing and analysis. For example, sets of economic entities of small (medium, large) business, financial and credit organizations, etc., may serve as the objects of study, i.e., as populations.
Each individual element of this set is called a unit of the statistical population. A unit of the population is the limit of decomposition of the object of study at which all the properties of the phenomenon (process) under study continue to be preserved. Each unit of the population possesses certain properties.
Definition
An attribute is the individual property of a unit of the population. An attribute can be represented either as a quantitative or as a qualitative characteristic of a unit of the population.
Attributes can be classified as qualitative (attributive) or quantitative. Qualitative attributes express an essential, inherent property of a unit of the population. Attributes whose values can be measured are called quantitative, for example, an organization's profit, authorized capital, the assets and liabilities of an enterprise, credit debt, and others.
In economic activity, alternative attributes are often identified. Alternative attributes are attributes (two or more) characterized by mutually exclusive properties or possibilities. These include attributes of possessing or not possessing some property. For example, depending on education, each employee can be assigned to the category of either having a higher education or not having a higher education.
Note!
An attribute characterizes each individual unit of the population under study. For the population as a whole, it is characteristic to use such characteristics of it as would reflect the properties of the system and make it possible to assess the effectiveness of the system as a whole.
In assessing the effectiveness of decision support systems, the concept of an «indicator» is the most widely used.
Definition
An indicator is understood as a characteristic of a group of units or of the population as a whole, representing a generalized characteristic of the properties of this group or of the entire population, presented in quantitative or verbal form.
The following may be used to describe any population under study:
• absolute indicators. For example, this could be the indicator «number of employees», the indicator «volume of trade turnover», profit, etc.;
Most foreign practical guides on the analysis and evaluation of the effectiveness of managerial decisions note that indicators must satisfy the basic requirements of the «4C» concept .
The requirements of the «4C» concept apply to both quantitative
and qualitative indicators.
Note!
In decision support and decision-making systems there may be indicators that do not meet all the stated requirements of the «4C» concept.
Criteria (optimality criteria) are used to evaluate the effectiveness of managerial decisions and must comply with the «SMART» concept, i.e. they must possess the following five properties :
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