MODEL OF RATING OF NON PHYSICAL QUANTITY

• Main Author: V. M. Romanchak
• Format: Article
• Language: English
• Published: Belarusian National Technical University 2018-02-01
• Series: Sistemnyj Analiz i Prikladnaâ Informatika
• Subjects: fekhner; stephens’s laws; utility function; fuzzy sets
• Online Access: https://sapi.bntu.by/jour/article/view/187

Physical quantities are distinguished from non-physical quantities the method of measurement. In addition, when measuring physical quantities, the concept of identical objects is considered. For example, is equally likely outcomes in classical probability theory or equality of scale interval of a measuring scale. For nonphysical size we will take measurements by subjective estimation in an order scale, but also to use an undefined notion of the sequence of equally different objects. This approach has been used successfully in some researches for subjective characteristics of the objects. For example, the sequence of stars in the sky of various brightness or levels of difficulty of the test. The numbers of members of such a sequence are called ratings. Having defined rating, it is possible to find values of size if to consider that to equally different objects there corresponds the identical result of paired comparison. As the expert compares objects, without determining the sizes of objects, it is natural to assume that the way of comparison is not known to him. It means that as mathematical model we defined an indirect way of finding of values of nonphysical size at an unknown way of comparison. Having chosen a way of comparison, each object can put number which we will call the subjective size of an object in compliance. In a metrology of ways of numerical comparison of physical quantities only two is a difference and the relation. Therefore at assessment of subjective sizes we will be limited in two ways – a difference and the relation of the sizes of sizes.As an example of application of the theory the functional communication, between physical quantity and nonphysical size, established by empirical laws is analyzed. It is noted that Fekhner and Stephens’s empirical laws use a difference or the relation of subjective sizes. But the difference or the relations of sizes can be expressed through the difference of ratings. Therefore there is an opportunity for each law to receive a ratio between the difference of ratings and physical quantity. Coincidence of two laws of Fekhner and Stephens, after transition to rating, confirms reliability of our model.