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A decomposition approach to type 2 interval arithmetic

Piegat Andrzej, Dobryakova Larisa

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 1

185--201

The classic interval has precise borders A = [a, ā] . Therefore, it can be called a type 1 interval. Because of great practical importance of such interval data, several versions of type 1 interval arithmetic have been created. However, sometimes precise borders a and ā of intervals cannot be determined in practice. If the borders are uncertain, then we have to do with type 2 intervals. A type 2 interval can be denoted as AT2 = [aL, aR], [āL, āR]. The paper presents multidimensional decomposition RDM type 2 interval arithmetic (D-RDM-T2-I arithmetic), where RDM means relative-distance measure. The decomposition approach considerably simplifies calculations and is transparent for users. Apart from this arithmetic, examples of its applications are also presented. To the authors’ best knowledge, no papers on this arithmetic exist. D-RDM-T2-I arithmetic is necessary to create type 2 fuzzy arithmetic based on horizontal µ-cuts, which the authors aim to do.

Cloud-based GNSS navigation spoofing detection

Dobryakova Larisa, Lemieszewski Łukasz, Ochin Evgeny

Zeszyty Naukowe Akademii Morskiej w Szczecinie

2019

nr 57 (129)

29--37

Satellite navigation systems are commonly used to precisely determine the trajectory of transportation equipment. The widespread deployment of GNSS is pushing the current receiver technology to its limits due to the stringent demands for seamless, ubiquitous and secure/reliable positioning information. This fact is further aggravated by the advent of new applications where the miniaturized size, low power consumption and limited computational capabilities of user terminals pose serious risks to the implementation of even the most basic GNSS signal processing tasks. This paper has presented the advantage of Cloud-based GNSS Navigation, which facilitates the possibility of developing innovative applications where their particularities (e.g. massive processing of data, cooperation among users, security-related applications, etc.) make them suitable for implementation using Cloud-based infrastructure.