On Uncertain Granular Numbers

Abstract

When a quantity is measured, the outcome depends on several factors like the measuring system, the measurement procedure, the skill of the operator, the environment, and other effects. In case of inexact quantity the outcome may also depends on the uncertainty representation.Recently inexact numbers got a lot of attention from many researchers in different fields. In this paper, we have tried to give an overview for the different representations of the inexact granular numbers. The objective of this overview is providing a certain insight into the essence of granular data representation being regarded as a framework of representing and manipulation of inexact information, and introduce a new representation of granular uncertain number to be as step in formulate a general form for all uncertain numbers.

Flood Damage Assessment: A Preliminary Studies

“…Regarding the previously highlighted issues and challenges, specifically on the issues of uncertainties, a fuzzy approach is proposed herein in order to increase its precision level. This method combines the application of a fuzzy and probabilistic information concept in translating the information into a natural language which makes it capable to evaluate the damage even under the situation of incomplete and imprecise information (Alsawy & Hefny, 2013).…”

Unified Granular-number-based AHP-VIKOR multi-criteria decision framework

“…, the arithmetic operations are defined in the following (Alsawy and Hefny 2013a;Mohamad and Rofai 2015). The validity of the operations is checked here for interval number [a, b], b > a.…”

“…As per Alsawy and Hefny (2013a), in representing various types of uncertain granular numbers, unified granular number (UGN) or simply granular number (G) does not neglect the membership function, which is the main idea of the fuzzy set. Even G-number represents the fuzzy number using two parameters of G c X , r X one being the center c X and another radius r X of that domain (granular), respectively.…”

“…• According to Alsawy and Hefny (2013a), a G-number can represent all types of multi-granular numbers (rough numbers, vague numbers, grey numbers, and interval numbers) due to its ability to convert them into a homogenous representation, as expressed in Eq. (1).…”

“…where c X is the center value and r X is the radius of G-number X, respectively (Alsawy and Hefny 2013a). Equation (1) of G-numbers as mentioned above guarantees representing the most common properties of uncertainty having both lower and upper bounds and known boundaries.…”