Grey Numbers and Their Operations
A grey system is described with grey numbers, grey sequences, grey equations, or matrices. Here, grey numbers are the elementary “atoms” or “cells”, and their exact values are unknown. In applications, a grey number stands for an indeterminate number that
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Grey Numbers and Their Operations
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Grey Numbers
A grey system is described with grey numbers, grey sequences, grey equations, or matrices. Here, grey numbers are the elementary “atoms” or “cells”, and their exact values are unknown. In applications, a grey number stands for an indeterminate number that takes its possible value within an interval or a general set of numbers. A grey number is generally represented using the symbol “.” There are several types of grey numbers, as discussed below. (1) Grey numbers with only a lower bound: This kind of grey number is represented as 2 ½a; 1Þ or ðaÞ, where ðaÞ stands for the definite, known lower bound of the grey number . The interval ½a; 1Þ is referred to as the field of . For example, the weight of a celestial body which is far away from the Earth is a grey number containing only a lower bound, because the weight of the celestial body must be greater than zero. However, the exact value of the weight cannot be obtained through normal means. If we use the symbol to represent the weight of the celestial body, we then have that 2 ½0; 1Þ. (2) Grey numbers with only an upper bound: This kind of grey number is written as 2 ð1; a or ðaÞ, where a stands for the definite, known upper bound of . A grey number containing only an upper bound is a grey number with a negative value, but its absolute value is infinitely great. For example, the opposite number of the weight of the celestial body mentioned above is a grey number with only an upper bound. (3) Interval grey numbers: This kind of grey number has both a lower bound a and an upper bound a, written 2 ½a; a. © Springer Science+Business Media Singapore 2017 S. Liu et al., Grey Data Analysis, Computational Risk Management, DOI 10.1007/978-981-10-1841-1_3
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3 Grey Numbers and Their Operations
For example, for an investment opportunity, there always exists an upper limit representing the maximum amount of money that can be mobilized. For an electrical equipment, there must be a maximum critical value for the equipment to function normally. The critical value could be for a maximum voltage or for a maximum amount of current allowed to be applied to the equipment. At the same time, the values of investment, voltage, and current are all greater than zero. Therefore, the amount of dollars that can be used for a specific investment opportunity, and the voltage and the current requirements for the electrical equipment are all examples of interval grey numbers. (4) Continuous and discrete grey numbers: This kind of grey number takes only a finite number or a countable number of potential values and is known as discrete. If a grey number can potentially take any value within an interval, then it is known as continuous. For example, if a person’s age is between 30 and 35, his or her age could be one of the values 30, 31, 32, 33, 34, 35. Thus, age is a discrete grey number. As for a person’s height and weight, they are continuous grey numbers. (5) Black and white numbers: Black numbers are represented a
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