Content area
Full text
1. Introduction
With the rapid development of economy, society and science, new problems are emerging. The uncertainty problem with “small amount of samples” and “poor information” that is widespread now is one of these new problems, and the grey system theory can solve these problems effectively (Li et al., 2015; Rao and Liu, 2015; Bindhu and Madhu, 2016; Dejamkhooy et al., 2017). In actual evaluation work, the observations of evaluation indexes are often too grey to be measured in real number. Meanwhile, the interval grey number (IGN) is one of the most common, most widely used and most valuable uncertainty expression forms in the grey system theory. So, it is particularly important to extend the grey system theory in the field of real number to the field of IGN.
In recent years, many scholars have attached great importance to the research of IGN. Stanujkic et al. (2012) combined the concept of IGNs and multi-objective optimisation by ratio analysis (MOORA) method to propose an extended MOORA method which is more appropriate to solve many complex real-world problems. The whitenisation weight function on real number field was extended to IGN by Zhou et al. (2013), and the grey clustering model for IGN with variable and fixed weight was established. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenisation value and greyness degree of correlation coefficient to form of IGNs are put forward by Wang (2013). An IGN decision model based on alpha–beta dominance relation is set up by Hu and Li (2014). To develop a mathematical model for evaluating and selecting efficient suppliers when facing supply and demand uncertainties, a novel ranking method was introduced for the units that their efficiencies are obtained in the form of grey numbers by Markabi and Sabbagh (2014). Zeng et al. (2014) discussed the position of the real parameter in an IGN sequence, and the real number was extended into an IGN by adopting the method of grey generation. On this basis, a prediction model of IGN with a real parameter was deduced and built. Liu et al. (2015) studied the situation that decision makers (DMs) have psychological thresholds for decision criteria in solving...