关键词: 区间灰数, 属性关联, 灰熵模型, 均衡接近度, 多属性决策

Abstract: Under the background of the information age, decision-makers often face many problems that are difficult to solve directly in daily life and production activities, and any problem may have multiple attributes to be considered at the same time. Multi-attribute decision-making problems are ubiquitous in real life. Nowadays, research on multi-attribute decision-making has made great progress and plays an important role in many fields such as economy, science and technology, and aviation. Due to the complexity of society and the high uncertainty of the problems faced, in most cases, it is difficult to accurately describe the relevant information with precise numbers. For this reason, how to solve multi-attribute problems under fuzzy or uncertain conditions has gradually attracted attention. Due to the limitations of human cognition, when the obtained decision information is “poor information” or “less samples”, grey numbers are often used to describe it. The interval grey number can represent uncertain numbers and express complex information effectively, which is not contained in precise numbers. Using the interval grey number can not only reflect the behavior of the decision-maker but also match the actual decision-making situation.
The complexity of decision-making problems and ambiguity of human thinking and cognition, often drive decision-making under uncertain contexts. Though the use of the grey system for dealing with the uncertainty in decision-making has yielded successful results, they are not enough because the use of just one single number to elicit preferences may not reflect experts’ opinions properly. Therefore, in such situations, interval grey numbers have been introduced to model experts’ uncertainty on multiple decision-making models. Despite an important number of decision models based on interval grey numbers, most of them do not consider the bounded rationality of human beings, although their need and convenience in many real-world decision problems are useful and in demand. Therefore, this paper aims to present a new grey multi-attribute decision-making method based on the geometric shape of the associated attributes. First of all, determining the distinguishing coefficient subjectively will cause adverse effects on the correlation ranking, so we propose a new method based on the sequence fluctuations. By determining the distinguishing coefficient of different sequences dynamically, we can effectively solve the problem that is subjectively given. Secondly, the formula of area phase separation is given to calculate the adjacent degree, instead of using the distance between points. The essential characteristics of the interval grey number defines a new formula that can better distinguish between the interval grey number and other ones, and provides a new way of constructing the grey relational model. Then, a new adjustment weight formula that reflects the correlation between attributes is proposed, and the balance degree is calculated. Finally, an example is solved to validate the proposed method.
In this paper, an interval grey entropy decision model considering attribute association is proposed which has a positive impact on the development of grey relational decision-making. In spite of this, this paper only considers the correlation between two attributes and does not analyze the complex situation of correlation between multiple indicators. In addition, grey relational decision-making can be extended to dynamic environments. In view of this, a dynamic interval grey number evaluation is one of the possible future research directions.

Key words: the interval grey number, attribute association, the grey entropy model, balanced adjacent degree, multi-attribute decision-making