Standard grey potential degree and its application in multiple attribute grey target decision

In real life, it is very hard to obtain complete information because of objective conditions and human cognition limitation; hence uncertainty theory becomes an important branch of decision-making problem. The parameters of model are usually of determined values in traditional decision-making theory. Under such environment, Grey systems theory is an important method to do with uncertain decision-making problems. Grey number is used to describe uncertain information. For a set of patterns in the sequence, the thought of Gray target is to find the data which is nearest to target value and construct a standard mode, each mode and standard mode constitutes gray target, the standard mode is the bull's-eye. Grey Target is a method for processing multiple program evaluation and optimization of multiple objective problem. To compare Grey number is very important to obtain scientific and reasonable results for a Grey target decision-making problem. But there is very little study on comparing or ranking Grey numbers. However, in the actual application of Grey number, there are some problems. (1) The probability density function or the whiten function of Grey number is difficult to know. (2) Much information of Grey number will be lost, and at the same time the value of Grey number in uncertainty is lost partly if Grey number is compared and deposed through whiten value which is most commonly used. (3) It is very hard to supply additional information for decision-making in normal condition. Therefore, this paper focuses on handling directly Grey number without whiten value and without distribution function in Grey target decision-making. Furthermore, approach of Grey potential degree could treat the data with both comparing and standardization work. Grey potential could be used as a form of metrics in Grey target decision-making. In order to compare alternatives, consistent standard should be built up. In Grey target decision problem, there are two levels of standard. The alternatives should be selected by values of indexes. So different indexes should be compared and integrated. For each index, which maybe have different source or evaluated by many experts, it needs to combine different information by consistent standard. It is considered that a standard Grey target is set for each index. And then compared to standard Grey target, the Grey potential degree could be used to compare and integrate. Because different index has different measurement scale, each standard Grey target, should be set for each index according to the character of index. However the most important thing is that if every standard Grey target for every index follows the same principle and their Grey potential degrees are calculated by the same approach, it is possible to integrate the judgment of different criteria directly. Hence principle of value-covered set of data of index is adopted. By the ways of Standard Grey Potential Degree, Grey target problem with Grey matrix could be deposed. In order to compare and sort different kinds of Grey numbers, standard Grey potential degree is put forward in the paper. Meanwhile, in multiple Attribute Grey target decision problem, the critical part is target which is complex in different situations. So six aspects of target is discussed and classified, and the series of Objects is sorted by five-step method according to the ascending of value of Standard Grey Total Potential Degree. Three typical examples are also given to verify the efficiency and practicability of our model and algorithm as well. The first one example shows grey target model with multiple index. This situation includes different types of index, income-based type, cost type, central type. The second presents the model of multiple source which have different standard and different weight. The third one is in order to compare with exiting method by the example in a public paper. The third example could not show the character of model fully. Results show that Standard Grey Target should be discussed and Standard Grey potential degree is put forward to connect all kinds of original data to Standard Grey Target. Because the Grey potential degree resolves the relation between two grey numbers, but grey target problem needs more specific application method. Just like the communication center, Standard Grey potential degree is the bridge from method of grey potential degree to grey target decision-making. It is shown from our running result that, the advantages of grey potential based method of grey target decision-making include that the method combines the process of target choosing and Standard deposing, Therefore, the standard grey target model proposed in this research is easy to deal with different kinds attributes of income-type, cost-type and center-type, and the method can be adjusted by superiority and inferior coefficients. The grey target model combined with grey potential degree proposed in this research is able to offer a good model expression, as well as an approach for resolution.