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

机译:标准灰度势度及其在多属性灰度目标决策中的应用

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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.
机译:在现实生活中,由于客观条件和人类认知的限制,很难获得完整的信息。因此,不确定性理论成为决策问题的重要分支。在传统的决策理论中,模型的参数通常具有确定的值。在这种环境下,灰色系统理论是解决不确定决策问题的重要方法。灰数用于描述不确定的信息。对于序列中的一组模式,灰度目标的思想是找到最接近目标值的数据并构造一个标准模式,每个模式和标准模式都构成灰度目标,标准模式就是靶心。灰色目标是一种用于处理多程序评估和优化多目标问题的方法。对于格雷目标决策问题,比较格雷数对于获得科学合理的结果非常重要。但是,很少有关于比较或排序格雷数的研究。但是,在格雷数的实际应用中,存在一些问题。 (1)灰度数的概率密度函数或白化函数很难知道。 (2)格雷数的许多信息将丢失,同时,如果将格雷数进行比较并通过最常用的白化值进行处理,则不确定性中的格雷数的值将部分丢失。 (3)为正常情况下的决策提供额外的信息非常困难。因此,本文的重点是在灰度目标决策中直接处理没有白化值且没有分布函数的灰度数。此外,格雷势度法可以通过比较和标准化工作来处理数据。灰色潜力可以用作灰色目标决策中的一种指标。为了比较替代方案,应建立一致的标准。在灰色目标决策问题中,有两个级别的标准。备选方案应通过索引值进行选择。因此,应该比较和整合不同的指标。对于每个可能有不同来源或被许多专家评估的索引,它都需要按照一致的标准来组合不同的信息。认为为每个索引设置了标准的灰度目标。然后,与标准灰度目标相比,可以将灰度势度进行比较和积分。由于不同的指标具有不同的测量范围,因此应根据指标的特性为每个指标设置每个标准的灰度目标。但是,最重要的是,如果每个指标的每个标准灰度目标都遵循相同的原理,并且它们的灰度势度是通过相同的方法计算的,则可以直接整合不同标准的判断。因此,采用了对索引数据进行赋值的原则。通过标准灰度势度的方法,可以解决带有灰度矩阵的灰度目标问题。为了比较和分类不同的格雷数,本文提出了标准的灰度势度。同时,在多属性灰色目标决策问题中,关键部分是目标,在不同情况下目标都是复杂的。因此,对目标的六个方面进行了讨论和分类,并根据标准灰度总势度值的升序采用五步法对目标系列进行了分类。还给出了三个典型的例子来验证我们的模型和算法的效率和实用性。第一个示例显示了具有多个索引的灰色目标模型。这种情况包括不同类型的索引,基于收入的类型,成本类型,中心类型。第二部分提出了具有不同标准和不同权重的多源模型。第三个是为了与公开论文中的示例与退出方法进行比较。第三个示例无法充分显示模型的特征。结果表明,应该讨论标准灰度目标,并提出了标准灰度电位度,以将各种原始数据连接到标准灰度目标。由于灰度势度解决了两个灰度数之间的关系,但是灰度目标问题需要更具体的应用方法。就像通信中心一样,标准灰度电位度是从灰度电位度方法到灰度目标决策的桥梁。从我们的运行结果可以看出,基于灰势的灰色目标决策方法的优点在于该方法结合了目标选择和标准沉积的过程,因此,本研究提出的标准灰色目标模型易于实现。处理收入类型,成本类型和中心类型的不同属性,并且该方法可以通过优劣系数进行调整。本研究提出的灰色目标模型与灰色潜在度相结合,能够提供良好的模型表达,以及一种解决方法。

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