| Making a decision is one of the most important parts in our social activities, playing significant roal in both economic and social development. To make a proper decision must take account of every attribute that might affect our thinking, that is, multi-attribute decision-making, which is of vital importance in the scientific area of decision-making. Now, this method has been gradually applied into practice of engineering, economics, marketing, management, etc. It is thus making systematic study on Multi-attribute Decision-making Method means much for solving practical problems.With the continuous development of economy, our society has become more and more complicated, bringing uncertainty into a mass of areas, and accordingly multi-attribute decision-making problems turn to be filled with uncertainty, which generally contain fuzziness and grey. A multi-attribute decision-making problem contains fuzziness and grey, known as a grey fuzzy Multi-attribute Decision-making (GFMADM) problem. We must consider fuzziness and grey simultaneously so as to solve such problems.In recent years, study on GFMADM has aroused great concern and achieved fruitful results. However, as the GFMADM, either in terms of theoretical research or method application is still immature, it is still need us go on exploring.This paper, taking full account of fuzziness and grey in multi-attribute decision-making problems, mainly researches the grey fuzzy weight value determination method of multi-attribute decision-making, as well as the analysis method of grey fuzzy multi-attribute decision-making.Research results of this paper are as follows:(1) Proposing the grey fuzzy weight value determination method of multi-attribute decision-making. First, based on considering the blur of human cognition and grey of object system, grey fuzzy number is introduced into the attribute hierarchical model to calculate subjective weight value. Then through behavior observation, objective information is used to establish a linear programming model and get subjective weight value as constraint of linear programming model, hence get an answer from linear programming model to resolve attribute weight value in reverse, which reflects not only subjective will and also objective information.(2) Giving out gray fuzzy Multi-attribute Decision-making Method on the basis of TOPSIS. Traditional TOPSIS paid little attention to "Grey-immortal" Principle, so when solving a problem, only fuzziness rather than both of fuzziness and grey was received full attention, then these methods were found useless when confronting a multi-attribute decision-making problem including both fuzziness and grey. This paper, taking into consideration of grey and fuzziness at the same time, establishes an ideal solution-based grey fuzzy multi-attribute decision-making pattern.(3) Suggesting gray fuzzy Multi-attribute Decision-making Method based on grey correlation. Gray correlation analysis enjoys distinctive advantages in respect of solving decision-making problems such as small sample, poor information, etc. It is safe to say that all the attribute values of gray correlation pattern proposed firstly by Professor Deng Julong are accurate. In this paper, we adopt the grey fuzzy numbers to indicate the attribute values, then establish the analysis pattern of gray correlation. Decision-making analysis, therefore, reflects the ambiguity of human thinking andcomplexity of objective things all the more.(4) Putting forward the grey fuzzy comprehensive evaluation pattern of vector correlation. All the existing grey fuzzy comprehensive evaluation patterns calculate membership degree and gray separately, which leads to the loss of a great deal of information, hence cause the evaluation results lack of reliability. Different from the above-mentioned methods, a new grey fuzzy comprehensive evaluation pattern of vector correlation is given in this paper by employing the conception of vector correlation between membership degree and gray. |
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