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The purpose of this paper is to present research methods in processing uncertain information.

Vague set and rough set are both‐wings‐mode for expressing uncertainty systems, and based on the both‐wings‐mode of expressing uncertainty systems, the connections of vague set and rough set are discussed.

This paper presents the relationships between vague set and rough set.

Based on these connections between vague set and rough set, theoretical and means of vague set can be used for rough set; also theoretical and means of rough set can be used for vague set.

The paper contributes to the discussion on the research of vague set and rough set. The conclusions are useful in information processing.

With respect to the multiple-attribute decision-making problem with subjective preference for a certain attribute whose weight-value range have been given over other attributes whose weight values are unknown, a method based on the mean value of the grey number is proposed to analyse the decision-making problem. This method is used to choose a supply-chain partner under the condition that the decision makers have a preference for a certain attribute of various alternatives. The paper aims to discuss these issues.

First, the middle value of the preferred attribute’s weight-value range is supposed to be its weight value according to the content of the mean value of the grey number. Second, to reflect the decision maker’s subjective preference information, an improved optimisation model that requests the minimum deviation between the actual and expected numerical value of each attribute is constructed to assess the attributes’ weights. Third, the correlated degree and the correlation matrix, which are determined by the weight values of all attributes, are used to rank all the alternatives.

This paper provides a method for making a decision when decision makers have a preference for a certain attribute from an array of various alternatives, and the range of the certain attribute’s weight value is given but the weight value of the other attributes is unknown. When applied to supply-chain partner selection, this method proves feasible and effective.

This method is feasible and effective when applied to supply-chain partner selection, and can be applied to other kinds of decision-making problems. This means it has significant theoretical importance and extensive practical value.

Based on the mean value of the grey number, an optimisation model is built to determine the importance degree of each attribute, then the correlated degree of each alternative is combined to rank all the alternatives. This method can suit the decision makers’ subjective preference for a certain attribute well.