Abstract: Concept is the carrier of knowledge, and its expression and definition are of great significance for the development of modern intelligent science. Due to the difficulty of computers in recognizing the connotationrepresentation of concepts, the field of artificial intelligence attempts to define concepts through extension representation. The essence of the extension representation of concepts is set representation, and therefore, how to determine the membership relationship between objects and concepts is the core issue. In the factor space, based on the Zadeh maximum extension principle and the minimum extension principle, the concept of max type representation extension and min type representation extension are proposed respectively. Furthermore, the feedback extension and envelope of the concept are proposed. Feedback extension envelope is essentially an approximation of concept extension. It should be pointed out that the underlying foundation of this approximation construction is the extension principle. When there is a large sample of data, the extension principle will inevitably lose a large amount of information during the information extraction process, resulting in low approximation accuracy. Considering the ambiguity and uncertainty of concepts, especially when facing complex decision-making problems, the intuitionistic fuzzy relationship portrays the fuzziness of the real world more objectively and delicately, and therefore, discussing the description of intuitionistic fuzzy concepts in factor space is of important practical significance.
Based on this, this article proposes the concept of intuitionistic fuzziness based on the theory of factor space, and starts from the original concept and its opposite concepts, constructs two approximations of intuitionistic fuzziness concept extension using the maximum extension principle and the minimum extension principle, and then defines the double envelope of concept feedback extension (which is essentially a bilateral approximation of concept extension). On this basis, a DFE decision-making method based on feedback extension double layer envelope is proposed. Finally, the operational steps are provided and the above theoretical method is applied through an example.

Key words: factor space, representation extension, feedback extension, intuitionistic fuzzy concept, reverse concept, double enveloping

摘要： 在因素空间理论基础上,提出直觉模糊概念,从原概念及其对立概念的表现外延出发,构造了直觉模糊概念外延的两种逼近,并在此基础上提出了基于反馈外延双层包络的DFE决策方法,最后,给出操作步骤并通过实例对上述理论方法进行了应用。

关键词: 因素空间, 表现外延, 反馈外延, 直觉模糊概念, 对立概念, 双层包络