关键词: 灰色聚类, 三支决策, 不确定聚类, 聚类阈值

Abstract: As an effective method to deal with the “small sample, poor information” clustering problem, the possibility function-based grey clustering evaluation approach is one of the important research contents of grey system theory. The possibility function-based grey clustering evaluation approaches mainly includes grey variable-weight clustering evaluation model, grey fixed-weight clustering evaluation model and grey clustering evaluation model based on mixed possibility function. However, the classic grey clustering evaluation model has problems such as low distinguishability of several components of the decision coefficient vector. In addition, its improved models still have problems such as more cumbersome calculations and low distinguishability and error tolerance.
Aiming at the problem of the grey possibility clustering model that it is difficult to determine the grey class ascription of decision objects and excessive clustering, based on the thought and method of three-way decisions, by introducing the concept of three-way grey class, it can describe the uncertain clustering relationship between the decision object and the grey class. The three-way grey class replaces the grey class and strict clustering relationship in grey possibility clustering, a grey possibility clustering method based on three-way decisions is constructed, and Bayesian reasoning in decision-theoretic rough set is used to determine the clustering thresholds. Finally, an example is used to verify the effectiveness and rationality of the proposed method. Compared with the classic possibility function-based grey clustering evaluation approach, The model constructed in this paper can provide more clustering information, and to a certain extent solve the problem of the balanced value of each component of the grey clustering coefficient vector or the problem that the grey clustering coefficient vector has several leading principal components with similar values, making it difficult to determine the ownership of the decision object. Therefore, excessive clustering can be avoided, decision-making risks can be reduced, clustering reliability and fault tolerance can be improved, and decision-makers can be provided with more detailed decision-making references. At the same time, classic grey fixed-weight clustering, grey variable-weight clustering and grey clustering based on mixed possibility functions are special cases of the model constructed in this article, and the proposed model is an extension and generalization of these grey clustering methods.
Product decision-making is the process by which a company determines which product (product combination) will meet the needs of the target market and launch the product in the future based on market sales results and the company’s own specific conditions. Therefore, product decisions are of great significance in business operations. We apply the constructed model to the solution of enterprise product decisions. For certain clustering results, enterprises can make decisions directly; for those uncertain clustering results, enterprises need to obtain more market information about these products or adjust the possibility function to further classify them into certain categories. This can effectively reduce decision-making risks.
Most real-world decision problems are dynamic, in the sense that the final decision is temporarily taken in a time cross-section of some constantly explored processes. In this process, decision-making objects, decision-makers, decision-making methods, evaluation standards, weights, decision-making information systems, etc. may change with changes in the environment, which may ultimately affect the clustering results. In view of this, dynamic grey three-way clustering evaluation is one of the possible future research directions.

Key words: grey clustering, three-way decisions, uncertain clustering, clustering thresholds