Clustering incomplete instance is still a challenging task since missing values maybe make the cluster information ambiguous, leading to the uncertainty and imprecision in results. This article investigates an enhanced fuzzy clustering with evidence combination method based on Dempster-Shafer theory (DST) to address this problem. First, the dataset is divided into several subsets, and missing values are imputed by neighbors with different weights in each subset. It aims to model missing values locally to reduce the negative impact of the bad estimations. Second, an objective function of enhanced fuzzy clustering is designed and then optimized until the best membership and reliability matrices are found. Each subset has a membership matrix that contains all sub-instances’ membership to different clusters. The fuzzy reliability matrix is employed to characterize the reliability of each subset on different clusters. Third, an adaptive evidence combination rule based on the DST is developed to combine the discounted subresults (memberships) with different reliability to make the final decision for each instance. The proposed method can characterize uncertainty and imprecision by assigning instances to specific clusters or meta-clusters composed of several specific clusters. Once an instance is assigned to a meta-cluster, the cluster information of this instance is (locally) imprecise. The effectiveness of proposed method is demonstrated on several real-world datasets by comparing with existing techniques.

Fermatean fuzzy sets (FFSs), as one of the representative variants of fuzzy sets, have broad application prospects. FFSs have advantages in modeling uncertain information and therefore have been widely applied. However, how to perfectly quantify the differences between FFS remains an open question. This paper introduces a new distance measure for FFSs, utilizing triangular divergence. The proposed measure is designed to rectify the limitations in the current measure, offering a more effective solution for analyzing FFSs. Moreover, we demonstrate that the proposed distance measure satisfies some basic properties and further show its effectiveness through several numerical examples. Finally, we explore the performance of the proposed distance measure in a medical diagnosis application, and the results show that the proposed distance measure can well overcome the limitations of the current measure.