Generalized Ordered Intuitionistic Fuzzy C-Means Clustering Algorithm Based on PROMETHEE and Intuitionistic Fuzzy C-Means

Abstract

The problem of ordered clustering in the context of decision-making with multiple criteria has garnered significant interest from researchers in the field of management science and operational research. In real-world scenarios, the datasets often exhibit imprecision or uncertainty, which can lead to suboptimal ordered-clustering outcomes. However, the intuitionistic fuzzy c-means (IFCM) clustering algorithm enhances the accuracy and effectiveness of decision-making processes by effectively handling uncertain dataset information for clustering. Therefore, we propose a new clustering algorithm, called the generalized ordered intuitionistic fuzzy c-means (G-OIFCM), based on PROMETHEE and the IFCM clustering algorithm. Different from the classical IFCM clustering algorithm, we use positive flow ( ${\phi }^{+}\left(s_i\right)\in \left[0,1\right]$ ) and negative flow ( ${\phi }^{-}\left(s_i\right)\in \left[0,1\right]$ ) of PROMETHEE to generate ordered clusters within the intuitionistic environment. We define a new objective function based on the positive and negative flow of the PROMETHEE and IFCM clustering algorithm, whose properties are mathematically justified in terms of convergence and optimization. The performance of the proposed algorithm is evaluated using two different real-world datasets to assess both the ordered clustering and the quality of partitioning. To demonstrate the effectiveness of G-OIFCM, a comparison is conducted with three other algorithms: fuzzy c-means (FCM), ordered fuzzy c-means (OFCM), and an adaptive generalized intuitionistic fuzzy c-means (G-IFCM). The results demonstrate the effectiveness of G-OIFCM in enhancing optimal ordered clustering and utility when dealing with uncertainty in datasets.