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    Biobjective Optimization Method for Large-Scale Group Decision Making Based on Hesitant Fuzzy Linguistic Preference Relations With Granularity Levels
    (IEEE, 2024) Zheng, Yuanhang; Xu, Zeshui; Li, Yufei; Pedrycz, Witold; Yi, Zhang
    Large-scale group decision making becomes increasingly common with the rapid development of society and the increasing complexity of practical problems. However, it is difficult to distinguish the semantic differences between the same linguistic term, and original linguistic term may not express flexible semantics, so that this will affect the precise of decision-making results. With the help of granular computing, this article adopts a new format of linguistic term, named as hesitant fuzzy linguistic term set with granularity level, to endow preference information with flexibility and at a specific granularity. Then, in this study, we propose a novel intelligent biobjective optimization method for large-scale group decision making, considering group consensus degree and group risk degree in the decision-making process, where group risk degree is measured from the motivation of portfolio risk. Differential evolution is used to handle biobjective optimization method to determine the optimal results. We also introduce an additive consistency measure and develop a method to derive the corresponding threshold values through Monte Carlo simulation. Finally, the case study and comparison results are covered to demonstrate the practicality and superiority of the proposed method. This work has some original points: 1) Hesitant fuzzy linguistic term set with granularity level brings flexibility to the decision-making process. 2) Group consensus degree and group risk degree are involved in biobjective optimization method, where the group risk degree is measured from the motivation of portfolio risk. 3) A novel additive consistency measure is proposed and different threshold values of preference relations in different dimensions are derived.
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    CBCG: A Clustering Algorithm Based on Bidirectional Conical Information Granularity
    (Institute of Electrical and Electronics Engineers Inc., 2024) Yu, Bin; Zheng, Zijian; Cai, Mingjie; Pedrycz, Witold; Xu, Zeshui
    In this article, we propose a novel center-based clustering algorithm based on bidirectional conical information granularity. The main purpose is to fully absorb the semantic information of the ordinal relationship between objects to improve the performance of central clustering in identifying interleaved and imbalanced data. The proposed algorithm includes two main stages: first, the stage of determining the cluster center and second, the division stage. In the stage of determining the cluster center, the first cluster center is determined by using the number of conical information granularity in the data, and the remaining cluster centers are determined by defining the statistical measure of 'fuzzy importance degree.' In the division stage, we divide the points to be clustered into stable and active areas. The former quickly and accurately identifies and assigns the objects belonging to a cluster by measuring the fuzzy similarity between the objects to be clustered and the cluster center, and the latter assigns the objects in the active area by using the information of the points already assigned. This method describes the position and sorting relationship of objects that are granulated through ordinal relationships more accurately in the global environment, thereby gaining a more comprehensive understanding of the structural characteristics of the data. This helps to improve the accuracy and stability of clustering algorithms in handling interleaved and imbalanced data. This article uses three clustering validity indicators to test the performance of our algorithm. We compare the results with those of six different types of popular clustering algorithms and new algorithms proposed in recent years. The experimental results show that the algorithm proposed in this article can identify clusters more accurately on the datasets with a complex and staggered distribution. It is significantly better than the clustering algorithm participating in the comparison and has good robustness on datasets with added noise. © 1993-2012 IEEE.