面向三支群决策的多粒度图像模糊概率粗糙集研究

Research on Multigranulation Picture Fuzzy Probabilistic Rough Sets for Three-way Group Decisions

随着新兴产业的快速发展,社会经济中各类复杂决策问题不断涌现,复杂决策问题的有效求解离不开推进体现科学化与民主化的群决策。图像模糊集作为直觉模糊集的推广形式,在实际应用中能够高效处理信息不一致的问题。本文针对图像模糊三支群决策问题,由于传统损失函数受决策者主观因素的影响进而在构造阈值时各有不同,探索了面向三支群决策的多粒度图像模糊概率粗糙集模型与方法。首先,本文将图像模糊的概念与三支群决策模型相结合,提出可调多粒度图像模糊概率粗糙集模型。然后,计算属性权重和专家权重时运用离差最大法。鉴于VIKOR(多准则妥协解排序)法能够同时考虑群体效用最大化和个体遗憾最小化并融入决策者主观偏好,利用VIKOR法进行多粒度图像模糊粗糙隶属度的最优粒度选择,进而建立图像模糊三支群决策方法。最后,通过一个UCI(University of California Irvine)数据库中的实例证实本文所构建方法的可行性。

With the rapid development of emerging industries, various complicated decision-making problems are constantly appearing in social economies, hence pursuing group decision-making that reflects the scientization and democratization is imperative for effectively addressing complex decision-making problems. Moreover, picture fuzzy sets act as the extension of intuitionistic fuzzy sets, which are conducive to addressing inconsistent problems in realistic applications. Aiming at picture fuzzy three-way group decision-making issues, in order to address the influence of decision-makers’ subjective factors when using classic loss functions to construct thresholds that may trigger different thresholds, the paper explores multigranulation picture fuzzy probabilistic rough set models and methods for three-way group decisions. First, the notion of picture fuzziness is introduced to three-way group decision models, and adjustable multigranulation picture fuzzy probabilistic rough sets are put forward. Then, attribute weights and expert weights are calculated according to the maximum deviation method. In view of the VIKOR(VlseKriterijumska Optimizacija I Kompromisno Resenje) method is able to incorporate maximum group utilities and minimum individual regrets with decision-makers’ subjective preferences, optimal granularity selections in terms of multi-granularity picture fuzzy rough memberships are conducted in light of the VIKOR method, and a picture fuzzy three-way group decision-making method is eventually established. At last, an example from the UCI(University of California Irvine) database is used to verity the feasibility of the proposed method.