基于严格三角模的图像模糊插值Bonferroni均值算子及其在多准则决策中的应用
Picture Fuzzy Interactional Bonferroni Mean Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making
摘要：
基于图像模糊数和严格三角模的封闭运算法则，将图像模糊环境下的Bonferroni均值（BM）算子进行了扩展，提出了图像模糊插值Bonferroni均值（PFIBM）、图像模糊插值加权Bonferroni均值（PFIWBM）和图像模糊插值归一化加权Bonferroni均值（PFIWBM）算子.我们证明的单调性，幂等性，有界性和交换性的PFIBM和PFINWBM运营商。我们还建立了一个新的多准则决策（MCDM）方法下的图片模糊环境下，通过应用PFINWBM算子。此外，我们应用我们的MCDM方法的企业资源计划（ERP）系统的选择。我们的MCDM方法的比较结果，由六类著名的三角规范，确保最佳选择总是相同的ERP系统。因此，我们的MCDM方法是有效的处理图片模糊MCDM问题。
英文摘要：
Based on the closed operational laws in picture fuzzy numbers and strict triangular norms, we extend the Bonferroni mean (BM) operator under the picture fuzzy environment to propose the picture fuzzy interactional Bonferroni mean (PFIBM), picture fuzzy interactional weighted Bonferroni mean (PFIWBM), and picture fuzzy interactional normalized weighted Bonferroni mean (PFINWBM) operators. We prove the monotonicity, idempotency, boundedness, and commutativity for the PFIBM and PFINWBM operators. We also establish a novel multi-criteria decision making (MCDM) method under the picture fuzzy environment by applying the PFINWBM operator. Furthermore, we apply our MCDM method to the enterprise resource planning (ERP) systems selection. The comparative results for our MCDM method induced by six classes of well-known triangular norms ensure that the best selection is always the same ERP system. Therefore, our MCDM method is effective for dealing with the picture fuzzy MCDM problems.
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