Azeem Muhammad, Ali Jawad, Ali Jawad, Syam Muhammad I
Department of Mathematics and Statistics, University of Agriculture Faisalabad, Punjab, 38000, Pakistan.
Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, 26000, KPK, Pakistan.
Sci Rep. 2024 Oct 5;14(1):23155. doi: 10.1038/s41598-024-72726-z.
Interval-valued picture fuzzy (IVPF) set is an extension of the picture fuzzy set theory used to represent uncertainty and vagueness in the processes of decision-making. This study focuses on exploring the interrelationships among multiple IVPFSs and criteria partitions. We investigate the IVPF partitioned Maclaurin symmetric mean operator and the weighted IVPF partitioned Maclaurin symmetric mean operator and discuss their respective properties. Subsequently, we identify certain special cases of these operators based on IVPF sets. Furthermore, we deploy a multi-criteria decision-making procedure utilizing the suggested IVPF partition operators. Through a numerical example, we demonstrate the practicality and validity of the presented approach. Finally, a thorough comparison with existing approaches is conducted to elucidate the superiority of the proposed method.
区间值图像模糊（IVPF）集是图像模糊集理论的一种扩展，用于表示决策过程中的不确定性和模糊性。本研究着重探讨多个IVPFS之间的相互关系以及准则划分。我们研究了IVPF划分的麦克劳林对称均值算子和加权IVPF划分的麦克劳林对称均值算子，并讨论了它们各自的性质。随后，我们基于IVPF集确定了这些算子的某些特殊情况。此外，我们利用所提出的IVPF划分算子部署了一种多准则决策程序。通过一个数值例子，我们证明了所提出方法的实用性和有效性。最后，与现有方法进行了全面比较，以阐明所提方法的优越性。
