Wasim Muhammad, Yousaf Awais, Alolaiyan Hanan, Akbar Muhammad Azeem, Alburaikan Alhanouf, El-Wahed Khalifa Hamiden Abd
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, 63100, Pakistan.
Department of Mathematics, King Saud University, 12271, Riyadh, Saudi Arabia.
Sci Rep. 2024 Jul 17;14(1):16538. doi: 10.1038/s41598-024-57461-9.
Intuitionistic fuzzy sets (IFSs) represent a significant advancement in classical fuzzy set (FS) theory. This study advances IFS theory to generalized intuitionistic fuzzy sets (GIFSs) and introduces novel operators GIFWAA, GIFWGA, GIFOWAA, and GIFOWGA, tailored for GIFSs. The primary aim is to enhance decision-making capabilities by introducing aggregation operators within the GIFS framework that align with preferences for optimal outcomes. The article introduces new operators for GIFSs characterized by attributes like idempotency, boundedness, monotonicity and commutativity, resulting in aggregated values aligned with GIFNs. A comprehensive analysis of the relationships among these operations is conducted, offering a thorough understanding of their applicability. These operators are practically demonstrated in a multiple-criteria decision-making process for evaluating startup success in the Tech Industry.
直觉模糊集（IFS）代表了经典模糊集（FS）理论的重大进展。本研究将IFS理论推进到广义直觉模糊集（GIFS），并引入了专门为GIFS量身定制的新型算子GIFWAA、GIFWGA、GIFOWAA和GIFOWGA。主要目的是通过在GIFS框架内引入与对最优结果的偏好相一致的聚合算子来增强决策能力。本文介绍了具有幂等性、有界性、单调性和交换性等属性的GIFS新算子，从而得到与GIFN一致的聚合值。对这些运算之间的关系进行了全面分析，以便深入了解它们的适用性。这些算子在评估科技行业初创企业成功与否的多准则决策过程中得到了实际验证。
