Zhang Nan, Khan Muhammad Rizwan, Ullah Kifayat, Saad Muhammad, Yin Shi
School of Marxism, Hebei Agricultural University, Baoding, 071001, China.
Department of Mathematics, Riphah International University Lahore, Lahore, 54000, Pakistan.
Heliyon. 2024 Mar 1;10(6):e26921. doi: 10.1016/j.heliyon.2024.e26921. eCollection 2024 Mar 30.
Data management and finding precise outcomes from large amounts of information are among the biggest challenges for scientists. The technique of multi-attribute group decision-making (MAGDM) is a valuable tool for investigating fuzzy data precisely. The key objective of the paper is to redefine the q-rung orthopair (q-RO) fuzzy set (FS) (q-ROFS) in the term of interval-valued and proposed new aggregation operators (AOs) based on the Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operations. The AA operational laws are a generalized form of existing TNs and TCNs and give more reliable results because they can fluctuate in their parametric values. The concept of interval-valued enlarges the space of membership degree (MD) and non-membership degree (NMD) for decision-makers. By taking qth power, the interval-valued q-ROFS (IV-q-ROFS) structure. The IV-q-ROFS can handle the uncertainty and vagueness in data, then interval-valued intuitionistic FS (IV-IFS) and interval-valued Pythagorean FS (PyFS) (IV-PyFS) and provide accurate results. The thought of power AOs (PAOs) makes the relationship between weight vectors and reduces the chances of uncertainty in aggregated results. By taking advantage of PAOs, this article is devoted to introducing the interval-valued q-ROF Aczel-Alsina power-weighted averaging (IV-q-ROFAAPWA) and interval-valued q-ROF Aczel-Alsina power-weighted geometric (IV-q-ROFAAPWG) operators. The fundamental axioms of AOs, idempotency, boundedness, and monotonicity, are also discussed. To illustrate the importance of suggested AOs, the real-life problem of electric car selection was solved by applying the MAGDM method using the proposed IV-q-ROFAAPWA and IV-q-ROFAAPWG operators. The comparison of proposed AOs with currently present AOs is also part of the article. We finally constructed solid conclusions.
数据管理以及从大量信息中找到精确结果是科学家面临的最大挑战之一。多属性群决策（MAGDM）技术是精确研究模糊数据的宝贵工具。本文的关键目标是以区间值的形式重新定义q阶正交对（q-RO）模糊集（FS）（q-ROFS），并基于阿泽尔 - 阿尔西纳（AA）三角范数（TN）和三角余范数（TCN）运算提出新的聚合算子（AO）。AA运算定律是现有TN和TCN的广义形式，并且由于其参数值可以波动，所以能给出更可靠的结果。区间值的概念为决策者扩大了隶属度（MD）和非隶属度（NMD）的空间。通过取q次幂，得到区间值q-ROFS（IV-q-ROFS）结构。IV-q-ROFS能够处理数据中的不确定性和模糊性，进而处理区间值直觉模糊集（IV-IFS）和区间值毕达哥拉斯模糊集（PyFS）（IV-PyFS）并提供准确结果。幂聚合算子（PAO）的思想建立了权重向量之间的关系，并减少了聚合结果中不确定性的机会。利用PAO，本文致力于引入区间值q-ROF阿泽尔 - 阿尔西纳幂加权平均（IV-q-ROFAAPWA）和区间值q-ROF阿泽尔 - 阿尔西纳幂加权几何（IV-q-ROFAAPWG）算子。还讨论了AO的基本公理，即幂等性、有界性和单调性。为了说明所提出AO的重要性，通过使用所提出的IV-q-ROFAAPWA和IV-q-ROFAAPWG算子应用MAGDM方法解决了电动汽车选择的实际问题。将所提出的AO与当前现有的AO进行比较也是本文的一部分。我们最终得出了可靠的结论。
