Khan Aziz, Abosuliman Shougi S, Abdullah Saleem, Ayaz Muhammad
Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan.
Department of Transportation and Port Management, Faculty of Maritime Studies, King Abdulaziz University, Jeddah 21588, Saudi Arabia.
Entropy (Basel). 2021 Apr 6;23(4):432. doi: 10.3390/e23040432.
Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.
球形犹豫模糊集近年来在各个领域越来越受欢迎。它是作为图像犹豫模糊集和毕达哥拉斯犹豫模糊集的推广而提出的，用于处理不确定性和模糊性信息。聚合技术是聚合信息的有益工具之一。它有许多关键应用领域，如决策、数据挖掘、医学诊断和模式识别。鉴于对数函数和聚合算子的重要性，我们提出了一种新颖的算法来解决多属性决策（MADM）问题。首先，基于对数、三角模和三角余模函数开发了新颖的对数运算定律。利用这些运算定律，我们开发了一系列对数球形犹豫模糊加权平均/几何聚合算子来聚合球形犹豫模糊信息。此外，我们开发了球形犹豫模糊熵来确定未知的属性权重信息。最后，制定了球形犹豫模糊决策的设计原则，并以基于在线消费者评论的酒店推荐实际案例研究来说明所提出方法的有效性和优越性。除此之外，还进行了有效性测试以揭示所开发方法的优点和有效性。结果表明，所提出的方法适用于决策过程并能有效地评估其最佳替代方案。
