Ranjbar Mahdi, Effati Sohrab
Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Member of the center of Excellent on Soft Computing and Intelligent Information Processing, Ferdowsi University of Mashhad, Mashhad, Iran.
Sci Rep. 2023 Dec 10;13(1):21864. doi: 10.1038/s41598-023-49076-3.
Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of hesitant fuzzy numbers (HFNs) which consists of several fuzzy numbers with special conditions can be suggested. HFNs are as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. Because of simple and fast calculations, in this paper, we use triangular HFNs in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the HFNs and a new method of comparing HFNs to get the hesitant fuzzy performance score. By using score function to hesitant fuzzy score we can get a final score for alternatives. Finally, a practical example is provided to show the the effectiveness of this study. The obtained results from this paper show that new method can get a better answer by keeping the experts' opinions in the process of solving the problem.
由于决策问题日益复杂，许多管理者在群体决策中聘请多位专家以做出良好决策。如今，如果专家评估存在模糊性，那么对每位专家而言，使用模糊数会很有用。在这些情况下，可以建议使用犹豫模糊数（HFNs），它由几个满足特殊条件的模糊数组成。犹豫模糊数是模糊数的一种扩展，以便更好地由多位专家确定参数的隶属函数。由于计算简单快速，在本文中，我们在犹豫模糊环境下，根据一组决策者的意见，在层次分析法的成对比较矩阵中使用三角犹豫模糊数。我们定义了犹豫模糊成对比较矩阵的一致性，并使用犹豫模糊数的算术运算以及一种新的犹豫模糊数比较方法来获得犹豫模糊性能得分。通过对犹豫模糊得分使用得分函数，我们可以得到备选方案的最终得分。最后，给出一个实际例子以说明本研究的有效性。本文得到的结果表明，新方法在解决问题的过程中通过保留专家意见能够得到更好的答案。
