In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

在本文中，我们提出了一种新的方法来解决多属性决策（MADM）问题，该方法以三角模糊偏好关系和三角模糊非偏好关系的形式分别考虑决策者的主观偏好和非偏好。这些关系的一些重要特征用于形成与三角模糊数的下，中和上限相对应的非线性规划问题。解决与上下限相对应的优化问题，以获得基本三角模糊可乘优先权（TFMPW）和基本三角模糊可乘非优先权（TFMNPW）的相应极限。所获得的最佳权重值用于查找TFMPW和TFMNPW的模态值，这有助于对替代方案进行排名。通过解决文献中的MADM问题，证明了该方法的有效性。此外，为了验证所提出方法的优越性，已经提供了与现有类似方法的比较分析。获得的结果揭示了该方法的适用性和实用性。