Fuzzy Sets and Systems ( IF 3.9 ) Pub Date : 2020-12-02 , DOI: 10.1016/j.fss.2020.11.022 Jaroslav Ramík
This paper deals with the pairwise comparisons matrix with fuzzy elements (FPCM). Fuzzy elements of the FPCM are applied whenever the decision maker is not sure about the value of his/her evaluation of the relative importance of elements in question. We investigate the pairwise comparisons matrices with elements from abelian linearly ordered group (alo-group) over a real interval, introduce the concept of reciprocity and (weak) consistency of FPCMs and derive their properties. Such an approach unifies several approaches known from the literature. Moreover, we propose a new general procedure for deriving the priority vector from the FPCM enabling ranking or rating a given set of alternatives.
中文翻译:
从具有模糊元素的成对比较矩阵中导出优先级向量
本文处理具有模糊元素的成对比较矩阵 (FPCM)。每当决策者不确定他/她对相关元素的相对重要性的评估的价值时,就会应用 FPCM 的模糊元素。我们研究了在真实区间内与来自阿贝尔线性有序群(alo-group)的元素的成对比较矩阵,介绍了互易性和 FPCM 的(弱)一致性的概念并推导了它们的属性。这种方法统一了从文献中已知的几种方法。此外,我们提出了一种新的通用程序,用于从 FPCM 中导出优先级向量,从而对给定的一组备选方案进行排序或评级。