Models of Fuzzy Multi-Criteria Decision Analysis (FMCDA) are based, as a rule, on different approaches to fuzzy extension of source MCDA methods. For this, simplified models are used to approximate the functions of fuzzy variables with propagation of parametric fuzzy numbers (FNs) through all calculations. In this paper, authors suggest a novel approach to fuzzy extension of MCDA methods, for PROMETHEE-I/II, through development of fuzzy PROMETHEE-I/II (FPOMETHEE-I/II) models of different complexity: in addition to simplified models, the standard fuzzy arithmetic (SFA), and transformation methods (TMs) are implemented for assessing functions of FNs corresponding to these models. For ranking of alternatives, two defuzzification based, and one pairwise comparison ranking methods are implemented within the developed models. Special attention is paid to analysis of the overestimation problem, which can occur when using SFA in the presence of dependent variables in corresponding expressions, and to “proper fuzzy extensions” of PROMETHEE-I/II (i.e., results of all functions of FNs within the model are in accordance with the extension principle) based on TMs and, for some models, on the SFA. One of the key goals of this contribution is comparison of the distinctions in ranking alternatives by different FPROMETHEE-II models. It is demonstrated by evaluating a large number of scenarios based on Monte Carlo simulation that the probability of distinction in ranking alternatives by “proper” and “approximated” FPROMETHEE-II models may be considered as significant for ranking multicriteria problems. Another goal of this paper is analysis of the correctness of FPROMETHEE-I/II models with respect to the basic MCDA axiom related to ranking of dominated and dominating alternatives. Authors demonstrate that the basic axiom can be violated, in the general case, by all developed FPROMETHEE-I/II models and suggest an approach to fix this problem.

模糊多准则决策分析 (FMCDA) 模型通常基于源 MCDA 方法的模糊扩展的不同方法。为此，简化模型用于通过所有计算通过参数模糊数 (FN) 的传播来近似模糊变量的函数。在本文中，作者通过开发不同复杂度的模糊 PROMETHEE-I/II (FPOMETHEE-I/II) 模型，为 PROMETHEE-I/II 提出了一种新的 MCDA 方法模糊扩展方法：除了简化模型，标准模糊算法 (SFA) 和转换方法 (TM) 用于评估与这些模型对应的 FN 的功能。对于备选方案的排名，在开发的模型中实施了两种基于去模糊化和一种成对比较的排名方法。特别注意分析在相应表达式中存在因变量的情况下使用 SFA 时可能出现的高估问题，以及 PROMETHEE-I/II 的“适当模糊扩展”（即，FNs 内所有函数的结果）该模型符合扩展原则）基于 TM，对于某些模型，基于 SFA。这项贡献的主要目标之一是比较不同 FPROMETHEE-II 模型在对备选方案进行排名方面的差异。通过评估基于蒙特卡罗模拟的大量场景证明，通过“适当的”和“近似的”FPROMETHEE-II 模型对备选方案进行排序的概率可能被认为对多标准问题的排序很重要。本文的另一个目标是分析 FPROMETHEE-I/II 模型相对于与支配和支配选择排序相关的基本 MCDA 公理的正确性。作者证明，在一般情况下，所有开发的 FPROMETHEE-I/II 模型都可能违反基本公理，并提出了解决此问题的方法。