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The operations on intuitionistic fuzzy values in the framework of Dempster-Shafer theory

机译：在Dempster-Shafer理论框架中对直觉模糊值的运算

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摘要

This paper presents a critical analysis of conventional operations on intuitionistic fuzzy values (7FVs) and their applicability to the solution of multiple criteria decision making (MCDM) problems in the intuitionistic fuzzy setting. Two sets of operations on IFVs based on the interpretation of intuitionistic fuzzy sets in the framework of the Dempster-Shafer theory of evidence (DST) are proposed and analysed. This interpretation makes it possible to represent mathematical operations on IFVs as operations on belief intervals. The corresponding methods for aggregation of local criteria presented by IFVs in the framework of DST are proposed and analysed. The proposed approach allows us to solve MCDM problems without intermediate defuzzification when not only criteria, but their weights are IFVs. The advantages of the proposed approach are illustrated by numerical examples.
机译：本文对直觉模糊值（7FV）的常规运算进行了批判性分析，并对其在直觉模糊设置中解决多准则决策（MCDM）问题的适用性进行了分析。提出并分析了基于Dempster-Shafer证据理论（DST）框架的直觉模糊集的解释对IFV进行的两组运算。这种解释可以将对IFV的数学运算表示为对置信区间的运算。提出并分析了IFV在DST框架下提出的用于汇总本地标准的相应方法。提出的方法使我们能够解决MCDM问题，而不仅仅是标准，但其权重为IFV，而无需进行中间的去模糊化处理。数值示例说明了该方法的优点。

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