The technique for order performance by similarity to ideal solution (TOPSIS) is one of the most well-known methods in multiple criteria decision making (MCDM) problems. The classical TOPSIS method employs a similarity index to rank alternatives. However, the chosen alternative sometimes does not have the shortest distance to the positive ideal solution (PIS) and remotest distance from the negative ideal solution (NIS), simultaneously. Besides, in some cases, TOPSIS cannot assign a unique rank to alternatives. The purpose of this paper is to propose a new similarity TOPSIS index based on the relative distance to the best and worst points. In the proposed method, by treating the separations of an alternative from the PIS and the NIS as negative criterion and positive criterion, respectively, we reduce the original MCDM problem to a new one with two criteria. The proposed index, based on different weights, in optimistic, pessimistic, and apathetic cases, easily determines the score of each alternative. Finally, we illustrate the proposed index using four numerical examples. The results are compared with those published in the literature.

中文翻译：

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基于最佳点和最差点的相对距离的 TOPSIS 新指标

通过与理想解决方案的相似性 (TOPSIS) 进行订单性能的技术是多准则决策 (MCDM) 问题中最著名的方法之一。经典的 TOPSIS 方法采用相似性指数对备选方案进行排名。然而，所选择的替代方案有时不会同时具有与正理想解 (PIS) 的最短距离和与负理想解 (NIS) 的最远距离。此外，在某些情况下，TOPSIS 无法为备选方案分配唯一的排名。本文的目的是提出一种新的基于到最佳点和最差点的相对距离的相似度 TOPSIS 指标。在所提出的方法中，通过将替代方案与 PIS 和 NIS 的分离分别视为负标准和正标准，我们将原始 MCDM 问题简化为具有两个标准的新问题。建议的指数基于不同的权重，在乐观、悲观和冷漠的情况下，很容易确定每个备选方案的得分。最后，我们使用四个数值示例来说明建议的索引。将结果与文献中发表的结果进行比较。