The purpose of this study is to introduce an innovative multi-attribute group decision making (MAGDM) based on bipolar fuzzy set (BFS) by unifying“ VIseKriterijumska Optimizacija I Kompromisno Rasenje (VIKOR)” method. The VIKOR method is considered to be a useful MAGDM method, specifically in conditions where an expert is unable to determine his choice correctly at the initiation of designing a system. The method of VIKOR is suitable for problems containing conflicting attributes, with an assumption that compromising is admissible for conflict decision, the expert wishes a solution very near to the best, and the different alternatives or choices are processed according to all developed attributes. The theory of set pair analysis is a state-of-the-art uncertainty theory which consists of three factors, including “identity degree”, “discrepancy degree”, and “contrary degree” of connection numbers (CNs) and coincidence with many existing theories dealing with vagueness in the given information. Consequently, inspired by this, in the present study, we make an effort to improve the theory of data measurement by introducing some metric spaces using CNs of BFSs. In this research paper, we extend VIKOR method in the context of CNs based metrics, which are obtained form bipolar fuzzy numbers (BFNs). Firstly, we develop CNs of BFNs as well as metric spaces based on CNs. We also discuss some interesting properties of proposed metric spaces. Secondly, we develop VIKOR method using CNs based metrics to handle an MAGDM problem under bipolar fuzzy type information. The predominance of proposed metric spaces is also studied by the means of examples. Furthermore, we demonstrate the efficiency of the extended VIKOR method by solving a numerical example, sensitivity analysis and a detailed comparison with some existing approaches.

中文翻译：

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基于 SPA 理论的度量空间的连接数对双极模糊集的 VIKOR 方法的鲁棒扩展

本研究的目的是通过统一“VIseKriterijumska Optimizacija I Kompromisno Rasenje (VIKOR)”方法，引入一种创新的基于双极模糊集（BFS）的多属性群决策（MAGDM）。VIKOR 方法被认为是一种有用的 MAGDM 方法，特别是在专家在开始设计系统时无法正确确定其选择的情况下。VIKOR 方法适用于包含冲突属性的问题，假设冲突决策允许妥协，专家希望解决方案非常接近最佳，并且根据所有开发的属性处理不同的替代方案或选择。集合对分析理论是一种最先进的不确定性理论，它由三个因素组成，包括“同一度”、连接数 (CN) 的“差异度”和“相反度”，并且与许多现有的处理给定信息中的模糊性的理论相吻合。因此，受此启发，在本研究中，我们通过使用 BFS 的 CN 引入一些度量空间来努力改进数据测量理论。在这篇研究论文中，我们在基于 CN 的度量的背景下扩展了 VIKOR 方法，这些度量是从双极模糊数 (BFN) 获得的。首先，我们开发了 BFN 的 CN 以及基于 CN 的度量空间。我们还讨论了所提出的度量空间的一些有趣的特性。其次，我们开发了使用基于 CN 的度量的 VIKOR 方法来处理双极模糊类型信息下的 MAGDM 问题。还通过示例研究了所提出的度量空间的优势。此外，