Single-valued neutrosophic ELECTRE II for multi-criteria group decision-making with unknown weight information
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Single‑valued neutrosophic ELECTRE II for multi‑criteria group decision‑making with unknown weight information Zhang‑peng Tian1,2 · Ru‑xin Nie1 · Xiao‑Kang Wang1 · Jian‑qiang Wang1 Received: 23 July 2018 / Revised: 21 May 2020 / Accepted: 20 June 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract This paper develops a novel multi-criteria group decision-making method for resolving single-valued neutrosophic group decision-making problems with unknown weight information. Firstly, considering the different knowledge backgrounds of decision-makers (DMs), two distance-based methods are developed to obtain the weights of DMs and criteria. One of these methods focuses on the closeness between the decision matrix given by an individual DM and that of the group judgment, and the proximity between the decision matrix given by an individual DM and the matrices given by all the other DMs to determine the weights of DMs with respect to each criterion. The other method extends the maximizing deviation method to objectively obtain the weights of criteria. Secondly, an extended ELECTRE (ELimination Et Choix Traduisant la REalité) II is investigated to effectively circumvent the issue that criteria cannot compensate for each other. In this method, three levels of concordance and discordance sets are constructed to fully denote the underlying preference information and specify the outranking degrees of alternatives. Finally, two illustrative examples are presented to demonstrate the feasibility of the proposed approach, followed by a sensitivity analysis and a comparative analysis to test its robustness and effectiveness. Keywords Multi-criteria decision-making · Single-valued neutrosophic sets · Maximizing deviation method · ELECTRE II Mathematics Subject Classification Primary 90B50 · Secondary 03E72
Communicated by Rosana Sueli da Motta Jafelice. * Xiao‑Kang Wang [email protected] 1
School of Business, Central South University, Changsha 410083, People’s Republic of China
2
School of Economics and Management, China University of Mining and Technology, Xuzhou 221116, People’s Republic of China
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Z. Tian et al.
1 Introduction The increasing complexity of the decision circumstances makes it hard for single decision-maker (DM) to provide meaningful and reliable solutions if these solutions only depend on his or her own knowledge and capabilities. Therefore, group decision-making (GDM) has received significant attention in both theoretical and practical perspectives (Kabak and Ervural 2017; Liu et al. 2018a, 2019a; Luo et al. 2019; Reddy et al. 2016; Tian et al. 2020; Tian et al. 2018). As an important branch of GDM, multi-criteria group decision-making (MCGDM) can be deemed as such a decision-making process where several DMs provide their assessments on a set of alternatives with respect to multiple criteria and then generate a common solution (Hwang and Yoon 1981). In practice, uncertainty information widely exists in real life MCGDM problems because of the in
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