Analysis of the consistency and consensus for group decision-making with interval-valued intuitionistic fuzzy preference
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Analysis of the consistency and consensus for group decision‑making with interval‑valued intuitionistic fuzzy preference relations Shaolin Zhang1 · Fanyong Meng1 Received: 12 January 2020 / Revised: 2 March 2020 / Accepted: 25 April 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract This paper aims to offer a new group decision-making (GDM) method based on intervalvalued intuitionistic fuzzy preference relations (IVIFPRs). To furnish this goal, a new additive consistency definition of IVIFPRs is first proposed. Then, a programming model is built to check the additive consistency of IVIFPRs. For incomplete IVIFPRs, two programming models are constructed, which aim at maximizing the consistency and minimizing the uncertainty of missing information. To achieve the minimum total adjustment, a goal programming model is established to repair inconsistent IVIFPRs. Considering the consensus, a programming model for improving the consensus degree is established, which permits different IVIFVs to have different adjustments and makes individual IVIFPRs have the smallest total adjustment to remain more original information. Based on these results, a consistency- and consensus-based GDM method is proposed. At length, a practical example for screening new majors of a private college in China is offered to illustrate the feasibility and efficiency of proposed method. Keywords Group decision-making · IVIFPR · Additive consistency and consensus · Programming model Mathematics Subject Classification 03E72 · 90B50 · 90Cxx
1 Introduction As the effectiveness and convenience of preference relations (PRs) for dealing with complex and timely decision-making problems, it has become an important branch in multi-criteria decision making (MCDM) to evaluate the possible alternatives under different criteria (Callejas et al. 2019). A lot of research results about decision-making with PRs have been achieved by scholars, which promote many new developing categories. Among of which Communicated by Leonardo Tomazeli Duarte. * Fanyong Meng [email protected] 1
School of Business, Central South University, Changsha 410083, China
123 Vol.:(0123456789)
S. Zhang, F. Meng
there are two basic types of PRs: multiplicative PRs (Saaty 1980) and fuzzy PRs (Tanino 1984). Based on this classification, several other kinds of PRs have been proposed, such as interval multiplicative PRs (IMPRs) (Saaty and Vargas 1987), fuzzy interval PRs (FIPRs) (Xu 2001), linguistic PRs (LPRs) (Herrera and Herrera-Viedma 2000), and interval linguistic PRs (ILPRs) (Tapia García et al. 2012). Their common feature is to only consider the membership degree of one compared object over the other. In view of the limitation of the decision makers (DMs)’ mastery knowledge, the judgements may be inconsistent. For example, a DM thinks that the preferred degree of one object over the other is 0.6. However, their non-preferred degree is judged as 0.3 rather than 0.4, namely, the hesitancy degree between them is 0.1. To solve this situat
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